# SLATEC Common Mathematical Library Ve

## Found at: ftp.icm.edu.pl:70/packages/netlib/slatec/toc

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```                       SLATEC Common Mathematical Library
```
```
```
```                                  Version 4.1
```
```
```
```                               Table of Contents
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```
```
```
```
```This table of contents of the SLATEC Common Mathematical Library (CML) has
```
```three sections.
```
```
```
```Section I contains the names and purposes of all user-callable CML routines,
```
```arranged by GAMS category.  Those unfamiliar with the GAMS scheme should
```
```consult the document "Guide to the SLATEC Common Mathematical Library".  The
```
```current library has routines in the following GAMS major categories:
```
```
```
```     A.  Arithmetic, error analysis
```
```     C.  Elementary and special functions (search also class L5)
```
```     D.  Linear Algebra
```
```     E.  Interpolation
```
```     F.  Solution of nonlinear equations
```
```     G.  Optimization (search also classes K, L8)
```
```     H.  Differentiation, integration
```
```     I.  Differential and integral equations
```
```     J.  Integral transforms
```
```     K.  Approximation (search also class L8)
```
```     L.  Statistics, probability
```
```     N.  Data handling (search also class L2)
```
```     R.  Service routines
```
```     Z.  Other
```
```
```
```The library contains routines which operate on different types of data but
```
```vertically before the purpose.  Immediately after each name is a hyphen (-)
```
```and one of the alphabetic characters S, D, C, I, H, L, or A, where
```
```S indicates a single precision routine, D double precision, C complex,
```
```that could not reasonably be converted to some other type.
```
```
```
```Section II contains the names and purposes of all subsidiary CML routines,
```
```arranged in alphabetical order.  Usually these routines are not referenced
```
```to avoid duplicating names that are used by the CML and for the benefit of
```
```for the library.
```
```
```
```Section III is an alphabetical list of every routine in the CML and the
```
```categories to which the routine is assigned.  Every user-callable routine
```
```name indicates a subsidiary routine.
```
```
```
```
```
```  SECTION I. User-callable Routines
```
```
```
```A.  Arithmetic, error analysis
```
```A3.  Real
```
```A3D.  Extended range
```
```
```
```          XADD-S    To provide single-precision floating-point arithmetic
```
```          DXADD-D   with an extended exponent range.
```
```
```
```          XADJ-S    To provide single-precision floating-point arithmetic
```
```          DXADJ-D   with an extended exponent range.
```
```
```
```          XC210-S   To provide single-precision floating-point arithmetic
```
```          DXC210-D  with an extended exponent range.
```
```
```
```          XCON-S    To provide single-precision floating-point arithmetic
```
```          DXCON-D   with an extended exponent range.
```
```
```
```          XRED-S    To provide single-precision floating-point arithmetic
```
```          DXRED-D   with an extended exponent range.
```
```
```
```          XSET-S    To provide single-precision floating-point arithmetic
```
```          DXSET-D   with an extended exponent range.
```
```
```
```A4.  Complex
```
```A4A.  Single precision
```
```
```
```          CARG-C    Compute the argument of a complex number.
```
```
```
```A6.  Change of representation
```
```A6B.  Base conversion
```
```
```
```          R9PAK-S   Pack a base 2 exponent into a floating point number.
```
```          D9PAK-D
```
```
```
```          R9UPAK-S  Unpack a floating point number X so that X = Y*2**N.
```
```          D9UPAK-D
```
```
```
```C.  Elementary and special functions (search also class L5)
```
```
```
```          FUNDOC-A  Documentation for FNLIB, a collection of routines for
```
```                    evaluating elementary and special functions.
```
```
```
```C1.  Integer-valued functions (e.g., floor, ceiling, factorial, binomial
```
```     coefficient)
```
```
```
```          BINOM-S   Compute the binomial coefficients.
```
```          DBINOM-D
```
```
```
```          FAC-S     Compute the factorial function.
```
```          DFAC-D
```
```
```
```          POCH-S    Evaluate a generalization of Pochhammer's symbol.
```
```          DPOCH-D
```
```
```
```          POCH1-S   Calculate a generalization of Pochhammer's symbol starting
```
```          DPOCH1-D  from first order.
```
```
```
```C2.  Powers, roots, reciprocals
```
```
```
```          CBRT-S    Compute the cube root.
```
```          DCBRT-D
```
```          CCBRT-C
```
```
```
```C3.  Polynomials
```
```C3A.  Orthogonal
```
```C3A2.  Chebyshev, Legendre
```
```
```
```          CSEVL-S   Evaluate a Chebyshev series.
```
```          DCSEVL-D
```
```
```
```          INITS-S   Determine the number of terms needed in an orthogonal
```
```          INITDS-D  polynomial series so that it meets a specified accuracy.
```
```
```
```          QMOMO-S   This routine computes modified Chebyshev moments.  The K-th
```
```          DQMOMO-D  modified Chebyshev moment is defined as the integral over
```
```                    (-1,1) of W(X)*T(K,X), where T(K,X) is the Chebyshev
```
```                    polynomial of degree K.
```
```
```
```          XLEGF-S   Compute normalized Legendre polynomials and associated
```
```          DXLEGF-D  Legendre functions.
```
```
```
```          XNRMP-S   Compute normalized Legendre polynomials.
```
```          DXNRMP-D
```
```
```
```C4.  Elementary transcendental functions
```
```C4A.  Trigonometric, inverse trigonometric
```
```
```
```          CACOS-C   Compute the complex arc cosine.
```
```
```
```          CASIN-C   Compute the complex arc sine.
```
```
```
```          CATAN-C   Compute the complex arc tangent.
```
```
```
```          CATAN2-C  Compute the complex arc tangent in the proper quadrant.
```
```
```
```          COSDG-S   Compute the cosine of an argument in degrees.
```
```          DCOSDG-D
```
```
```
```          COT-S     Compute the cotangent.
```
```          DCOT-D
```
```          CCOT-C
```
```
```
```          CTAN-C    Compute the complex tangent.
```
```
```
```          SINDG-S   Compute the sine of an argument in degrees.
```
```          DSINDG-D
```
```
```
```C4B.  Exponential, logarithmic
```
```
```
```          ALNREL-S  Evaluate ln(1+X) accurate in the sense of relative error.
```
```          DLNREL-D
```
```          CLNREL-C
```
```
```
```          CLOG10-C  Compute the principal value of the complex base 10
```
```                    logarithm.
```
```
```
```          EXPREL-S  Calculate the relative error exponential (EXP(X)-1)/X.
```
```          DEXPRL-D
```
```          CEXPRL-C
```
```
```
```C4C.  Hyperbolic, inverse hyperbolic
```
```
```
```          ACOSH-S   Compute the arc hyperbolic cosine.
```
```          DACOSH-D
```
```          CACOSH-C
```
```
```
```          ASINH-S   Compute the arc hyperbolic sine.
```
```          DASINH-D
```
```          CASINH-C
```
```
```
```          ATANH-S   Compute the arc hyperbolic tangent.
```
```          DATANH-D
```
```          CATANH-C
```
```
```
```          CCOSH-C   Compute the complex hyperbolic cosine.
```
```
```
```          CSINH-C   Compute the complex hyperbolic sine.
```
```
```
```          CTANH-C   Compute the complex hyperbolic tangent.
```
```
```
```C5.  Exponential and logarithmic integrals
```
```
```
```          ALI-S     Compute the logarithmic integral.
```
```          DLI-D
```
```
```
```          E1-S      Compute the exponential integral E1(X).
```
```          DE1-D
```
```
```
```          EI-S      Compute the exponential integral Ei(X).
```
```          DEI-D
```
```
```
```          EXINT-S   Compute an M member sequence of exponential integrals
```
```          DEXINT-D  E(N+K,X), K=0,1,...,M-1 for N .GE. 1 and X .GE. 0.
```
```
```
```          SPENC-S   Compute a form of Spence's integral due to K. Mitchell.
```
```          DSPENC-D
```
```
```
```C7.  Gamma
```
```C7A.  Gamma, log gamma, reciprocal gamma
```
```
```
```          ALGAMS-S  Compute the logarithm of the absolute value of the Gamma
```
```          DLGAMS-D  function.
```
```
```
```          ALNGAM-S  Compute the logarithm of the absolute value of the Gamma
```
```          DLNGAM-D  function.
```
```          CLNGAM-C
```
```
```
```          C0LGMC-C  Evaluate (Z+0.5)*LOG((Z+1.)/Z) - 1.0 with relative
```
```                    accuracy.
```
```
```
```          GAMLIM-S  Compute the minimum and maximum bounds for the argument in
```
```          DGAMLM-D  the Gamma function.
```
```
```
```          GAMMA-S   Compute the complete Gamma function.
```
```          DGAMMA-D
```
```          CGAMMA-C
```
```
```
```          GAMR-S    Compute the reciprocal of the Gamma function.
```
```          DGAMR-D
```
```          CGAMR-C
```
```
```
```          POCH-S    Evaluate a generalization of Pochhammer's symbol.
```
```          DPOCH-D
```
```
```
```          POCH1-S   Calculate a generalization of Pochhammer's symbol starting
```
```          DPOCH1-D  from first order.
```
```
```
```C7B.  Beta, log beta
```
```
```
```          ALBETA-S  Compute the natural logarithm of the complete Beta
```
```          DLBETA-D  function.
```
```          CLBETA-C
```
```
```
```          BETA-S    Compute the complete Beta function.
```
```          DBETA-D
```
```          CBETA-C
```
```
```
```C7C.  Psi function
```
```
```
```          PSI-S     Compute the Psi (or Digamma) function.
```
```          DPSI-D
```
```          CPSI-C
```
```
```
```          PSIFN-S   Compute derivatives of the Psi function.
```
```          DPSIFN-D
```
```
```
```C7E.  Incomplete gamma
```
```
```
```          GAMI-S    Evaluate the incomplete Gamma function.
```
```          DGAMI-D
```
```
```
```          GAMIC-S   Calculate the complementary incomplete Gamma function.
```
```          DGAMIC-D
```
```
```
```          GAMIT-S   Calculate Tricomi's form of the incomplete Gamma function.
```
```          DGAMIT-D
```
```
```
```C7F.  Incomplete beta
```
```
```
```          BETAI-S   Calculate the incomplete Beta function.
```
```          DBETAI-D
```
```
```
```C8.  Error functions
```
```C8A.  Error functions, their inverses, integrals, including the normal
```
```      distribution function
```
```
```
```          ERF-S     Compute the error function.
```
```          DERF-D
```
```
```
```          ERFC-S    Compute the complementary error function.
```
```          DERFC-D
```
```
```
```C8C.  Dawson's integral
```
```
```
```          DAWS-S    Compute Dawson's function.
```
```          DDAWS-D
```
```
```
```C9.  Legendre functions
```
```
```
```          XLEGF-S   Compute normalized Legendre polynomials and associated
```
```          DXLEGF-D  Legendre functions.
```
```
```
```          XNRMP-S   Compute normalized Legendre polynomials.
```
```          DXNRMP-D
```
```
```
```C10.  Bessel functions
```
```C10A.  J, Y, H-(1), H-(2)
```
```C10A1.  Real argument, integer order
```
```
```
```          BESJ0-S   Compute the Bessel function of the first kind of order
```
```          DBESJ0-D  zero.
```
```
```
```          BESJ1-S   Compute the Bessel function of the first kind of order one.
```
```          DBESJ1-D
```
```
```
```          BESY0-S   Compute the Bessel function of the second kind of order
```
```          DBESY0-D  zero.
```
```
```
```          BESY1-S   Compute the Bessel function of the second kind of order
```
```          DBESY1-D  one.
```
```
```
```C10A3.  Real argument, real order
```
```
```
```          BESJ-S    Compute an N member sequence of J Bessel functions
```
```          DBESJ-D   J/SUB(ALPHA+K-1)/(X), K=1,...,N for non-negative ALPHA
```
```                    and X.
```
```
```
```          BESY-S    Implement forward recursion on the three term recursion
```
```          DBESY-D   relation for a sequence of non-negative order Bessel
```
```                    functions Y/SUB(FNU+I-1)/(X), I=1,...,N for real, positive
```
```                    X and non-negative orders FNU.
```
```
```
```C10A4.  Complex argument, real order
```
```
```
```          CBESH-C   Compute a sequence of the Hankel functions H(m,a,z)
```
```          ZBESH-C   for superscript m=1 or 2, real nonnegative orders a=b,
```
```                    b+1,... where b>0, and nonzero complex argument z.  A
```
```                    scaling option is available to help avoid overflow.
```
```
```
```          CBESJ-C   Compute a sequence of the Bessel functions J(a,z) for
```
```          ZBESJ-C   complex argument z and real nonnegative orders a=b,b+1,
```
```                    b+2,... where b>0.  A scaling option is available to
```
```                    help avoid overflow.
```
```
```
```          CBESY-C   Compute a sequence of the Bessel functions Y(a,z) for
```
```          ZBESY-C   complex argument z and real nonnegative orders a=b,b+1,
```
```                    b+2,... where b>0.  A scaling option is available to
```
```                    help avoid overflow.
```
```
```
```C10B.  I, K
```
```C10B1.  Real argument, integer order
```
```
```
```          BESI0-S   Compute the hyperbolic Bessel function of the first kind
```
```          DBESI0-D  of order zero.
```
```
```
```          BESI0E-S  Compute the exponentially scaled modified (hyperbolic)
```
```          DBSI0E-D  Bessel function of the first kind of order zero.
```
```
```
```          BESI1-S   Compute the modified (hyperbolic) Bessel function of the
```
```          DBESI1-D  first kind of order one.
```
```
```
```          BESI1E-S  Compute the exponentially scaled modified (hyperbolic)
```
```          DBSI1E-D  Bessel function of the first kind of order one.
```
```
```
```          BESK0-S   Compute the modified (hyperbolic) Bessel function of the
```
```          DBESK0-D  third kind of order zero.
```
```
```
```          BESK0E-S  Compute the exponentially scaled modified (hyperbolic)
```
```          DBSK0E-D  Bessel function of the third kind of order zero.
```
```
```
```          BESK1-S   Compute the modified (hyperbolic) Bessel function of the
```
```          DBESK1-D  third kind of order one.
```
```
```
```          BESK1E-S  Compute the exponentially scaled modified (hyperbolic)
```
```          DBSK1E-D  Bessel function of the third kind of order one.
```
```
```
```C10B3.  Real argument, real order
```
```
```
```          BESI-S    Compute an N member sequence of I Bessel functions
```
```          DBESI-D   I/SUB(ALPHA+K-1)/(X), K=1,...,N or scaled Bessel functions
```
```                    EXP(-X)*I/SUB(ALPHA+K-1)/(X), K=1,...,N for non-negative
```
```                    ALPHA and X.
```
```
```
```          BESK-S    Implement forward recursion on the three term recursion
```
```          DBESK-D   relation for a sequence of non-negative order Bessel
```
```                    functions K/SUB(FNU+I-1)/(X), or scaled Bessel functions
```
```                    EXP(X)*K/SUB(FNU+I-1)/(X), I=1,...,N for real, positive
```
```                    X and non-negative orders FNU.
```
```
```
```          BESKES-S  Compute a sequence of exponentially scaled modified Bessel
```
```          DBSKES-D  functions of the third kind of fractional order.
```
```
```
```          BESKS-S   Compute a sequence of modified Bessel functions of the
```
```          DBESKS-D  third kind of fractional order.
```
```
```
```C10B4.  Complex argument, real order
```
```
```
```          CBESI-C   Compute a sequence of the Bessel functions I(a,z) for
```
```          ZBESI-C   complex argument z and real nonnegative orders a=b,b+1,
```
```                    b+2,... where b>0.  A scaling option is available to
```
```                    help avoid overflow.
```
```
```
```          CBESK-C   Compute a sequence of the Bessel functions K(a,z) for
```
```          ZBESK-C   complex argument z and real nonnegative orders a=b,b+1,
```
```                    b+2,... where b>0.  A scaling option is available to
```
```                    help avoid overflow.
```
```
```
```C10D.  Airy and Scorer functions
```
```
```
```          AI-S      Evaluate the Airy function.
```
```          DAI-D
```
```
```
```          AIE-S     Calculate the Airy function for a negative argument and an
```
```          DAIE-D    exponentially scaled Airy function for a non-negative
```
```                    argument.
```
```
```
```          BI-S      Evaluate the Bairy function (the Airy function of the
```
```          DBI-D     second kind).
```
```
```
```          BIE-S     Calculate the Bairy function for a negative argument and an
```
```          DBIE-D    exponentially scaled Bairy function for a non-negative
```
```                    argument.
```
```
```
```          CAIRY-C   Compute the Airy function Ai(z) or its derivative dAi/dz
```
```          ZAIRY-C   for complex argument z.  A scaling option is available
```
```                    to help avoid underflow and overflow.
```
```
```
```          CBIRY-C   Compute the Airy function Bi(z) or its derivative dBi/dz
```
```          ZBIRY-C   for complex argument z.  A scaling option is available
```
```                    to help avoid overflow.
```
```
```
```C10F.  Integrals of Bessel functions
```
```
```
```          BSKIN-S   Compute repeated integrals of the K-zero Bessel function.
```
```          DBSKIN-D
```
```
```
```C11.  Confluent hypergeometric functions
```
```
```
```          CHU-S     Compute the logarithmic confluent hypergeometric function.
```
```          DCHU-D
```
```
```
```C14.  Elliptic integrals
```
```
```
```          RC-S      Calculate an approximation to
```
```          DRC-D      RC(X,Y) = Integral from zero to infinity of
```
```                                      -1/2     -1
```
```                            (1/2)(t+X)    (t+Y)  dt,
```
```                    where X is nonnegative and Y is positive.
```
```
```
```          RD-S      Compute the incomplete or complete elliptic integral of the
```
```          DRD-D     2nd kind.  For X and Y nonnegative, X+Y and Z positive,
```
```                     RD(X,Y,Z) = Integral from zero to infinity of
```
```                                        -1/2     -1/2     -3/2
```
```                              (3/2)(t+X)    (t+Y)    (t+Z)    dt.
```
```                    If X or Y is zero, the integral is complete.
```
```
```
```          RF-S      Compute the incomplete or complete elliptic integral of the
```
```          DRF-D     1st kind.  For X, Y, and Z non-negative and at most one of
```
```                    them zero, RF(X,Y,Z) = Integral from zero to infinity of
```
```                                        -1/2     -1/2     -1/2
```
```                              (1/2)(t+X)    (t+Y)    (t+Z)    dt.
```
```                    If X, Y or Z is zero, the integral is complete.
```
```
```
```          RJ-S      Compute the incomplete or complete (X or Y or Z is zero)
```
```          DRJ-D     elliptic integral of the 3rd kind.  For X, Y, and Z non-
```
```                    negative, at most one of them zero, and P positive,
```
```                     RJ(X,Y,Z,P) = Integral from zero to infinity of
```
```                                          -1/2     -1/2     -1/2     -1
```
```                                (3/2)(t+X)    (t+Y)    (t+Z)    (t+P)  dt.
```
```
```
```C19.  Other special functions
```
```
```
```          RC3JJ-S   Evaluate the 3j symbol f(L1) = (  L1   L2 L3)
```
```          DRC3JJ-D                                 (-M2-M3 M2 M3)
```
```                    for all allowed values of L1, the other parameters
```
```                    being held fixed.
```
```
```
```          RC3JM-S   Evaluate the 3j symbol g(M2) = (L1 L2   L3  )
```
```          DRC3JM-D                                 (M1 M2 -M1-M2)
```
```                    for all allowed values of M2, the other parameters
```
```                    being held fixed.
```
```
```
```          RC6J-S    Evaluate the 6j symbol h(L1) = {L1 L2 L3}
```
```          DRC6J-D                                  {L4 L5 L6}
```
```                    for all allowed values of L1, the other parameters
```
```                    being held fixed.
```
```
```
```D.  Linear Algebra
```
```D1.  Elementary vector and matrix operations
```
```D1A.  Elementary vector operations
```
```D1A2.  Minimum and maximum components
```
```
```
```          ISAMAX-S  Find the smallest index of that component of a vector
```
```          IDAMAX-D  having the maximum magnitude.
```
```          ICAMAX-C
```
```
```
```D1A3.  Norm
```
```D1A3A.  L-1 (sum of magnitudes)
```
```
```
```          SASUM-S   Compute the sum of the magnitudes of the elements of a
```
```          DASUM-D   vector.
```
```          SCASUM-C
```
```
```
```D1A3B.  L-2 (Euclidean norm)
```
```
```
```          SNRM2-S   Compute the Euclidean length (L2 norm) of a vector.
```
```          DNRM2-D
```
```          SCNRM2-C
```
```
```
```D1A4.  Dot product (inner product)
```
```
```
```          CDOTC-C   Dot product of two complex vectors using the complex
```
```                    conjugate of the first vector.
```
```
```
```          DQDOTA-D  Compute the inner product of two vectors with extended
```
```                    precision accumulation and result.
```
```
```
```          DQDOTI-D  Compute the inner product of two vectors with extended
```
```                    precision accumulation and result.
```
```
```
```          DSDOT-D   Compute the inner product of two vectors with extended
```
```          DCDOT-C   precision accumulation and result.
```
```
```
```          SDOT-S    Compute the inner product of two vectors.
```
```          DDOT-D
```
```          CDOTU-C
```
```
```
```          SDSDOT-S  Compute the inner product of two vectors with extended
```
```          CDCDOT-C  precision accumulation.
```
```
```
```D1A5.  Copy or exchange (swap)
```
```
```
```          ICOPY-S   Copy a vector.
```
```          DCOPY-D
```
```          CCOPY-C
```
```          ICOPY-I
```
```
```
```          SCOPY-S   Copy a vector.
```
```          DCOPY-D
```
```          CCOPY-C
```
```          ICOPY-I
```
```
```
```          SCOPYM-S  Copy the negative of a vector to a vector.
```
```          DCOPYM-D
```
```
```
```          SSWAP-S   Interchange two vectors.
```
```          DSWAP-D
```
```          CSWAP-C
```
```          ISWAP-I
```
```
```
```D1A6.  Multiplication by scalar
```
```
```
```          CSSCAL-C  Scale a complex vector.
```
```
```
```          SSCAL-S   Multiply a vector by a constant.
```
```          DSCAL-D
```
```          CSCAL-C
```
```
```
```D1A7.  Triad (a*x+y for vectors x,y and scalar a)
```
```
```
```          SAXPY-S   Compute a constant times a vector plus a vector.
```
```          DAXPY-D
```
```          CAXPY-C
```
```
```
```D1A8.  Elementary rotation (Givens transformation)
```
```
```
```          SROT-S    Apply a plane Givens rotation.
```
```          DROT-D
```
```          CSROT-C
```
```
```
```          SROTM-S   Apply a modified Givens transformation.
```
```          DROTM-D
```
```
```
```D1B.  Elementary matrix operations
```
```D1B4.  Multiplication by vector
```
```
```
```          CHPR-C    Perform the hermitian rank 1 operation.
```
```
```
```          DGER-D    Perform the rank 1 operation.
```
```
```
```          DSPR-D    Perform the symmetric rank 1 operation.
```
```
```
```          DSYR-D    Perform the symmetric rank 1 operation.
```
```
```
```          SGBMV-S   Multiply a real vector by a real general band matrix.
```
```          DGBMV-D
```
```          CGBMV-C
```
```
```
```          SGEMV-S   Multiply a real vector by a real general matrix.
```
```          DGEMV-D
```
```          CGEMV-C
```
```
```
```          SGER-S    Perform rank 1 update of a real general matrix.
```
```
```
```          CGERC-C   Perform conjugated rank 1 update of a complex general
```
```          SGERC-S   matrix.
```
```          DGERC-D
```
```
```
```          CGERU-C   Perform unconjugated rank 1 update of a complex general
```
```          SGERU-S   matrix.
```
```          DGERU-D
```
```
```
```          CHBMV-C   Multiply a complex vector by a complex Hermitian band
```
```          SHBMV-S   matrix.
```
```          DHBMV-D
```
```
```
```          CHEMV-C   Multiply a complex vector by a complex Hermitian matrix.
```
```          SHEMV-S
```
```          DHEMV-D
```
```
```
```          CHER-C    Perform Hermitian rank 1 update of a complex Hermitian
```
```          SHER-S    matrix.
```
```          DHER-D
```
```
```
```          CHER2-C   Perform Hermitian rank 2 update of a complex Hermitian
```
```          SHER2-S   matrix.
```
```          DHER2-D
```
```
```
```          CHPMV-C   Perform the matrix-vector operation.
```
```          SHPMV-S
```
```          DHPMV-D
```
```
```
```          CHPR2-C   Perform the hermitian rank 2 operation.
```
```          SHPR2-S
```
```          DHPR2-D
```
```
```
```          SSBMV-S   Multiply a real vector by a real symmetric band matrix.
```
```          DSBMV-D
```
```          CSBMV-C
```
```
```
```          SSDI-S    Diagonal Matrix Vector Multiply.
```
```          DSDI-D    Routine to calculate the product  X = DIAG*B, where DIAG
```
```                    is a diagonal matrix.
```
```
```
```          SSMTV-S   SLAP Column Format Sparse Matrix Transpose Vector Product.
```
```          DSMTV-D   Routine to calculate the sparse matrix vector product:
```
```                    Y = A'*X, where ' denotes transpose.
```
```
```
```          SSMV-S    SLAP Column Format Sparse Matrix Vector Product.
```
```          DSMV-D    Routine to calculate the sparse matrix vector product:
```
```                    Y = A*X.
```
```
```
```          SSPMV-S   Perform the matrix-vector operation.
```
```          DSPMV-D
```
```          CSPMV-C
```
```
```
```          SSPR-S    Performs the symmetric rank 1 operation.
```
```
```
```          SSPR2-S   Perform the symmetric rank 2 operation.
```
```          DSPR2-D
```
```          CSPR2-C
```
```
```
```          SSYMV-S   Multiply a real vector by a real symmetric matrix.
```
```          DSYMV-D
```
```          CSYMV-C
```
```
```
```          SSYR-S    Perform symmetric rank 1 update of a real symmetric matrix.
```
```
```
```          SSYR2-S   Perform symmetric rank 2 update of a real symmetric matrix.
```
```          DSYR2-D
```
```          CSYR2-C
```
```
```
```          STBMV-S   Multiply a real vector by a real triangular band matrix.
```
```          DTBMV-D
```
```          CTBMV-C
```
```
```
```          STBSV-S   Solve a real triangular banded system of linear equations.
```
```          DTBSV-D
```
```          CTBSV-C
```
```
```
```          STPMV-S   Perform one of the matrix-vector operations.
```
```          DTPMV-D
```
```          CTPMV-C
```
```
```
```          STPSV-S   Solve one of the systems of equations.
```
```          DTPSV-D
```
```          CTPSV-C
```
```
```
```          STRMV-S   Multiply a real vector by a real triangular matrix.
```
```          DTRMV-D
```
```          CTRMV-C
```
```
```
```          STRSV-S   Solve a real triangular system of linear equations.
```
```          DTRSV-D
```
```          CTRSV-C
```
```
```
```D1B6.  Multiplication
```
```
```
```          SGEMM-S   Multiply a real general matrix by a real general matrix.
```
```          DGEMM-D
```
```          CGEMM-C
```
```
```
```          CHEMM-C   Multiply a complex general matrix by a complex Hermitian
```
```          SHEMM-S   matrix.
```
```          DHEMM-D
```
```
```
```          CHER2K-C  Perform Hermitian rank 2k update of a complex.
```
```          SHER2-S
```
```          DHER2-D
```
```          CHER2-C
```
```
```
```          CHERK-C   Perform Hermitian rank k update of a complex Hermitian
```
```          SHERK-S   matrix.
```
```          DHERK-D
```
```
```
```          SSYMM-S   Multiply a real general matrix by a real symmetric matrix.
```
```          DSYMM-D
```
```          CSYMM-C
```
```
```
```          DSYR2K-D  Perform one of the symmetric rank 2k operations.
```
```          SSYR2-S
```
```          DSYR2-D
```
```          CSYR2-C
```
```
```
```          SSYRK-S   Perform symmetric rank k update of a real symmetric matrix.
```
```          DSYRK-D
```
```          CSYRK-C
```
```
```
```          STRMM-S   Multiply a real general matrix by a real triangular matrix.
```
```          DTRMM-D
```
```          CTRMM-C
```
```
```
```          STRSM-S   Solve a real triangular system of equations with multiple
```
```          DTRSM-D   right-hand sides.
```
```          CTRSM-C
```
```
```
```D1B9.  Storage mode conversion
```
```
```
```          SS2Y-S    SLAP Triad to SLAP Column Format Converter.
```
```          DS2Y-D    Routine to convert from the SLAP Triad to SLAP Column
```
```                    format.
```
```
```
```D1B10.  Elementary rotation (Givens transformation)
```
```
```
```          CSROT-C   Apply a plane Givens rotation.
```
```          SROT-S
```
```          DROT-D
```
```
```
```          SROTG-S   Construct a plane Givens rotation.
```
```          DROTG-D
```
```          CROTG-C
```
```
```
```          SROTMG-S  Construct a modified Givens transformation.
```
```          DROTMG-D
```
```
```
```D2.  Solution of systems of linear equations (including inversion, LU and
```
```     related decompositions)
```
```D2A.  Real nonsymmetric matrices
```
```D2A1.  General
```
```
```
```          SGECO-S   Factor a matrix using Gaussian elimination and estimate
```
```          DGECO-D   the condition number of the matrix.
```
```          CGECO-C
```
```
```
```          SGEDI-S   Compute the determinant and inverse of a matrix using the
```
```          DGEDI-D   factors computed by SGECO or SGEFA.
```
```          CGEDI-C
```
```
```
```          SGEFA-S   Factor a matrix using Gaussian elimination.
```
```          DGEFA-D
```
```          CGEFA-C
```
```
```
```          SGEFS-S   Solve a general system of linear equations.
```
```          DGEFS-D
```
```          CGEFS-C
```
```
```
```          SGEIR-S   Solve a general system of linear equations.  Iterative
```
```          CGEIR-C   refinement is used to obtain an error estimate.
```
```
```
```          SGESL-S   Solve the real system A*X=B or TRANS(A)*X=B using the
```
```          DGESL-D   factors of SGECO or SGEFA.
```
```          CGESL-C
```
```
```
```          SQRSL-S   Apply the output of SQRDC to compute coordinate transfor-
```
```          DQRSL-D   mations, projections, and least squares solutions.
```
```          CQRSL-C
```
```
```
```D2A2.  Banded
```
```
```
```          SGBCO-S   Factor a band matrix by Gaussian elimination and
```
```          DGBCO-D   estimate the condition number of the matrix.
```
```          CGBCO-C
```
```
```
```          SGBFA-S   Factor a band matrix using Gaussian elimination.
```
```          DGBFA-D
```
```          CGBFA-C
```
```
```
```          SGBSL-S   Solve the real band system A*X=B or TRANS(A)*X=B using
```
```          DGBSL-D   the factors computed by SGBCO or SGBFA.
```
```          CGBSL-C
```
```
```
```          SNBCO-S   Factor a band matrix using Gaussian elimination and
```
```          DNBCO-D   estimate the condition number.
```
```          CNBCO-C
```
```
```
```          SNBFA-S   Factor a real band matrix by elimination.
```
```          DNBFA-D
```
```          CNBFA-C
```
```
```
```          SNBFS-S   Solve a general nonsymmetric banded system of linear
```
```          DNBFS-D   equations.
```
```          CNBFS-C
```
```
```
```          SNBIR-S   Solve a general nonsymmetric banded system of linear
```
```          CNBIR-C   equations.  Iterative refinement is used to obtain an error
```
```                    estimate.
```
```
```
```          SNBSL-S   Solve a real band system using the factors computed by
```
```          DNBSL-D   SNBCO or SNBFA.
```
```          CNBSL-C
```
```
```
```D2A2A.  Tridiagonal
```
```
```
```          SGTSL-S   Solve a tridiagonal linear system.
```
```          DGTSL-D
```
```          CGTSL-C
```
```
```
```D2A3.  Triangular
```
```
```
```          SSLI-S    SLAP MSOLVE for Lower Triangle Matrix.
```
```          DSLI-D    This routine acts as an interface between the SLAP generic
```
```                    MSOLVE calling convention and the routine that actually
```
```                              -1
```
```                    computes L  B = X.
```
```
```
```          SSLI2-S   SLAP Lower Triangle Matrix Backsolve.
```
```          DSLI2-D   Routine to solve a system of the form  Lx = b , where L
```
```                    is a lower triangular matrix.
```
```
```
```          STRCO-S   Estimate the condition number of a triangular matrix.
```
```          DTRCO-D
```
```          CTRCO-C
```
```
```
```          STRDI-S   Compute the determinant and inverse of a triangular matrix.
```
```          DTRDI-D
```
```          CTRDI-C
```
```
```
```          STRSL-S   Solve a system of the form  T*X=B or TRANS(T)*X=B, where
```
```          DTRSL-D   T is a triangular matrix.
```
```          CTRSL-C
```
```
```
```D2A4.  Sparse
```
```
```
```          SBCG-S    Preconditioned BiConjugate Gradient Sparse Ax = b Solver.
```
```          DBCG-D    Routine to solve a Non-Symmetric linear system  Ax = b
```
```                    using the Preconditioned BiConjugate Gradient method.
```
```
```
```          SCGN-S    Preconditioned CG Sparse Ax=b Solver for Normal Equations.
```
```          DCGN-D    Routine to solve a general linear system  Ax = b  using the
```
```                    Preconditioned Conjugate Gradient method applied to the
```
```                    normal equations  AA'y = b, x=A'y.
```
```
```
```          SCGS-S    Preconditioned BiConjugate Gradient Squared Ax=b Solver.
```
```          DCGS-D    Routine to solve a Non-Symmetric linear system  Ax = b
```
```                    using the Preconditioned BiConjugate Gradient Squared
```
```                    method.
```
```
```
```          SGMRES-S  Preconditioned GMRES Iterative Sparse Ax=b Solver.
```
```          DGMRES-D  This routine uses the generalized minimum residual
```
```                    (GMRES) method with preconditioning to solve
```
```                    non-symmetric linear systems of the form: Ax = b.
```
```
```
```          SIR-S     Preconditioned Iterative Refinement Sparse Ax = b Solver.
```
```          DIR-D     Routine to solve a general linear system  Ax = b  using
```
```                    iterative refinement with a matrix splitting.
```
```
```
```          SLPDOC-S  Sparse Linear Algebra Package Version 2.0.2 Documentation.
```
```          DLPDOC-D  Routines to solve large sparse symmetric and nonsymmetric
```
```                    positive definite linear systems, Ax = b, using precondi-
```
```                    tioned iterative methods.
```
```
```
```          SOMN-S    Preconditioned Orthomin Sparse Iterative Ax=b Solver.
```
```          DOMN-D    Routine to solve a general linear system  Ax = b  using
```
```                    the Preconditioned Orthomin method.
```
```
```
```          SSDBCG-S  Diagonally Scaled BiConjugate Gradient Sparse Ax=b Solver.
```
```          DSDBCG-D  Routine to solve a linear system  Ax = b  using the
```
```                    BiConjugate Gradient method with diagonal scaling.
```
```
```
```          SSDCGN-S  Diagonally Scaled CG Sparse Ax=b Solver for Normal Eqn's.
```
```          DSDCGN-D  Routine to solve a general linear system  Ax = b  using
```
```                    diagonal scaling with the Conjugate Gradient method
```
```                    applied to the the normal equations, viz.,  AA'y = b,
```
```                    where  x = A'y.
```
```
```
```          SSDCGS-S  Diagonally Scaled CGS Sparse Ax=b Solver.
```
```          DSDCGS-D  Routine to solve a linear system  Ax = b  using the
```
```                    BiConjugate Gradient Squared method with diagonal scaling.
```
```
```
```          SSDGMR-S  Diagonally Scaled GMRES Iterative Sparse Ax=b Solver.
```
```          DSDGMR-D  This routine uses the generalized minimum residual
```
```                    (GMRES) method with diagonal scaling to solve possibly
```
```                    non-symmetric linear systems of the form: Ax = b.
```
```
```
```          SSDOMN-S  Diagonally Scaled Orthomin Sparse Iterative Ax=b Solver.
```
```          DSDOMN-D  Routine to solve a general linear system  Ax = b  using
```
```                    the Orthomin method with diagonal scaling.
```
```
```
```          SSGS-S    Gauss-Seidel Method Iterative Sparse Ax = b Solver.
```
```          DSGS-D    Routine to solve a general linear system  Ax = b  using
```
```                    Gauss-Seidel iteration.
```
```
```
```          SSILUR-S  Incomplete LU Iterative Refinement Sparse Ax = b Solver.
```
```          DSILUR-D  Routine to solve a general linear system  Ax = b  using
```
```                    the incomplete LU decomposition with iterative refinement.
```
```
```
```          SSJAC-S   Jacobi's Method Iterative Sparse Ax = b Solver.
```
```          DSJAC-D   Routine to solve a general linear system  Ax = b  using
```
```                    Jacobi iteration.
```
```
```
```          SSLUBC-S  Incomplete LU BiConjugate Gradient Sparse Ax=b Solver.
```
```          DSLUBC-D  Routine to solve a linear system  Ax = b  using the
```
```                    BiConjugate Gradient method with Incomplete LU
```
```                    decomposition preconditioning.
```
```
```
```          SSLUCN-S  Incomplete LU CG Sparse Ax=b Solver for Normal Equations.
```
```          DSLUCN-D  Routine to solve a general linear system  Ax = b  using the
```
```                    incomplete LU decomposition with the Conjugate Gradient
```
```                    method applied to the normal equations, viz.,  AA'y = b,
```
```                    x = A'y.
```
```
```
```          SSLUCS-S  Incomplete LU BiConjugate Gradient Squared Ax=b Solver.
```
```          DSLUCS-D  Routine to solve a linear system  Ax = b  using the
```
```                    BiConjugate Gradient Squared method with Incomplete LU
```
```                    decomposition preconditioning.
```
```
```
```          SSLUGM-S  Incomplete LU GMRES Iterative Sparse Ax=b Solver.
```
```          DSLUGM-D  This routine uses the generalized minimum residual
```
```                    (GMRES) method with incomplete LU factorization for
```
```                    preconditioning to solve possibly non-symmetric linear
```
```                    systems of the form: Ax = b.
```
```
```
```          SSLUOM-S  Incomplete LU Orthomin Sparse Iterative Ax=b Solver.
```
```          DSLUOM-D  Routine to solve a general linear system  Ax = b  using
```
```                    the Orthomin method with Incomplete LU decomposition.
```
```
```
```D2B.  Real symmetric matrices
```
```D2B1.  General
```
```D2B1A.  Indefinite
```
```
```
```          SSICO-S   Factor a symmetric matrix by elimination with symmetric
```
```          DSICO-D   pivoting and estimate the condition number of the matrix.
```
```          CHICO-C
```
```          CSICO-C
```
```
```
```          SSIDI-S   Compute the determinant, inertia and inverse of a real
```
```          DSIDI-D   symmetric matrix using the factors from SSIFA.
```
```          CHIDI-C
```
```          CSIDI-C
```
```
```
```          SSIFA-S   Factor a real symmetric matrix by elimination with
```
```          DSIFA-D   symmetric pivoting.
```
```          CHIFA-C
```
```          CSIFA-C
```
```
```
```          SSISL-S   Solve a real symmetric system using the factors obtained
```
```          DSISL-D   from SSIFA.
```
```          CHISL-C
```
```          CSISL-C
```
```
```
```          SSPCO-S   Factor a real symmetric matrix stored in packed form
```
```          DSPCO-D   by elimination with symmetric pivoting and estimate the
```
```          CHPCO-C   condition number of the matrix.
```
```          CSPCO-C
```
```
```
```          SSPDI-S   Compute the determinant, inertia, inverse of a real
```
```          DSPDI-D   symmetric matrix stored in packed form using the factors
```
```          CHPDI-C   from SSPFA.
```
```          CSPDI-C
```
```
```
```          SSPFA-S   Factor a real symmetric matrix stored in packed form by
```
```          DSPFA-D   elimination with symmetric pivoting.
```
```          CHPFA-C
```
```          CSPFA-C
```
```
```
```          SSPSL-S   Solve a real symmetric system using the factors obtained
```
```          DSPSL-D   from SSPFA.
```
```          CHPSL-C
```
```          CSPSL-C
```
```
```
```D2B1B.  Positive definite
```
```
```
```          SCHDC-S   Compute the Cholesky decomposition of a positive definite
```
```          DCHDC-D   matrix.  A pivoting option allows the user to estimate the
```
```          CCHDC-C   condition number of a positive definite matrix or determine
```
```                    the rank of a positive semidefinite matrix.
```
```
```
```          SPOCO-S   Factor a real symmetric positive definite matrix
```
```          DPOCO-D   and estimate the condition number of the matrix.
```
```          CPOCO-C
```
```
```
```          SPODI-S   Compute the determinant and inverse of a certain real
```
```          DPODI-D   symmetric positive definite matrix using the factors
```
```          CPODI-C   computed by SPOCO, SPOFA or SQRDC.
```
```
```
```          SPOFA-S   Factor a real symmetric positive definite matrix.
```
```          DPOFA-D
```
```          CPOFA-C
```
```
```
```          SPOFS-S   Solve a positive definite symmetric system of linear
```
```          DPOFS-D   equations.
```
```          CPOFS-C
```
```
```
```          SPOIR-S   Solve a positive definite symmetric system of linear
```
```          CPOIR-C   equations.  Iterative refinement is used to obtain an error
```
```                    estimate.
```
```
```
```          SPOSL-S   Solve the real symmetric positive definite linear system
```
```          DPOSL-D   using the factors computed by SPOCO or SPOFA.
```
```          CPOSL-C
```
```
```
```          SPPCO-S   Factor a symmetric positive definite matrix stored in
```
```          DPPCO-D   packed form and estimate the condition number of the
```
```          CPPCO-C   matrix.
```
```
```
```          SPPDI-S   Compute the determinant and inverse of a real symmetric
```
```          DPPDI-D   positive definite matrix using factors from SPPCO or SPPFA.
```
```          CPPDI-C
```
```
```
```          SPPFA-S   Factor a real symmetric positive definite matrix stored in
```
```          DPPFA-D   packed form.
```
```          CPPFA-C
```
```
```
```          SPPSL-S   Solve the real symmetric positive definite system using
```
```          DPPSL-D   the factors computed by SPPCO or SPPFA.
```
```          CPPSL-C
```
```
```
```D2B2.  Positive definite banded
```
```
```
```          SPBCO-S   Factor a real symmetric positive definite matrix stored in
```
```          DPBCO-D   band form and estimate the condition number of the matrix.
```
```          CPBCO-C
```
```
```
```          SPBFA-S   Factor a real symmetric positive definite matrix stored in
```
```          DPBFA-D   band form.
```
```          CPBFA-C
```
```
```
```          SPBSL-S   Solve a real symmetric positive definite band system
```
```          DPBSL-D   using the factors computed by SPBCO or SPBFA.
```
```          CPBSL-C
```
```
```
```D2B2A.  Tridiagonal
```
```
```
```          SPTSL-S   Solve a positive definite tridiagonal linear system.
```
```          DPTSL-D
```
```          CPTSL-C
```
```
```
```D2B4.  Sparse
```
```
```
```          SBCG-S    Preconditioned BiConjugate Gradient Sparse Ax = b Solver.
```
```          DBCG-D    Routine to solve a Non-Symmetric linear system  Ax = b
```
```                    using the Preconditioned BiConjugate Gradient method.
```
```
```
```          SCG-S     Preconditioned Conjugate Gradient Sparse Ax=b Solver.
```
```          DCG-D     Routine to solve a symmetric positive definite linear
```
```                    system  Ax = b  using the Preconditioned Conjugate
```
```                    Gradient method.
```
```
```
```          SCGN-S    Preconditioned CG Sparse Ax=b Solver for Normal Equations.
```
```          DCGN-D    Routine to solve a general linear system  Ax = b  using the
```
```                    Preconditioned Conjugate Gradient method applied to the
```
```                    normal equations  AA'y = b, x=A'y.
```
```
```
```          SCGS-S    Preconditioned BiConjugate Gradient Squared Ax=b Solver.
```
```          DCGS-D    Routine to solve a Non-Symmetric linear system  Ax = b
```
```                    using the Preconditioned BiConjugate Gradient Squared
```
```                    method.
```
```
```
```          SGMRES-S  Preconditioned GMRES Iterative Sparse Ax=b Solver.
```
```          DGMRES-D  This routine uses the generalized minimum residual
```
```                    (GMRES) method with preconditioning to solve
```
```                    non-symmetric linear systems of the form: Ax = b.
```
```
```
```          SIR-S     Preconditioned Iterative Refinement Sparse Ax = b Solver.
```
```          DIR-D     Routine to solve a general linear system  Ax = b  using
```
```                    iterative refinement with a matrix splitting.
```
```
```
```          SLPDOC-S  Sparse Linear Algebra Package Version 2.0.2 Documentation.
```
```          DLPDOC-D  Routines to solve large sparse symmetric and nonsymmetric
```
```                    positive definite linear systems, Ax = b, using precondi-
```
```                    tioned iterative methods.
```
```
```
```          SOMN-S    Preconditioned Orthomin Sparse Iterative Ax=b Solver.
```
```          DOMN-D    Routine to solve a general linear system  Ax = b  using
```
```                    the Preconditioned Orthomin method.
```
```
```
```          SSDBCG-S  Diagonally Scaled BiConjugate Gradient Sparse Ax=b Solver.
```
```          DSDBCG-D  Routine to solve a linear system  Ax = b  using the
```
```                    BiConjugate Gradient method with diagonal scaling.
```
```
```
```          SSDCG-S   Diagonally Scaled Conjugate Gradient Sparse Ax=b Solver.
```
```          DSDCG-D   Routine to solve a symmetric positive definite linear
```
```                    system  Ax = b  using the Preconditioned Conjugate
```
```                    Gradient method.  The preconditioner is diagonal scaling.
```
```
```
```          SSDCGN-S  Diagonally Scaled CG Sparse Ax=b Solver for Normal Eqn's.
```
```          DSDCGN-D  Routine to solve a general linear system  Ax = b  using
```
```                    diagonal scaling with the Conjugate Gradient method
```
```                    applied to the the normal equations, viz.,  AA'y = b,
```
```                    where  x = A'y.
```
```
```
```          SSDCGS-S  Diagonally Scaled CGS Sparse Ax=b Solver.
```
```          DSDCGS-D  Routine to solve a linear system  Ax = b  using the
```
```                    BiConjugate Gradient Squared method with diagonal scaling.
```
```
```
```          SSDGMR-S  Diagonally Scaled GMRES Iterative Sparse Ax=b Solver.
```
```          DSDGMR-D  This routine uses the generalized minimum residual
```
```                    (GMRES) method with diagonal scaling to solve possibly
```
```                    non-symmetric linear systems of the form: Ax = b.
```
```
```
```          SSDOMN-S  Diagonally Scaled Orthomin Sparse Iterative Ax=b Solver.
```
```          DSDOMN-D  Routine to solve a general linear system  Ax = b  using
```
```                    the Orthomin method with diagonal scaling.
```
```
```
```          SSGS-S    Gauss-Seidel Method Iterative Sparse Ax = b Solver.
```
```          DSGS-D    Routine to solve a general linear system  Ax = b  using
```
```                    Gauss-Seidel iteration.
```
```
```
```          SSICCG-S  Incomplete Cholesky Conjugate Gradient Sparse Ax=b Solver.
```
```          DSICCG-D  Routine to solve a symmetric positive definite linear
```
```                    system  Ax = b  using the incomplete Cholesky
```
```                    Preconditioned Conjugate Gradient method.
```
```
```
```          SSILUR-S  Incomplete LU Iterative Refinement Sparse Ax = b Solver.
```
```          DSILUR-D  Routine to solve a general linear system  Ax = b  using
```
```                    the incomplete LU decomposition with iterative refinement.
```
```
```
```          SSJAC-S   Jacobi's Method Iterative Sparse Ax = b Solver.
```
```          DSJAC-D   Routine to solve a general linear system  Ax = b  using
```
```                    Jacobi iteration.
```
```
```
```          SSLUBC-S  Incomplete LU BiConjugate Gradient Sparse Ax=b Solver.
```
```          DSLUBC-D  Routine to solve a linear system  Ax = b  using the
```
```                    BiConjugate Gradient method with Incomplete LU
```
```                    decomposition preconditioning.
```
```
```
```          SSLUCN-S  Incomplete LU CG Sparse Ax=b Solver for Normal Equations.
```
```          DSLUCN-D  Routine to solve a general linear system  Ax = b  using the
```
```                    incomplete LU decomposition with the Conjugate Gradient
```
```                    method applied to the normal equations, viz.,  AA'y = b,
```
```                    x = A'y.
```
```
```
```          SSLUCS-S  Incomplete LU BiConjugate Gradient Squared Ax=b Solver.
```
```          DSLUCS-D  Routine to solve a linear system  Ax = b  using the
```
```                    BiConjugate Gradient Squared method with Incomplete LU
```
```                    decomposition preconditioning.
```
```
```
```          SSLUGM-S  Incomplete LU GMRES Iterative Sparse Ax=b Solver.
```
```          DSLUGM-D  This routine uses the generalized minimum residual
```
```                    (GMRES) method with incomplete LU factorization for
```
```                    preconditioning to solve possibly non-symmetric linear
```
```                    systems of the form: Ax = b.
```
```
```
```          SSLUOM-S  Incomplete LU Orthomin Sparse Iterative Ax=b Solver.
```
```          DSLUOM-D  Routine to solve a general linear system  Ax = b  using
```
```                    the Orthomin method with Incomplete LU decomposition.
```
```
```
```D2C.  Complex non-Hermitian matrices
```
```D2C1.  General
```
```
```
```          CGECO-C   Factor a matrix using Gaussian elimination and estimate
```
```          SGECO-S   the condition number of the matrix.
```
```          DGECO-D
```
```
```
```          CGEDI-C   Compute the determinant and inverse of a matrix using the
```
```          SGEDI-S   factors computed by CGECO or CGEFA.
```
```          DGEDI-D
```
```
```
```          CGEFA-C   Factor a matrix using Gaussian elimination.
```
```          SGEFA-S
```
```          DGEFA-D
```
```
```
```          CGEFS-C   Solve a general system of linear equations.
```
```          SGEFS-S
```
```          DGEFS-D
```
```
```
```          CGEIR-C   Solve a general system of linear equations.  Iterative
```
```          SGEIR-S   refinement is used to obtain an error estimate.
```
```
```
```          CGESL-C   Solve the complex system A*X=B or CTRANS(A)*X=B using the
```
```          SGESL-S   factors computed by CGECO or CGEFA.
```
```          DGESL-D
```
```
```
```          CQRSL-C   Apply the output of CQRDC to compute coordinate transfor-
```
```          SQRSL-S   mations, projections, and least squares solutions.
```
```          DQRSL-D
```
```
```
```          CSICO-C   Factor a complex symmetric matrix by elimination with
```
```          SSICO-S   symmetric pivoting and estimate the condition number of the
```
```          DSICO-D   matrix.
```
```          CHICO-C
```
```
```
```          CSIDI-C   Compute the determinant and inverse of a complex symmetric
```
```          SSIDI-S   matrix using the factors from CSIFA.
```
```          DSIDI-D
```
```          CHIDI-C
```
```
```
```          CSIFA-C   Factor a complex symmetric matrix by elimination with
```
```          SSIFA-S   symmetric pivoting.
```
```          DSIFA-D
```
```          CHIFA-C
```
```
```
```          CSISL-C   Solve a complex symmetric system using the factors obtained
```
```          SSISL-S   from CSIFA.
```
```          DSISL-D
```
```          CHISL-C
```
```
```
```          CSPCO-C   Factor a complex symmetric matrix stored in packed form
```
```          SSPCO-S   by elimination with symmetric pivoting and estimate the
```
```          DSPCO-D   condition number of the matrix.
```
```          CHPCO-C
```
```
```
```          CSPDI-C   Compute the determinant and inverse of a complex symmetric
```
```          SSPDI-S   matrix stored in packed form using the factors from CSPFA.
```
```          DSPDI-D
```
```          CHPDI-C
```
```
```
```          CSPFA-C   Factor a complex symmetric matrix stored in packed form by
```
```          SSPFA-S   elimination with symmetric pivoting.
```
```          DSPFA-D
```
```          CHPFA-C
```
```
```
```          CSPSL-C   Solve a complex symmetric system using the factors obtained
```
```          SSPSL-S   from CSPFA.
```
```          DSPSL-D
```
```          CHPSL-C
```
```
```
```D2C2.  Banded
```
```
```
```          CGBCO-C   Factor a band matrix by Gaussian elimination and
```
```          SGBCO-S   estimate the condition number of the matrix.
```
```          DGBCO-D
```
```
```
```          CGBFA-C   Factor a band matrix using Gaussian elimination.
```
```          SGBFA-S
```
```          DGBFA-D
```
```
```
```          CGBSL-C   Solve the complex band system A*X=B or CTRANS(A)*X=B using
```
```          SGBSL-S   the factors computed by CGBCO or CGBFA.
```
```          DGBSL-D
```
```
```
```          CNBCO-C   Factor a band matrix using Gaussian elimination and
```
```          SNBCO-S   estimate the condition number.
```
```          DNBCO-D
```
```
```
```          CNBFA-C   Factor a band matrix by elimination.
```
```          SNBFA-S
```
```          DNBFA-D
```
```
```
```          CNBFS-C   Solve a general nonsymmetric banded system of linear
```
```          SNBFS-S   equations.
```
```          DNBFS-D
```
```
```
```          CNBIR-C   Solve a general nonsymmetric banded system of linear
```
```          SNBIR-S   equations.  Iterative refinement is used to obtain an error
```
```                    estimate.
```
```
```
```          CNBSL-C   Solve a complex band system using the factors computed by
```
```          SNBSL-S   CNBCO or CNBFA.
```
```          DNBSL-D
```
```
```
```D2C2A.  Tridiagonal
```
```
```
```          CGTSL-C   Solve a tridiagonal linear system.
```
```          SGTSL-S
```
```          DGTSL-D
```
```
```
```D2C3.  Triangular
```
```
```
```          CTRCO-C   Estimate the condition number of a triangular matrix.
```
```          STRCO-S
```
```          DTRCO-D
```
```
```
```          CTRDI-C   Compute the determinant and inverse of a triangular matrix.
```
```          STRDI-S
```
```          DTRDI-D
```
```
```
```          CTRSL-C   Solve a system of the form  T*X=B or CTRANS(T)*X=B, where
```
```          STRSL-S   T is a triangular matrix.  Here CTRANS(T) is the conjugate
```
```          DTRSL-D   transpose.
```
```
```
```D2D.  Complex Hermitian matrices
```
```D2D1.  General
```
```D2D1A.  Indefinite
```
```
```
```          CHICO-C   Factor a complex Hermitian matrix by elimination with sym-
```
```          SSICO-S   metric pivoting and estimate the condition of the matrix.
```
```          DSICO-D
```
```          CSICO-C
```
```
```
```          CHIDI-C   Compute the determinant, inertia and inverse of a complex
```
```          SSIDI-S   Hermitian matrix using the factors obtained from CHIFA.
```
```          DSISI-D
```
```          CSIDI-C
```
```
```
```          CHIFA-C   Factor a complex Hermitian matrix by elimination
```
```          SSIFA-S   (symmetric pivoting).
```
```          DSIFA-D
```
```          CSIFA-C
```
```
```
```          CHISL-C   Solve the complex Hermitian system using factors obtained
```
```          SSISL-S   from CHIFA.
```
```          DSISL-D
```
```          CSISL-C
```
```
```
```          CHPCO-C   Factor a complex Hermitian matrix stored in packed form by
```
```          SSPCO-S   elimination with symmetric pivoting and estimate the
```
```          DSPCO-D   condition number of the matrix.
```
```          CSPCO-C
```
```
```
```          CHPDI-C   Compute the determinant, inertia and inverse of a complex
```
```          SSPDI-S   Hermitian matrix stored in packed form using the factors
```
```          DSPDI-D   obtained from CHPFA.
```
```          DSPDI-C
```
```
```
```          CHPFA-C   Factor a complex Hermitian matrix stored in packed form by
```
```          SSPFA-S   elimination with symmetric pivoting.
```
```          DSPFA-D
```
```          DSPFA-C
```
```
```
```          CHPSL-C   Solve a complex Hermitian system using factors obtained
```
```          SSPSL-S   from CHPFA.
```
```          DSPSL-D
```
```          CSPSL-C
```
```
```
```D2D1B.  Positive definite
```
```
```
```          CCHDC-C   Compute the Cholesky decomposition of a positive definite
```
```          SCHDC-S   matrix.  A pivoting option allows the user to estimate the
```
```          DCHDC-D   condition number of a positive definite matrix or determine
```
```                    the rank of a positive semidefinite matrix.
```
```
```
```          CPOCO-C   Factor a complex Hermitian positive definite matrix
```
```          SPOCO-S   and estimate the condition number of the matrix.
```
```          DPOCO-D
```
```
```
```          CPODI-C   Compute the determinant and inverse of a certain complex
```
```          SPODI-S   Hermitian positive definite matrix using the factors
```
```          DPODI-D   computed by CPOCO, CPOFA, or CQRDC.
```
```
```
```          CPOFA-C   Factor a complex Hermitian positive definite matrix.
```
```          SPOFA-S
```
```          DPOFA-D
```
```
```
```          CPOFS-C   Solve a positive definite symmetric complex system of
```
```          SPOFS-S   linear equations.
```
```          DPOFS-D
```
```
```
```          CPOIR-C   Solve a positive definite Hermitian system of linear
```
```          SPOIR-S   equations.  Iterative refinement is used to obtain an
```
```                    error estimate.
```
```
```
```          CPOSL-C   Solve the complex Hermitian positive definite linear system
```
```          SPOSL-S   using the factors computed by CPOCO or CPOFA.
```
```          DPOSL-D
```
```
```
```          CPPCO-C   Factor a complex Hermitian positive definite matrix stored
```
```          SPPCO-S   in packed form and estimate the condition number of the
```
```          DPPCO-D   matrix.
```
```
```
```          CPPDI-C   Compute the determinant and inverse of a complex Hermitian
```
```          SPPDI-S   positive definite matrix using factors from CPPCO or CPPFA.
```
```          DPPDI-D
```
```
```
```          CPPFA-C   Factor a complex Hermitian positive definite matrix stored
```
```          SPPFA-S   in packed form.
```
```          DPPFA-D
```
```
```
```          CPPSL-C   Solve the complex Hermitian positive definite system using
```
```          SPPSL-S   the factors computed by CPPCO or CPPFA.
```
```          DPPSL-D
```
```
```
```D2D2.  Positive definite banded
```
```
```
```          CPBCO-C   Factor a complex Hermitian positive definite matrix stored
```
```          SPBCO-S   in band form and estimate the condition number of the
```
```          DPBCO-D   matrix.
```
```
```
```          CPBFA-C   Factor a complex Hermitian positive definite matrix stored
```
```          SPBFA-S   in band form.
```
```          DPBFA-D
```
```
```
```          CPBSL-C   Solve the complex Hermitian positive definite band system
```
```          SPBSL-S   using the factors computed by CPBCO or CPBFA.
```
```          DPBSL-D
```
```
```
```D2D2A.  Tridiagonal
```
```
```
```          CPTSL-C   Solve a positive definite tridiagonal linear system.
```
```          SPTSL-S
```
```          DPTSL-D
```
```
```
```D2E.  Associated operations (e.g., matrix reorderings)
```
```
```
```          SLLTI2-S  SLAP Backsolve routine for LDL' Factorization.
```
```          DLLTI2-D  Routine to solve a system of the form  L*D*L' X = B,
```
```                    where L is a unit lower triangular matrix and D is a
```
```                    diagonal matrix and ' means transpose.
```
```
```
```          SS2LT-S   Lower Triangle Preconditioner SLAP Set Up.
```
```          DS2LT-D   Routine to store the lower triangle of a matrix stored
```
```                    in the SLAP Column format.
```
```
```
```          SSD2S-S   Diagonal Scaling Preconditioner SLAP Normal Eqns Set Up.
```
```          DSD2S-D   Routine to compute the inverse of the diagonal of the
```
```                    matrix A*A', where A is stored in SLAP-Column format.
```
```
```
```          SSDS-S    Diagonal Scaling Preconditioner SLAP Set Up.
```
```          DSDS-D    Routine to compute the inverse of the diagonal of a matrix
```
```                    stored in the SLAP Column format.
```
```
```
```          SSDSCL-S  Diagonal Scaling of system Ax = b.
```
```          DSDSCL-D  This routine scales (and unscales) the system  Ax = b
```
```                    by symmetric diagonal scaling.
```
```
```
```          SSICS-S   Incompl. Cholesky Decomposition Preconditioner SLAP Set Up.
```
```          DSICS-D   Routine to generate the Incomplete Cholesky decomposition,
```
```                    L*D*L-trans, of a symmetric positive definite matrix, A,
```
```                    which is stored in SLAP Column format.  The unit lower
```
```                    triangular matrix L is stored by rows, and the inverse of
```
```                    the diagonal matrix D is stored.
```
```
```
```          SSILUS-S  Incomplete LU Decomposition Preconditioner SLAP Set Up.
```
```          DSILUS-D  Routine to generate the incomplete LDU decomposition of a
```
```                    matrix.  The unit lower triangular factor L is stored by
```
```                    rows and the unit upper triangular factor U is stored by
```
```                    columns.  The inverse of the diagonal matrix D is stored.
```
```                    No fill in is allowed.
```
```
```
```          SSLLTI-S  SLAP MSOLVE for LDL' (IC) Factorization.
```
```          DSLLTI-D  This routine acts as an interface between the SLAP generic
```
```                    MSOLVE calling convention and the routine that actually
```
```                                   -1
```
```                    computes (LDL')  B = X.
```
```
```
```          SSLUI-S   SLAP MSOLVE for LDU Factorization.
```
```          DSLUI-D   This routine acts as an interface between the SLAP generic
```
```                    MSOLVE calling convention and the routine that actually
```
```                                   -1
```
```                    computes  (LDU)  B = X.
```
```
```
```          SSLUI2-S  SLAP Backsolve for LDU Factorization.
```
```          DSLUI2-D  Routine to solve a system of the form  L*D*U X = B,
```
```                    where L is a unit lower triangular matrix, D is a diagonal
```
```                    matrix, and U is a unit upper triangular matrix.
```
```
```
```          SSLUI4-S  SLAP Backsolve for LDU Factorization.
```
```          DSLUI4-D  Routine to solve a system of the form  (L*D*U)' X = B,
```
```                    where L is a unit lower triangular matrix, D is a diagonal
```
```                    matrix, and U is a unit upper triangular matrix and '
```
```                    denotes transpose.
```
```
```
```          SSLUTI-S  SLAP MTSOLV for LDU Factorization.
```
```          DSLUTI-D  This routine acts as an interface between the SLAP generic
```
```                    MTSOLV calling convention and the routine that actually
```
```                                   -T
```
```                    computes  (LDU)  B = X.
```
```
```
```          SSMMI2-S  SLAP Backsolve for LDU Factorization of Normal Equations.
```
```          DSMMI2-D  To solve a system of the form  (L*D*U)*(L*D*U)' X = B,
```
```                    where L is a unit lower triangular matrix, D is a diagonal
```
```                    matrix, and U is a unit upper triangular matrix and '
```
```                    denotes transpose.
```
```
```
```          SSMMTI-S  SLAP MSOLVE for LDU Factorization of Normal Equations.
```
```          DSMMTI-D  This routine acts as an interface between the SLAP generic
```
```                    MMTSLV calling convention and the routine that actually
```
```                                            -1
```
```                    computes  [(LDU)*(LDU)']  B = X.
```
```
```
```D3.  Determinants
```
```D3A.  Real nonsymmetric matrices
```
```D3A1.  General
```
```
```
```          SGEDI-S   Compute the determinant and inverse of a matrix using the
```
```          DGEDI-D   factors computed by SGECO or SGEFA.
```
```          CGEDI-C
```
```
```
```D3A2.  Banded
```
```
```
```          SGBDI-S   Compute the determinant of a band matrix using the factors
```
```          DGBDI-D   computed by SGBCO or SGBFA.
```
```          CGBDI-C
```
```
```
```          SNBDI-S   Compute the determinant of a band matrix using the factors
```
```          DNBDI-D   computed by SNBCO or SNBFA.
```
```          CNBDI-C
```
```
```
```D3A3.  Triangular
```
```
```
```          STRDI-S   Compute the determinant and inverse of a triangular matrix.
```
```          DTRDI-D
```
```          CTRDI-C
```
```
```
```D3B.  Real symmetric matrices
```
```D3B1.  General
```
```D3B1A.  Indefinite
```
```
```
```          SSIDI-S   Compute the determinant, inertia and inverse of a real
```
```          DSIDI-D   symmetric matrix using the factors from SSIFA.
```
```          CHIDI-C
```
```          CSIDI-C
```
```
```
```          SSPDI-S   Compute the determinant, inertia, inverse of a real
```
```          DSPDI-D   symmetric matrix stored in packed form using the factors
```
```          CHPDI-C   from SSPFA.
```
```          CSPDI-C
```
```
```
```D3B1B.  Positive definite
```
```
```
```          SPODI-S   Compute the determinant and inverse of a certain real
```
```          DPODI-D   symmetric positive definite matrix using the factors
```
```          CPODI-C   computed by SPOCO, SPOFA or SQRDC.
```
```
```
```          SPPDI-S   Compute the determinant and inverse of a real symmetric
```
```          DPPDI-D   positive definite matrix using factors from SPPCO or SPPFA.
```
```          CPPDI-C
```
```
```
```D3B2.  Positive definite banded
```
```
```
```          SPBDI-S   Compute the determinant of a symmetric positive definite
```
```          DPBDI-D   band matrix using the factors computed by SPBCO or SPBFA.
```
```          CPBDI-C
```
```
```
```D3C.  Complex non-Hermitian matrices
```
```D3C1.  General
```
```
```
```          CGEDI-C   Compute the determinant and inverse of a matrix using the
```
```          SGEDI-S   factors computed by CGECO or CGEFA.
```
```          DGEDI-D
```
```
```
```          CSIDI-C   Compute the determinant and inverse of a complex symmetric
```
```          SSIDI-S   matrix using the factors from CSIFA.
```
```          DSIDI-D
```
```          CHIDI-C
```
```
```
```          CSPDI-C   Compute the determinant and inverse of a complex symmetric
```
```          SSPDI-S   matrix stored in packed form using the factors from CSPFA.
```
```          DSPDI-D
```
```          CHPDI-C
```
```
```
```D3C2.  Banded
```
```
```
```          CGBDI-C   Compute the determinant of a complex band matrix using the
```
```          SGBDI-S   factors from CGBCO or CGBFA.
```
```          DGBDI-D
```
```
```
```          CNBDI-C   Compute the determinant of a band matrix using the factors
```
```          SNBDI-S   computed by CNBCO or CNBFA.
```
```          DNBDI-D
```
```
```
```D3C3.  Triangular
```
```
```
```          CTRDI-C   Compute the determinant and inverse of a triangular matrix.
```
```          STRDI-S
```
```          DTRDI-D
```
```
```
```D3D.  Complex Hermitian matrices
```
```D3D1.  General
```
```D3D1A.  Indefinite
```
```
```
```          CHIDI-C   Compute the determinant, inertia and inverse of a complex
```
```          SSIDI-S   Hermitian matrix using the factors obtained from CHIFA.
```
```          DSISI-D
```
```          CSIDI-C
```
```
```
```          CHPDI-C   Compute the determinant, inertia and inverse of a complex
```
```          SSPDI-S   Hermitian matrix stored in packed form using the factors
```
```          DSPDI-D   obtained from CHPFA.
```
```          DSPDI-C
```
```
```
```D3D1B.  Positive definite
```
```
```
```          CPODI-C   Compute the determinant and inverse of a certain complex
```
```          SPODI-S   Hermitian positive definite matrix using the factors
```
```          DPODI-D   computed by CPOCO, CPOFA, or CQRDC.
```
```
```
```          CPPDI-C   Compute the determinant and inverse of a complex Hermitian
```
```          SPPDI-S   positive definite matrix using factors from CPPCO or CPPFA.
```
```          DPPDI-D
```
```
```
```D3D2.  Positive definite banded
```
```
```
```          CPBDI-C   Compute the determinant of a complex Hermitian positive
```
```          SPBDI-S   definite band matrix using the factors computed by CPBCO or
```
```          DPBDI-D   CPBFA.
```
```
```
```D4.  Eigenvalues, eigenvectors
```
```
```
```          EISDOC-A  Documentation for EISPACK, a collection of subprograms for
```
```                    solving matrix eigen-problems.
```
```
```
```D4A.  Ordinary eigenvalue problems (Ax = (lambda) * x)
```
```D4A1.  Real symmetric
```
```
```
```          RS-S      Compute the eigenvalues and, optionally, the eigenvectors
```
```          CH-C      of a real symmetric matrix.
```
```
```
```          RSP-S     Compute the eigenvalues and, optionally, the eigenvectors
```
```                    of a real symmetric matrix packed into a one dimensional
```
```                    array.
```
```
```
```          SSIEV-S   Compute the eigenvalues and, optionally, the eigenvectors
```
```          CHIEV-C   of a real symmetric matrix.
```
```
```
```          SSPEV-S   Compute the eigenvalues and, optionally, the eigenvectors
```
```                    of a real symmetric matrix stored in packed form.
```
```
```
```D4A2.  Real nonsymmetric
```
```
```
```          RG-S      Compute the eigenvalues and, optionally, the eigenvectors
```
```          CG-C      of a real general matrix.
```
```
```
```          SGEEV-S   Compute the eigenvalues and, optionally, the eigenvectors
```
```          CGEEV-C   of a real general matrix.
```
```
```
```D4A3.  Complex Hermitian
```
```
```
```          CH-C      Compute the eigenvalues and, optionally, the eigenvectors
```
```          RS-S      of a complex Hermitian matrix.
```
```
```
```          CHIEV-C   Compute the eigenvalues and, optionally, the eigenvectors
```
```          SSIEV-S   of a complex Hermitian matrix.
```
```
```
```D4A4.  Complex non-Hermitian
```
```
```
```          CG-C      Compute the eigenvalues and, optionally, the eigenvectors
```
```          RG-S      of a complex general matrix.
```
```
```
```          CGEEV-C   Compute the eigenvalues and, optionally, the eigenvectors
```
```          SGEEV-S   of a complex general matrix.
```
```
```
```D4A5.  Tridiagonal
```
```
```
```          BISECT-S  Compute the eigenvalues of a symmetric tridiagonal matrix
```
```                    in a given interval using Sturm sequencing.
```
```
```
```          IMTQL1-S  Compute the eigenvalues of a symmetric tridiagonal matrix
```
```                    using the implicit QL method.
```
```
```
```          IMTQL2-S  Compute the eigenvalues and eigenvectors of a symmetric
```
```                    tridiagonal matrix using the implicit QL method.
```
```
```
```          IMTQLV-S  Compute the eigenvalues of a symmetric tridiagonal matrix
```
```                    using the implicit QL method.  Eigenvectors may be computed
```
```                    later.
```
```
```
```          RATQR-S   Compute the largest or smallest eigenvalues of a symmetric
```
```                    tridiagonal matrix using the rational QR method with Newton
```
```                    correction.
```
```
```
```          RST-S     Compute the eigenvalues and, optionally, the eigenvectors
```
```                    of a real symmetric tridiagonal matrix.
```
```
```
```          RT-S      Compute the eigenvalues and eigenvectors of a special real
```
```                    tridiagonal matrix.
```
```
```
```          TQL1-S    Compute the eigenvalues of symmetric tridiagonal matrix by
```
```                    the QL method.
```
```
```
```          TQL2-S    Compute the eigenvalues and eigenvectors of symmetric
```
```                    tridiagonal matrix.
```
```
```
```          TQLRAT-S  Compute the eigenvalues of symmetric tridiagonal matrix
```
```                    using a rational variant of the QL method.
```
```
```
```          TRIDIB-S  Compute the eigenvalues of a symmetric tridiagonal matrix
```
```                    in a given interval using Sturm sequencing.
```
```
```
```          TSTURM-S  Find those eigenvalues of a symmetric tridiagonal matrix
```
```                    in a given interval and their associated eigenvectors by
```
```                    Sturm sequencing.
```
```
```
```D4A6.  Banded
```
```
```
```          BQR-S     Compute some of the eigenvalues of a real symmetric
```
```                    matrix using the QR method with shifts of origin.
```
```
```
```          RSB-S     Compute the eigenvalues and, optionally, the eigenvectors
```
```                    of a symmetric band matrix.
```
```
```
```D4B.  Generalized eigenvalue problems (e.g., Ax = (lambda)*Bx)
```
```D4B1.  Real symmetric
```
```
```
```          RSG-S     Compute the eigenvalues and, optionally, the eigenvectors
```
```                    of a symmetric generalized eigenproblem.
```
```
```
```          RSGAB-S   Compute the eigenvalues and, optionally, the eigenvectors
```
```                    of a symmetric generalized eigenproblem.
```
```
```
```          RSGBA-S   Compute the eigenvalues and, optionally, the eigenvectors
```
```                    of a symmetric generalized eigenproblem.
```
```
```
```D4B2.  Real general
```
```
```
```          RGG-S     Compute the eigenvalues and eigenvectors for a real
```
```                    generalized eigenproblem.
```
```
```
```D4C.  Associated operations
```
```D4C1.  Transform problem
```
```D4C1A.  Balance matrix
```
```
```
```          BALANC-S  Balance a real general matrix and isolate eigenvalues
```
```          CBAL-C    whenever possible.
```
```
```
```D4C1B.  Reduce to compact form
```
```D4C1B1.  Tridiagonal
```
```
```
```          BANDR-S   Reduce a real symmetric band matrix to symmetric
```
```                    tridiagonal matrix and, optionally, accumulate
```
```                    orthogonal similarity transformations.
```
```
```
```          HTRID3-S  Reduce a complex Hermitian (packed) matrix to a real
```
```                    symmetric tridiagonal matrix by unitary similarity
```
```                    transformations.
```
```
```
```          HTRIDI-S  Reduce a complex Hermitian matrix to a real symmetric
```
```                    tridiagonal matrix using unitary similarity
```
```                    transformations.
```
```
```
```          TRED1-S   Reduce a real symmetric matrix to symmetric tridiagonal
```
```                    matrix using orthogonal similarity transformations.
```
```
```
```          TRED2-S   Reduce a real symmetric matrix to a symmetric tridiagonal
```
```                    matrix using and accumulating orthogonal transformations.
```
```
```
```          TRED3-S   Reduce a real symmetric matrix stored in packed form to
```
```                    symmetric tridiagonal matrix using orthogonal
```
```                    transformations.
```
```
```
```D4C1B2.  Hessenberg
```
```
```
```          ELMHES-S  Reduce a real general matrix to upper Hessenberg form
```
```          COMHES-C  using stabilized elementary similarity transformations.
```
```
```
```          ORTHES-S  Reduce a real general matrix to upper Hessenberg form
```
```          CORTH-C   using orthogonal similarity transformations.
```
```
```
```D4C1B3.  Other
```
```
```
```          QZHES-S   The first step of the QZ algorithm for solving generalized
```
```                    matrix eigenproblems.  Accepts a pair of real general
```
```                    matrices and reduces one of them to upper Hessenberg
```
```                    and the other to upper triangular form using orthogonal
```
```                    transformations. Usually followed by QZIT, QZVAL, QZVEC.
```
```
```
```          QZIT-S    The second step of the QZ algorithm for generalized
```
```                    eigenproblems.  Accepts an upper Hessenberg and an upper
```
```                    triangular matrix and reduces the former to
```
```                    quasi-triangular form while preserving the form of the
```
```                    latter.  Usually preceded by QZHES and followed by QZVAL
```
```                    and QZVEC.
```
```
```
```D4C1C.  Standardize problem
```
```
```
```          FIGI-S    Transforms certain real non-symmetric tridiagonal matrix
```
```                    to symmetric tridiagonal matrix.
```
```
```
```          FIGI2-S   Transforms certain real non-symmetric tridiagonal matrix
```
```                    to symmetric tridiagonal matrix.
```
```
```
```          REDUC-S   Reduce a generalized symmetric eigenproblem to a standard
```
```                    symmetric eigenproblem using Cholesky factorization.
```
```
```
```          REDUC2-S  Reduce a certain generalized symmetric eigenproblem to a
```
```                    standard symmetric eigenproblem using Cholesky
```
```                    factorization.
```
```
```
```D4C2.  Compute eigenvalues of matrix in compact form
```
```D4C2A.  Tridiagonal
```
```
```
```          BISECT-S  Compute the eigenvalues of a symmetric tridiagonal matrix
```
```                    in a given interval using Sturm sequencing.
```
```
```
```          IMTQL1-S  Compute the eigenvalues of a symmetric tridiagonal matrix
```
```                    using the implicit QL method.
```
```
```
```          IMTQL2-S  Compute the eigenvalues and eigenvectors of a symmetric
```
```                    tridiagonal matrix using the implicit QL method.
```
```
```
```          IMTQLV-S  Compute the eigenvalues of a symmetric tridiagonal matrix
```
```                    using the implicit QL method.  Eigenvectors may be computed
```
```                    later.
```
```
```
```          RATQR-S   Compute the largest or smallest eigenvalues of a symmetric
```
```                    tridiagonal matrix using the rational QR method with Newton
```
```                    correction.
```
```
```
```          TQL1-S    Compute the eigenvalues of symmetric tridiagonal matrix by
```
```                    the QL method.
```
```
```
```          TQL2-S    Compute the eigenvalues and eigenvectors of symmetric
```
```                    tridiagonal matrix.
```
```
```
```          TQLRAT-S  Compute the eigenvalues of symmetric tridiagonal matrix
```
```                    using a rational variant of the QL method.
```
```
```
```          TRIDIB-S  Compute the eigenvalues of a symmetric tridiagonal matrix
```
```                    in a given interval using Sturm sequencing.
```
```
```
```          TSTURM-S  Find those eigenvalues of a symmetric tridiagonal matrix
```
```                    in a given interval and their associated eigenvectors by
```
```                    Sturm sequencing.
```
```
```
```D4C2B.  Hessenberg
```
```
```
```          COMLR-C   Compute the eigenvalues of a complex upper Hessenberg
```
```                    matrix using the modified LR method.
```
```
```
```          COMLR2-C  Compute the eigenvalues and eigenvectors of a complex upper
```
```                    Hessenberg matrix using the modified LR method.
```
```
```
```          HQR-S     Compute the eigenvalues of a real upper Hessenberg matrix
```
```          COMQR-C   using the QR method.
```
```
```
```          HQR2-S    Compute the eigenvalues and eigenvectors of a real upper
```
```          COMQR2-C  Hessenberg matrix using QR method.
```
```
```
```          INVIT-S   Compute the eigenvectors of a real upper Hessenberg
```
```          CINVIT-C  matrix associated with specified eigenvalues by inverse
```
```                    iteration.
```
```
```
```D4C2C.  Other
```
```
```
```          QZVAL-S   The third step of the QZ algorithm for generalized
```
```                    eigenproblems.  Accepts a pair of real matrices, one in
```
```                    quasi-triangular form and the other in upper triangular
```
```                    form and computes the eigenvalues of the associated
```
```                    eigenproblem.  Usually preceded by QZHES, QZIT, and
```
```                    followed by QZVEC.
```
```
```
```D4C3.  Form eigenvectors from eigenvalues
```
```
```
```          BANDV-S   Form the eigenvectors of a real symmetric band matrix
```
```                    associated with a set of ordered approximate eigenvalues
```
```                    by inverse iteration.
```
```
```
```          QZVEC-S   The optional fourth step of the QZ algorithm for
```
```                    generalized eigenproblems.  Accepts a matrix in
```
```                    quasi-triangular form and another in upper triangular
```
```                    and computes the eigenvectors of the triangular problem
```
```                    and transforms them back to the original coordinates
```
```                    Usually preceded by QZHES, QZIT, and QZVAL.
```
```
```
```          TINVIT-S  Compute the eigenvectors of symmetric tridiagonal matrix
```
```                    corresponding to specified eigenvalues, using inverse
```
```                    iteration.
```
```
```
```D4C4.  Back transform eigenvectors
```
```
```
```          BAKVEC-S  Form the eigenvectors of a certain real non-symmetric
```
```                    tridiagonal matrix from a symmetric tridiagonal matrix
```
```                    output from FIGI.
```
```
```
```          BALBAK-S  Form the eigenvectors of a real general matrix from the
```
```          CBABK2-C  eigenvectors of matrix output from BALANC.
```
```
```
```          ELMBAK-S  Form the eigenvectors of a real general matrix from the
```
```          COMBAK-C  eigenvectors of the upper Hessenberg matrix output from
```
```                    ELMHES.
```
```
```
```          ELTRAN-S  Accumulates the stabilized elementary similarity
```
```                    transformations used in the reduction of a real general
```
```                    matrix to upper Hessenberg form by ELMHES.
```
```
```
```          HTRIB3-S  Compute the eigenvectors of a complex Hermitian matrix from
```
```                    the eigenvectors of a real symmetric tridiagonal matrix
```
```                    output from HTRID3.
```
```
```
```          HTRIBK-S  Form the eigenvectors of a complex Hermitian matrix from
```
```                    the eigenvectors of a real symmetric tridiagonal matrix
```
```                    output from HTRIDI.
```
```
```
```          ORTBAK-S  Form the eigenvectors of a general real matrix from the
```
```          CORTB-C   eigenvectors of the upper Hessenberg matrix output from
```
```                    ORTHES.
```
```
```
```          ORTRAN-S  Accumulate orthogonal similarity transformations in the
```
```                    reduction of real general matrix by ORTHES.
```
```
```
```          REBAK-S   Form the eigenvectors of a generalized symmetric
```
```                    eigensystem from the eigenvectors of derived matrix output
```
```                    from REDUC or REDUC2.
```
```
```
```          REBAKB-S  Form the eigenvectors of a generalized symmetric
```
```                    eigensystem from the eigenvectors of derived matrix output
```
```                    from REDUC2.
```
```
```
```          TRBAK1-S  Form the eigenvectors of real symmetric matrix from
```
```                    the eigenvectors of a symmetric tridiagonal matrix formed
```
```                    by TRED1.
```
```
```
```          TRBAK3-S  Form the eigenvectors of a real symmetric matrix from the
```
```                    eigenvectors of a symmetric tridiagonal matrix formed
```
```                    by TRED3.
```
```
```
```D5.  QR decomposition, Gram-Schmidt orthogonalization
```
```
```
```          LLSIA-S   Solve a linear least squares problems by performing a QR
```
```          DLLSIA-D  factorization of the matrix using Householder
```
```                    transformations.  Emphasis is put on detecting possible
```
```                    rank deficiency.
```
```
```
```          SGLSS-S   Solve a linear least squares problems by performing a QR
```
```          DGLSS-D   factorization of the matrix using Householder
```
```                    transformations.  Emphasis is put on detecting possible
```
```                    rank deficiency.
```
```
```
```          SQRDC-S   Use Householder transformations to compute the QR
```
```          DQRDC-D   factorization of an N by P matrix.  Column pivoting is a
```
```          CQRDC-C   users option.
```
```
```
```D6.  Singular value decomposition
```
```
```
```          SSVDC-S   Perform the singular value decomposition of a rectangular
```
```          DSVDC-D   matrix.
```
```          CSVDC-C
```
```
```
```D7.  Update matrix decompositions
```
```D7B.  Cholesky
```
```
```
```          SCHDD-S   Downdate an augmented Cholesky decomposition or the
```
```          DCHDD-D   triangular factor of an augmented QR decomposition.
```
```          CCHDD-C
```
```
```
```          SCHEX-S   Update the Cholesky factorization  A=TRANS(R)*R  of A
```
```          DCHEX-D   positive definite matrix A of order P under diagonal
```
```          CCHEX-C   permutations of the form TRANS(E)*A*E, where E is a
```
```                    permutation matrix.
```
```
```
```          SCHUD-S   Update an augmented Cholesky decomposition of the
```
```          DCHUD-D   triangular part of an augmented QR decomposition.
```
```          CCHUD-C
```
```
```
```D9.  Overdetermined or underdetermined systems of equations, singular systems,
```
```     pseudo-inverses (search also classes D5, D6, K1a, L8a)
```
```
```
```          BNDACC-S  Compute the LU factorization of a banded matrices using
```
```          DBNDAC-D  sequential accumulation of rows of the data matrix.
```
```                    Exactly one right-hand side vector is permitted.
```
```
```
```          BNDSOL-S  Solve the least squares problem for a banded matrix using
```
```          DBNDSL-D  sequential accumulation of rows of the data matrix.
```
```                    Exactly one right-hand side vector is permitted.
```
```
```
```          HFTI-S    Solve a linear least squares problems by performing a QR
```
```          DHFTI-D   factorization of the matrix using Householder
```
```                    transformations.
```
```
```
```          LLSIA-S   Solve a linear least squares problems by performing a QR
```
```          DLLSIA-D  factorization of the matrix using Householder
```
```                    transformations.  Emphasis is put on detecting possible
```
```                    rank deficiency.
```
```
```
```          LSEI-S    Solve a linearly constrained least squares problem with
```
```          DLSEI-D   equality and inequality constraints, and optionally compute
```
```                    a covariance matrix.
```
```
```
```          MINFIT-S  Compute the singular value decomposition of a rectangular
```
```                    matrix and solve the related linear least squares problem.
```
```
```
```          SGLSS-S   Solve a linear least squares problems by performing a QR
```
```          DGLSS-D   factorization of the matrix using Householder
```
```                    transformations.  Emphasis is put on detecting possible
```
```                    rank deficiency.
```
```
```
```          SQRSL-S   Apply the output of SQRDC to compute coordinate transfor-
```
```          DQRSL-D   mations, projections, and least squares solutions.
```
```          CQRSL-C
```
```
```
```          ULSIA-S   Solve an underdetermined linear system of equations by
```
```          DULSIA-D  performing an LQ factorization of the matrix using
```
```                    Householder transformations.  Emphasis is put on detecting
```
```                    possible rank deficiency.
```
```
```
```E.  Interpolation
```
```
```
```          BSPDOC-A  Documentation for BSPLINE, a package of subprograms for
```
```                    working with piecewise polynomial functions
```
```                    in B-representation.
```
```
```
```E1.  Univariate data (curve fitting)
```
```E1A.  Polynomial splines (piecewise polynomials)
```
```
```
```          BINT4-S   Compute the B-representation of a cubic spline
```
```          DBINT4-D  which interpolates given data.
```
```
```
```          BINTK-S   Compute the B-representation of a spline which interpolates
```
```          DBINTK-D  given data.
```
```
```
```          BSPDOC-A  Documentation for BSPLINE, a package of subprograms for
```
```                    working with piecewise polynomial functions
```
```                    in B-representation.
```
```
```
```          PCHDOC-A  Documentation for PCHIP, a Fortran package for piecewise
```
```                    cubic Hermite interpolation of data.
```
```
```
```          PCHIC-S   Set derivatives needed to determine a piecewise monotone
```
```          DPCHIC-D  piecewise cubic Hermite interpolant to given data.
```
```                    User control is available over boundary conditions and/or
```
```                    treatment of points where monotonicity switches direction.
```
```
```
```          PCHIM-S   Set derivatives needed to determine a monotone piecewise
```
```          DPCHIM-D  cubic Hermite interpolant to given data.  Boundary values
```
```                    are provided which are compatible with monotonicity.  The
```
```                    interpolant will have an extremum at each point where mono-
```
```                    tonicity switches direction.  (See PCHIC if user control is
```
```                    desired over boundary or switch conditions.)
```
```
```
```          PCHSP-S   Set derivatives needed to determine the Hermite represen-
```
```          DPCHSP-D  tation of the cubic spline interpolant to given data, with
```
```                    specified boundary conditions.
```
```
```
```E1B.  Polynomials
```
```
```
```          POLCOF-S  Compute the coefficients of the polynomial fit (including
```
```          DPOLCF-D  Hermite polynomial fits) produced by a previous call to
```
```                    POLINT.
```
```
```
```          POLINT-S  Produce the polynomial which interpolates a set of discrete
```
```          DPLINT-D  data points.
```
```
```
```E3.  Service routines (e.g., grid generation, evaluation of fitted functions)
```
```     (search also class N5)
```
```
```
```          BFQAD-S   Compute the integral of a product of a function and a
```
```          DBFQAD-D  derivative of a B-spline.
```
```
```
```          BSPDR-S   Use the B-representation to construct a divided difference
```
```          DBSPDR-D  table preparatory to a (right) derivative calculation.
```
```
```
```          BSPEV-S   Calculate the value of the spline and its derivatives from
```
```          DBSPEV-D  the B-representation.
```
```
```
```          BSPPP-S   Convert the B-representation of a B-spline to the piecewise
```
```          DBSPPP-D  polynomial (PP) form.
```
```
```
```          BSPVD-S   Calculate the value and all derivatives of order less than
```
```          DBSPVD-D  NDERIV of all basis functions which do not vanish at X.
```
```
```
```          BSPVN-S   Calculate the value of all (possibly) nonzero basis
```
```          DBSPVN-D  functions at X.
```
```
```
```          BSQAD-S   Compute the integral of a K-th order B-spline using the
```
```          DBSQAD-D  B-representation.
```
```
```
```          BVALU-S   Evaluate the B-representation of a B-spline at X for the
```
```          DBVALU-D  function value or any of its derivatives.
```
```
```
```          CHFDV-S   Evaluate a cubic polynomial given in Hermite form and its
```
```          DCHFDV-D  first derivative at an array of points.  While designed for
```
```                    use by PCHFD, it may be useful directly as an evaluator
```
```                    for a piecewise cubic Hermite function in applications,
```
```                    such as graphing, where the interval is known in advance.
```
```                    If only function values are required, use CHFEV instead.
```
```
```
```          CHFEV-S   Evaluate a cubic polynomial given in Hermite form at an
```
```          DCHFEV-D  array of points.  While designed for use by PCHFE, it may
```
```                    be useful directly as an evaluator for a piecewise cubic
```
```                    Hermite function in applications, such as graphing, where
```
```                    the interval is known in advance.
```
```
```
```          INTRV-S   Compute the largest integer ILEFT in 1 .LE. ILEFT .LE. LXT
```
```          DINTRV-D  such that XT(ILEFT) .LE. X where XT(*) is a subdivision
```
```                    of the X interval.
```
```
```
```          PCHBS-S   Piecewise Cubic Hermite to B-Spline converter.
```
```          DPCHBS-D
```
```
```
```          PCHCM-S   Check a cubic Hermite function for monotonicity.
```
```          DPCHCM-D
```
```
```
```          PCHFD-S   Evaluate a piecewise cubic Hermite function and its first
```
```          DPCHFD-D  derivative at an array of points.  May be used by itself
```
```                    for Hermite interpolation, or as an evaluator for PCHIM
```
```                    or PCHIC.  If only function values are required, use
```
```                    PCHFE instead.
```
```
```
```          PCHFE-S   Evaluate a piecewise cubic Hermite function at an array of
```
```          DPCHFE-D  points.  May be used by itself for Hermite interpolation,
```
```                    or as an evaluator for PCHIM or PCHIC.
```
```
```
```          PCHIA-S   Evaluate the definite integral of a piecewise cubic
```
```          DPCHIA-D  Hermite function over an arbitrary interval.
```
```
```
```          PCHID-S   Evaluate the definite integral of a piecewise cubic
```
```          DPCHID-D  Hermite function over an interval whose endpoints are data
```
```                    points.
```
```
```
```          PFQAD-S   Compute the integral on (X1,X2) of a product of a function
```
```          DPFQAD-D  F and the ID-th derivative of a B-spline,
```
```                    (PP-representation).
```
```
```
```          POLYVL-S  Calculate the value of a polynomial and its first NDER
```
```          DPOLVL-D  derivatives where the polynomial was produced by a previous
```
```                    call to POLINT.
```
```
```
```          PPQAD-S   Compute the integral on (X1,X2) of a K-th order B-spline
```
```          DPPQAD-D  using the piecewise polynomial (PP) representation.
```
```
```
```          PPVAL-S   Calculate the value of the IDERIV-th derivative of the
```
```          DPPVAL-D  B-spline from the PP-representation.
```
```
```
```F.  Solution of nonlinear equations
```
```F1.  Single equation
```
```F1A.  Smooth
```
```F1A1.  Polynomial
```
```F1A1A.  Real coefficients
```
```
```
```          RPQR79-S  Find the zeros of a polynomial with real coefficients.
```
```          CPQR79-C
```
```
```
```          RPZERO-S  Find the zeros of a polynomial with real coefficients.
```
```          CPZERO-C
```
```
```
```F1A1B.  Complex coefficients
```
```
```
```          CPQR79-C  Find the zeros of a polynomial with complex coefficients.
```
```          RPQR79-S
```
```
```
```          CPZERO-C  Find the zeros of a polynomial with complex coefficients.
```
```          RPZERO-S
```
```
```
```F1B.  General (no smoothness assumed)
```
```
```
```          FZERO-S   Search for a zero of a function F(X) in a given interval
```
```          DFZERO-D  (B,C).  It is designed primarily for problems where F(B)
```
```                    and F(C) have opposite signs.
```
```
```
```F2.  System of equations
```
```F2A.  Smooth
```
```
```
```          SNSQ-S    Find a zero of a system of a N nonlinear functions in N
```
```          DNSQ-D    variables by a modification of the Powell hybrid method.
```
```
```
```          SNSQE-S   An easy-to-use code to find a zero of a system of N
```
```          DNSQE-D   nonlinear functions in N variables by a modification of
```
```                    the Powell hybrid method.
```
```
```
```          SOS-S     Solve a square system of nonlinear equations.
```
```          DSOS-D
```
```
```
```F3.  Service routines (e.g., check user-supplied derivatives)
```
```
```
```          CHKDER-S  Check the gradients of M nonlinear functions in N
```
```          DCKDER-D  variables, evaluated at a point X, for consistency
```
```                    with the functions themselves.
```
```
```
```G.  Optimization (search also classes K, L8)
```
```G2.  Constrained
```
```G2A.  Linear programming
```
```G2A2.  Sparse matrix of constraints
```
```
```
```          SPLP-S    Solve linear programming problems involving at
```
```          DSPLP-D   most a few thousand constraints and variables.
```
```                    Takes advantage of sparsity in the constraint matrix.
```
```
```
```G2E.  Quadratic programming
```
```
```
```          SBOCLS-S  Solve the bounded and constrained least squares
```
```          DBOCLS-D  problem consisting of solving the equation
```
```                              E*X = F  (in the least squares sense)
```
```                     subject to the linear constraints
```
```                                    C*X = Y.
```
```
```
```          SBOLS-S   Solve the problem
```
```          DBOLS-D        E*X = F (in the least  squares  sense)
```
```                    with bounds on selected X values.
```
```
```
```G2H.  General nonlinear programming
```
```G2H1.  Simple bounds
```
```
```
```          SBOCLS-S  Solve the bounded and constrained least squares
```
```          DBOCLS-D  problem consisting of solving the equation
```
```                              E*X = F  (in the least squares sense)
```
```                     subject to the linear constraints
```
```                                    C*X = Y.
```
```
```
```          SBOLS-S   Solve the problem
```
```          DBOLS-D        E*X = F (in the least  squares  sense)
```
```                    with bounds on selected X values.
```
```
```
```G2H2.  Linear equality or inequality constraints
```
```
```
```          SBOCLS-S  Solve the bounded and constrained least squares
```
```          DBOCLS-D  problem consisting of solving the equation
```
```                              E*X = F  (in the least squares sense)
```
```                     subject to the linear constraints
```
```                                    C*X = Y.
```
```
```
```          SBOLS-S   Solve the problem
```
```          DBOLS-D        E*X = F (in the least  squares  sense)
```
```                    with bounds on selected X values.
```
```
```
```G4.  Service routines
```
```G4C.  Check user-supplied derivatives
```
```
```
```          CHKDER-S  Check the gradients of M nonlinear functions in N
```
```          DCKDER-D  variables, evaluated at a point X, for consistency
```
```                    with the functions themselves.
```
```
```
```H.  Differentiation, integration
```
```H1.  Numerical differentiation
```
```
```
```          CHFDV-S   Evaluate a cubic polynomial given in Hermite form and its
```
```          DCHFDV-D  first derivative at an array of points.  While designed for
```
```                    use by PCHFD, it may be useful directly as an evaluator
```
```                    for a piecewise cubic Hermite function in applications,
```
```                    such as graphing, where the interval is known in advance.
```
```                    If only function values are required, use CHFEV instead.
```
```
```
```          PCHFD-S   Evaluate a piecewise cubic Hermite function and its first
```
```          DPCHFD-D  derivative at an array of points.  May be used by itself
```
```                    for Hermite interpolation, or as an evaluator for PCHIM
```
```                    or PCHIC.  If only function values are required, use
```
```                    PCHFE instead.
```
```
```
```H2.  Quadrature (numerical evaluation of definite integrals)
```
```
```
```          QPDOC-A   Documentation for QUADPACK, a package of subprograms for
```
```                    automatic evaluation of one-dimensional definite integrals.
```
```
```
```H2A.  One-dimensional integrals
```
```H2A1.  Finite interval (general integrand)
```
```H2A1A.  Integrand available via user-defined procedure
```
```H2A1A1.  Automatic (user need only specify required accuracy)
```
```
```
```          GAUS8-S   Integrate a real function of one variable over a finite
```
```          DGAUS8-D  interval using an adaptive 8-point Legendre-Gauss
```
```                    algorithm.  Intended primarily for high accuracy
```
```                    integration or integration of smooth functions.
```
```
```
```          QAG-S     The routine calculates an approximation result to a given
```
```          DQAG-D    definite integral I = integral of F over (A,B),
```
```                    hopefully satisfying following claim for accuracy
```
```                    ABS(I-RESULT)LE.MAX(EPSABS,EPSREL*ABS(I)).
```
```
```
```          QAGE-S    The routine calculates an approximation result to a given
```
```          DQAGE-D   definite integral   I = Integral of F over (A,B),
```
```                    hopefully satisfying following claim for accuracy
```
```                    ABS(I-RESLT).LE.MAX(EPSABS,EPSREL*ABS(I)).
```
```
```
```          QAGS-S    The routine calculates an approximation result to a given
```
```          DQAGS-D   Definite integral  I = Integral of F over (A,B),
```
```                    Hopefully satisfying following claim for accuracy
```
```                    ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).
```
```
```
```          QAGSE-S   The routine calculates an approximation result to a given
```
```          DQAGSE-D  definite integral I = Integral of F over (A,B),
```
```                    hopefully satisfying following claim for accuracy
```
```                    ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).
```
```
```
```          QNC79-S   Integrate a function using a 7-point adaptive Newton-Cotes
```
```          DQNC79-D  quadrature rule.
```
```
```
```          QNG-S     The routine calculates an approximation result to a
```
```          DQNG-D    given definite integral I = integral of F over (A,B),
```
```                    hopefully satisfying following claim for accuracy
```
```                    ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).
```
```
```
```H2A1A2.  Nonautomatic
```
```
```
```          QK15-S    To compute I = Integral of F over (A,B), with error
```
```          DQK15-D                  estimate
```
```                               J = integral of ABS(F) over (A,B)
```
```
```
```          QK21-S    To compute I = Integral of F over (A,B), with error
```
```          DQK21-D                  estimate
```
```                               J = Integral of ABS(F) over (A,B)
```
```
```
```          QK31-S    To compute I = Integral of F over (A,B) with error
```
```          DQK31-D                  estimate
```
```                               J = Integral of ABS(F) over (A,B)
```
```
```
```          QK41-S    To compute I = Integral of F over (A,B), with error
```
```          DQK41-D                  estimate
```
```                               J = Integral of ABS(F) over (A,B)
```
```
```
```          QK51-S    To compute I = Integral of F over (A,B) with error
```
```          DQK51-D                  estimate
```
```                               J = Integral of ABS(F) over (A,B)
```
```
```
```          QK61-S    To compute I = Integral of F over (A,B) with error
```
```          DQK61-D                  estimate
```
```                               J = Integral of ABS(F) over (A,B)
```
```
```
```H2A1B.  Integrand available only on grid
```
```H2A1B2.  Nonautomatic
```
```
```
```          AVINT-S   Integrate a function tabulated at arbitrarily spaced
```
```          DAVINT-D  abscissas using overlapping parabolas.
```
```
```
```          PCHIA-S   Evaluate the definite integral of a piecewise cubic
```
```          DPCHIA-D  Hermite function over an arbitrary interval.
```
```
```
```          PCHID-S   Evaluate the definite integral of a piecewise cubic
```
```          DPCHID-D  Hermite function over an interval whose endpoints are data
```
```                    points.
```
```
```
```H2A2.  Finite interval (specific or special type integrand including weight
```
```       functions, oscillating and singular integrands, principal value
```
```       integrals, splines, etc.)
```
```H2A2A.  Integrand available via user-defined procedure
```
```H2A2A1.  Automatic (user need only specify required accuracy)
```
```
```
```          BFQAD-S   Compute the integral of a product of a function and a
```
```          DBFQAD-D  derivative of a B-spline.
```
```
```
```          BSQAD-S   Compute the integral of a K-th order B-spline using the
```
```          DBSQAD-D  B-representation.
```
```
```
```          PFQAD-S   Compute the integral on (X1,X2) of a product of a function
```
```          DPFQAD-D  F and the ID-th derivative of a B-spline,
```
```                    (PP-representation).
```
```
```
```          PPQAD-S   Compute the integral on (X1,X2) of a K-th order B-spline
```
```          DPPQAD-D  using the piecewise polynomial (PP) representation.
```
```
```
```          QAGP-S    The routine calculates an approximation result to a given
```
```          DQAGP-D   definite integral I = Integral of F over (A,B),
```
```                    hopefully satisfying following claim for accuracy
```
```                    break points of the integration interval, where local
```
```                    difficulties of the integrand may occur(e.g. SINGULARITIES,
```
```                    DISCONTINUITIES), are provided by the user.
```
```
```
```          QAGPE-S   Approximate a given definite integral I = Integral of F
```
```          DQAGPE-D  over (A,B), hopefully satisfying the accuracy claim:
```
```                          ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).
```
```                    Break points of the integration interval, where local
```
```                    difficulties of the integrand may occur (e.g. singularities
```
```                    or discontinuities) are provided by the user.
```
```
```
```          QAWC-S    The routine calculates an approximation result to a
```
```          DQAWC-D   Cauchy principal value I = INTEGRAL of F*W over (A,B)
```
```                    (W(X) = 1/((X-C), C.NE.A, C.NE.B), hopefully satisfying
```
```                    following claim for accuracy
```
```                    ABS(I-RESULT).LE.MAX(EPSABE,EPSREL*ABS(I)).
```
```
```
```          QAWCE-S   The routine calculates an approximation result to a
```
```          DQAWCE-D  CAUCHY PRINCIPAL VALUE I = Integral of F*W over (A,B)
```
```                    (W(X) = 1/(X-C), (C.NE.A, C.NE.B), hopefully satisfying
```
```                    following claim for accuracy
```
```                    ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))
```
```
```
```          QAWO-S    Calculate an approximation to a given definite integral
```
```          DQAWO-D    I = Integral of F(X)*W(X) over (A,B), where
```
```                           W(X) = COS(OMEGA*X)
```
```                        or W(X) = SIN(OMEGA*X),
```
```                    hopefully satisfying the following claim for accuracy
```
```                        ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).
```
```
```
```          QAWOE-S   Calculate an approximation to a given definite integral
```
```          DQAWOE-D     I = Integral of F(X)*W(X) over (A,B), where
```
```                          W(X) = COS(OMEGA*X)
```
```                       or W(X) = SIN(OMEGA*X),
```
```                    hopefully satisfying the following claim for accuracy
```
```                       ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).
```
```
```
```          QAWS-S    The routine calculates an approximation result to a given
```
```          DQAWS-D   definite integral I = Integral of F*W over (A,B),
```
```                    (where W shows a singular behaviour at the end points
```
```                    see parameter INTEGR).
```
```                    Hopefully satisfying following claim for accuracy
```
```                    ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).
```
```
```
```          QAWSE-S   The routine calculates an approximation result to a given
```
```          DQAWSE-D  definite integral I = Integral of F*W over (A,B),
```
```                    (where W shows a singular behaviour at the end points,
```
```                    see parameter INTEGR).
```
```                    Hopefully satisfying following claim for accuracy
```
```                    ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).
```
```
```
```          QMOMO-S   This routine computes modified Chebyshev moments.  The K-th
```
```          DQMOMO-D  modified Chebyshev moment is defined as the integral over
```
```                    (-1,1) of W(X)*T(K,X), where T(K,X) is the Chebyshev
```
```                    polynomial of degree K.
```
```
```
```H2A2A2.  Nonautomatic
```
```
```
```          QC25C-S   To compute I = Integral of F*W over (A,B) with
```
```          DQC25C-D  error estimate, where W(X) = 1/(X-C)
```
```
```
```          QC25F-S   To compute the integral I=Integral of F(X) over (A,B)
```
```          DQC25F-D  Where W(X) = COS(OMEGA*X) Or (WX)=SIN(OMEGA*X)
```
```                    and to compute J=Integral of ABS(F) over (A,B). For small
```
```                    value of OMEGA or small intervals (A,B) 15-point GAUSS-
```
```                    KRONROD Rule used. Otherwise generalized CLENSHAW-CURTIS us
```
```
```
```          QC25S-S   To compute I = Integral of F*W over (BL,BR), with error
```
```          DQC25S-D  estimate, where the weight function W has a singular
```
```                    behaviour of ALGEBRAICO-LOGARITHMIC type at the points
```
```                    A and/or B. (BL,BR) is a part of (A,B).
```
```
```
```          QK15W-S   To compute I = Integral of F*W over (A,B), with error
```
```          DQK15W-D                 estimate
```
```                               J = Integral of ABS(F*W) over (A,B)
```
```
```
```H2A3.  Semi-infinite interval (including e**(-x) weight function)
```
```H2A3A.  Integrand available via user-defined procedure
```
```H2A3A1.  Automatic (user need only specify required accuracy)
```
```
```
```          QAGI-S    The routine calculates an approximation result to a given
```
```          DQAGI-D   INTEGRAL   I = Integral of F over (BOUND,+INFINITY)
```
```                            OR I = Integral of F over (-INFINITY,BOUND)
```
```                            OR I = Integral of F over (-INFINITY,+INFINITY)
```
```                    Hopefully satisfying following claim for accuracy
```
```                    ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).
```
```
```
```          QAGIE-S   The routine calculates an approximation result to a given
```
```          DQAGIE-D  integral   I = Integral of F over (BOUND,+INFINITY)
```
```                            or I = Integral of F over (-INFINITY,BOUND)
```
```                            or I = Integral of F over (-INFINITY,+INFINITY),
```
```                            hopefully satisfying following claim for accuracy
```
```                            ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))
```
```
```
```          QAWF-S    The routine calculates an approximation result to a given
```
```          DQAWF-D   Fourier integral
```
```                    I = Integral of F(X)*W(X) over (A,INFINITY)
```
```                    where W(X) = COS(OMEGA*X) or W(X) = SIN(OMEGA*X).
```
```                    Hopefully satisfying following claim for accuracy
```
```                    ABS(I-RESULT).LE.EPSABS.
```
```
```
```          QAWFE-S   The routine calculates an approximation result to a
```
```          DQAWFE-D  given Fourier integral
```
```                    I = Integral of F(X)*W(X) over (A,INFINITY)
```
```                     where W(X) = COS(OMEGA*X) or W(X) = SIN(OMEGA*X),
```
```                    hopefully satisfying following claim for accuracy
```
```                    ABS(I-RESULT).LE.EPSABS.
```
```
```
```H2A3A2.  Nonautomatic
```
```
```
```          QK15I-S   The original (infinite integration range is mapped
```
```          DQK15I-D  onto the interval (0,1) and (A,B) is a part of (0,1).
```
```                    it is the purpose to compute
```
```                    I = Integral of transformed integrand over (A,B),
```
```                    J = Integral of ABS(Transformed Integrand) over (A,B).
```
```
```
```H2A4.  Infinite interval (including e**(-x**2)) weight function)
```
```H2A4A.  Integrand available via user-defined procedure
```
```H2A4A1.  Automatic (user need only specify required accuracy)
```
```
```
```          QAGI-S    The routine calculates an approximation result to a given
```
```          DQAGI-D   INTEGRAL   I = Integral of F over (BOUND,+INFINITY)
```
```                            OR I = Integral of F over (-INFINITY,BOUND)
```
```                            OR I = Integral of F over (-INFINITY,+INFINITY)
```
```                    Hopefully satisfying following claim for accuracy
```
```                    ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I)).
```
```
```
```          QAGIE-S   The routine calculates an approximation result to a given
```
```          DQAGIE-D  integral   I = Integral of F over (BOUND,+INFINITY)
```
```                            or I = Integral of F over (-INFINITY,BOUND)
```
```                            or I = Integral of F over (-INFINITY,+INFINITY),
```
```                            hopefully satisfying following claim for accuracy
```
```                            ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))
```
```
```
```H2A4A2.  Nonautomatic
```
```
```
```          QK15I-S   The original (infinite integration range is mapped
```
```          DQK15I-D  onto the interval (0,1) and (A,B) is a part of (0,1).
```
```                    it is the purpose to compute
```
```                    I = Integral of transformed integrand over (A,B),
```
```                    J = Integral of ABS(Transformed Integrand) over (A,B).
```
```
```
```
```
```          DERKF-S   Solve an initial value problem in ordinary differential
```
```          DDERKF-D  equations using a Runge-Kutta-Fehlberg scheme.
```
```
```
```
```
```          DEABM-S   Solve an initial value problem in ordinary differential
```
```          DDEABM-D  equations using an Adams-Bashforth method.
```
```
```
```          SDRIV1-S  The function of SDRIV1 is to solve N (200 or fewer)
```
```          DDRIV1-D  ordinary differential equations of the form
```
```          CDRIV1-C  dY(I)/dT = F(Y(I),T), given the initial conditions
```
```                    Y(I) = YI.  SDRIV1 uses single precision arithmetic.
```
```
```
```          SDRIV2-S  The function of SDRIV2 is to solve N ordinary differential
```
```          DDRIV2-D  equations of the form dY(I)/dT = F(Y(I),T), given the
```
```          CDRIV2-C  initial conditions Y(I) = YI.  The program has options to
```
```                    allow the solution of both stiff and non-stiff differential
```
```                    equations.  SDRIV2 uses single precision arithmetic.
```
```
```
```          SDRIV3-S  The function of SDRIV3 is to solve N ordinary differential
```
```          DDRIV3-D  equations of the form dY(I)/dT = F(Y(I),T), given the
```
```          CDRIV3-C  initial conditions Y(I) = YI.  The program has options to
```
```                    allow the solution of both stiff and non-stiff differential
```
```                    equations.  Other important options are available.  SDRIV3
```
```                    uses single precision arithmetic.
```
```
```
```          SINTRP-S  Approximate the solution at XOUT by evaluating the
```
```          DINTP-D   polynomial computed in STEPS at XOUT.  Must be used in
```
```                    conjunction with STEPS.
```
```
```
```          STEPS-S   Integrate a system of first order ordinary differential
```
```          DSTEPS-D  equations one step.
```
```
```
```
```
```          DEBDF-S   Solve an initial value problem in ordinary differential
```
```          DDEBDF-D  equations using backward differentiation formulas.  It is
```
```                    intended primarily for stiff problems.
```
```
```
```          SDASSL-S  This code solves a system of differential/algebraic
```
```          DDASSL-D  equations of the form G(T,Y,YPRIME) = 0.
```
```
```
```          SDRIV1-S  The function of SDRIV1 is to solve N (200 or fewer)
```
```          DDRIV1-D  ordinary differential equations of the form
```
```          CDRIV1-C  dY(I)/dT = F(Y(I),T), given the initial conditions
```
```                    Y(I) = YI.  SDRIV1 uses single precision arithmetic.
```
```
```
```          SDRIV2-S  The function of SDRIV2 is to solve N ordinary differential
```
```          DDRIV2-D  equations of the form dY(I)/dT = F(Y(I),T), given the
```
```          CDRIV2-C  initial conditions Y(I) = YI.  The program has options to
```
```                    allow the solution of both stiff and non-stiff differential
```
```                    equations.  SDRIV2 uses single precision arithmetic.
```
```
```
```          SDRIV3-S  The function of SDRIV3 is to solve N ordinary differential
```
```          DDRIV3-D  equations of the form dY(I)/dT = F(Y(I),T), given the
```
```          CDRIV3-C  initial conditions Y(I) = YI.  The program has options to
```
```                    allow the solution of both stiff and non-stiff differential
```
```                    equations.  Other important options are available.  SDRIV3
```
```                    uses single precision arithmetic.
```
```
```
```
```
```          BVSUP-S   Solve a linear two-point boundary value problem using
```
```          DBVSUP-D  superposition coupled with an orthonormalization procedure
```
```                    and a variable-step integration scheme.
```
```
```
```          system)
```
```
```
```          HSTCRT-S  Solve the standard five-point finite difference
```
```                    approximation on a staggered grid to the Helmholtz equation
```
```                    in Cartesian coordinates.
```
```
```
```          HSTCSP-S  Solve the standard five-point finite difference
```
```                    approximation on a staggered grid to the modified Helmholtz
```
```                    equation in spherical coordinates assuming axisymmetry
```
```                    (no dependence on longitude).
```
```
```
```          HSTCYL-S  Solve the standard five-point finite difference
```
```                    approximation on a staggered grid to the modified
```
```                    Helmholtz equation in cylindrical coordinates.
```
```
```
```          HSTPLR-S  Solve the standard five-point finite difference
```
```                    approximation on a staggered grid to the Helmholtz equation
```
```                    in polar coordinates.
```
```
```
```          HSTSSP-S  Solve the standard five-point finite difference
```
```                    approximation on a staggered grid to the Helmholtz
```
```                    equation in spherical coordinates and on the surface of
```
```                    the unit sphere (radius of 1).
```
```
```
```          HW3CRT-S  Solve the standard seven-point finite difference
```
```                    approximation to the Helmholtz equation in Cartesian
```
```                    coordinates.
```
```
```
```          HWSCRT-S  Solves the standard five-point finite difference
```
```                    approximation to the Helmholtz equation in Cartesian
```
```                    coordinates.
```
```
```
```          HWSCSP-S  Solve a finite difference approximation to the modified
```
```                    Helmholtz equation in spherical coordinates assuming
```
```                    axisymmetry  (no dependence on longitude).
```
```
```
```          HWSCYL-S  Solve a standard finite difference approximation
```
```                    to the Helmholtz equation in cylindrical coordinates.
```
```
```
```          HWSPLR-S  Solve a finite difference approximation to the Helmholtz
```
```                    equation in polar coordinates.
```
```
```
```          HWSSSP-S  Solve a finite difference approximation to the Helmholtz
```
```                    equation in spherical coordinates and on the surface of the
```
```                    unit sphere (radius of 1).
```
```
```
```
```
```          SEPELI-S  Discretize and solve a second and, optionally, a fourth
```
```                    order finite difference approximation on a uniform grid to
```
```                    the general separable elliptic partial differential
```
```                    equation on a rectangle with any combination of periodic or
```
```                    mixed boundary conditions.
```
```
```
```          SEPX4-S   Solve for either the second or fourth order finite
```
```                    difference approximation to the solution of a separable
```
```                    elliptic partial differential equation on a rectangle.
```
```                    Any combination of periodic or mixed boundary conditions is
```
```                    allowed.
```
```
```
```
```
```          BLKTRI-S  Solve a block tridiagonal system of linear equations
```
```          CBLKTR-C  (usually resulting from the discretization of separable
```
```                    two-dimensional elliptic equations).
```
```
```
```          GENBUN-S  Solve by a cyclic reduction algorithm the linear system
```
```          CMGNBN-C  of equations that results from a finite difference
```
```                    approximation to certain 2-d elliptic PDE's on a centered
```
```                    grid .
```
```
```
```          POIS3D-S  Solve a three-dimensional block tridiagonal linear system
```
```                    which arises from a finite difference approximation to a
```
```                    three-dimensional Poisson equation using the Fourier
```
```                    transform package FFTPAK written by Paul Swarztrauber.
```
```
```
```          POISTG-S  Solve a block tridiagonal system of linear equations
```
```                    that results from a staggered grid finite difference
```
```                    approximation to 2-D elliptic PDE's.
```
```
```
```J.  Integral transforms
```
```J1.  Fast Fourier transforms (search class L10 for time series analysis)
```
```
```
```          FFTDOC-A  Documentation for FFTPACK, a collection of Fast Fourier
```
```                    Transform routines.
```
```
```
```J1A.  One-dimensional
```
```J1A1.  Real
```
```
```
```          EZFFTB-S  A simplified real, periodic, backward fast Fourier
```
```                    transform.
```
```
```
```          EZFFTF-S  Compute a simplified real, periodic, fast Fourier forward
```
```                    transform.
```
```
```
```          EZFFTI-S  Initialize a work array for EZFFTF and EZFFTB.
```
```
```
```          RFFTB1-S  Compute the backward fast Fourier transform of a real
```
```          CFFTB1-C  coefficient array.
```
```
```
```          RFFTF1-S  Compute the forward transform of a real, periodic sequence.
```
```          CFFTF1-C
```
```
```
```          RFFTI1-S  Initialize a real and an integer work array for RFFTF1 and
```
```          CFFTI1-C  RFFTB1.
```
```
```
```J1A2.  Complex
```
```
```
```          CFFTB1-C  Compute the unnormalized inverse of CFFTF1.
```
```          RFFTB1-S
```
```
```
```          CFFTF1-C  Compute the forward transform of a complex, periodic
```
```          RFFTF1-S  sequence.
```
```
```
```          CFFTI1-C  Initialize a real and an integer work array for CFFTF1 and
```
```          RFFTI1-S  CFFTB1.
```
```
```
```J1A3.  Trigonometric (sine, cosine)
```
```
```
```          COSQB-S   Compute the unnormalized inverse cosine transform.
```
```
```
```          COSQF-S   Compute the forward cosine transform with odd wave numbers.
```
```
```
```          COSQI-S   Initialize a work array for COSQF and COSQB.
```
```
```
```          COST-S    Compute the cosine transform of a real, even sequence.
```
```
```
```          COSTI-S   Initialize a work array for COST.
```
```
```
```          SINQB-S   Compute the unnormalized inverse of SINQF.
```
```
```
```          SINQF-S   Compute the forward sine transform with odd wave numbers.
```
```
```
```          SINQI-S   Initialize a work array for SINQF and SINQB.
```
```
```
```          SINT-S    Compute the sine transform of a real, odd sequence.
```
```
```
```          SINTI-S   Initialize a work array for SINT.
```
```
```
```J4.  Hilbert transforms
```
```
```
```          QAWC-S    The routine calculates an approximation result to a
```
```          DQAWC-D   Cauchy principal value I = INTEGRAL of F*W over (A,B)
```
```                    (W(X) = 1/((X-C), C.NE.A, C.NE.B), hopefully satisfying
```
```                    following claim for accuracy
```
```                    ABS(I-RESULT).LE.MAX(EPSABE,EPSREL*ABS(I)).
```
```
```
```          QAWCE-S   The routine calculates an approximation result to a
```
```          DQAWCE-D  CAUCHY PRINCIPAL VALUE I = Integral of F*W over (A,B)
```
```                    (W(X) = 1/(X-C), (C.NE.A, C.NE.B), hopefully satisfying
```
```                    following claim for accuracy
```
```                    ABS(I-RESULT).LE.MAX(EPSABS,EPSREL*ABS(I))
```
```
```
```          QC25C-S   To compute I = Integral of F*W over (A,B) with
```
```          DQC25C-D  error estimate, where W(X) = 1/(X-C)
```
```
```
```K.  Approximation (search also class L8)
```
```
```
```          BSPDOC-A  Documentation for BSPLINE, a package of subprograms for
```
```                    working with piecewise polynomial functions
```
```                    in B-representation.
```
```
```
```K1.  Least squares (L-2) approximation
```
```K1A.  Linear least squares (search also classes D5, D6, D9)
```
```K1A1.  Unconstrained
```
```K1A1A.  Univariate data (curve fitting)
```
```K1A1A1.  Polynomial splines (piecewise polynomials)
```
```
```
```          EFC-S     Fit a piecewise polynomial curve to discrete data.
```
```          DEFC-D    The piecewise polynomials are represented as B-splines.
```
```                    The fitting is done in a weighted least squares sense.
```
```
```
```          FC-S      Fit a piecewise polynomial curve to discrete data.
```
```          DFC-D     The piecewise polynomials are represented as B-splines.
```
```                    The fitting is done in a weighted least squares sense.
```
```                    Equality and inequality constraints can be imposed on the
```
```                    fitted curve.
```
```
```
```K1A1A2.  Polynomials
```
```
```
```          PCOEF-S   Convert the POLFIT coefficients to Taylor series form.
```
```          DPCOEF-D
```
```
```
```          POLFIT-S  Fit discrete data in a least squares sense by polynomials
```
```          DPOLFT-D  in one variable.
```
```
```
```K1A2.  Constrained
```
```K1A2A.  Linear constraints
```
```
```
```          EFC-S     Fit a piecewise polynomial curve to discrete data.
```
```          DEFC-D    The piecewise polynomials are represented as B-splines.
```
```                    The fitting is done in a weighted least squares sense.
```
```
```
```          FC-S      Fit a piecewise polynomial curve to discrete data.
```
```          DFC-D     The piecewise polynomials are represented as B-splines.
```
```                    The fitting is done in a weighted least squares sense.
```
```                    Equality and inequality constraints can be imposed on the
```
```                    fitted curve.
```
```
```
```          LSEI-S    Solve a linearly constrained least squares problem with
```
```          DLSEI-D   equality and inequality constraints, and optionally compute
```
```                    a covariance matrix.
```
```
```
```          SBOCLS-S  Solve the bounded and constrained least squares
```
```          DBOCLS-D  problem consisting of solving the equation
```
```                              E*X = F  (in the least squares sense)
```
```                     subject to the linear constraints
```
```                                    C*X = Y.
```
```
```
```          SBOLS-S   Solve the problem
```
```          DBOLS-D        E*X = F (in the least  squares  sense)
```
```                    with bounds on selected X values.
```
```
```
```          WNNLS-S   Solve a linearly constrained least squares problem with
```
```          DWNNLS-D  equality constraints and nonnegativity constraints on
```
```                    selected variables.
```
```
```
```K1B.  Nonlinear least squares
```
```K1B1.  Unconstrained
```
```
```
```          SCOV-S    Calculate the covariance matrix for a nonlinear data
```
```          DCOV-D    fitting problem.  It is intended to be used after a
```
```                    successful return from either SNLS1 or SNLS1E.
```
```
```
```K1B1A.  Smooth functions
```
```K1B1A1.  User provides no derivatives
```
```
```
```          SNLS1-S   Minimize the sum of the squares of M nonlinear functions
```
```          DNLS1-D   in N variables by a modification of the Levenberg-Marquardt
```
```                    algorithm.
```
```
```
```          SNLS1E-S  An easy-to-use code which minimizes the sum of the squares
```
```          DNLS1E-D  of M nonlinear functions in N variables by a modification
```
```                    of the Levenberg-Marquardt algorithm.
```
```
```
```K1B1A2.  User provides first derivatives
```
```
```
```          SNLS1-S   Minimize the sum of the squares of M nonlinear functions
```
```          DNLS1-D   in N variables by a modification of the Levenberg-Marquardt
```
```                    algorithm.
```
```
```
```          SNLS1E-S  An easy-to-use code which minimizes the sum of the squares
```
```          DNLS1E-D  of M nonlinear functions in N variables by a modification
```
```                    of the Levenberg-Marquardt algorithm.
```
```
```
```K6.  Service routines (e.g., mesh generation, evaluation of fitted functions)
```
```     (search also class N5)
```
```
```
```          BFQAD-S   Compute the integral of a product of a function and a
```
```          DBFQAD-D  derivative of a B-spline.
```
```
```
```          DBSPDR-D  Use the B-representation to construct a divided difference
```
```          BSPDR-S   table preparatory to a (right) derivative calculation.
```
```
```
```          BSPEV-S   Calculate the value of the spline and its derivatives from
```
```          DBSPEV-D  the B-representation.
```
```
```
```          BSPPP-S   Convert the B-representation of a B-spline to the piecewise
```
```          DBSPPP-D  polynomial (PP) form.
```
```
```
```          BSPVD-S   Calculate the value and all derivatives of order less than
```
```          DBSPVD-D  NDERIV of all basis functions which do not vanish at X.
```
```
```
```          BSPVN-S   Calculate the value of all (possibly) nonzero basis
```
```          DBSPVN-D  functions at X.
```
```
```
```          BSQAD-S   Compute the integral of a K-th order B-spline using the
```
```          DBSQAD-D  B-representation.
```
```
```
```          BVALU-S   Evaluate the B-representation of a B-spline at X for the
```
```          DBVALU-D  function value or any of its derivatives.
```
```
```
```          INTRV-S   Compute the largest integer ILEFT in 1 .LE. ILEFT .LE. LXT
```
```          DINTRV-D  such that XT(ILEFT) .LE. X where XT(*) is a subdivision
```
```                    of the X interval.
```
```
```
```          PFQAD-S   Compute the integral on (X1,X2) of a product of a function
```
```          DPFQAD-D  F and the ID-th derivative of a B-spline,
```
```                    (PP-representation).
```
```
```
```          PPQAD-S   Compute the integral on (X1,X2) of a K-th order B-spline
```
```          DPPQAD-D  using the piecewise polynomial (PP) representation.
```
```
```
```          PPVAL-S   Calculate the value of the IDERIV-th derivative of the
```
```          DPPVAL-D  B-spline from the PP-representation.
```
```
```
```          PVALUE-S  Use the coefficients generated by POLFIT to evaluate the
```
```          DP1VLU-D  polynomial fit of degree L, along with the first NDER of
```
```                    its derivatives, at a specified point.
```
```
```
```L.  Statistics, probability
```
```L5.  Function evaluation (search also class C)
```
```L5A.  Univariate
```
```L5A1.  Cumulative distribution functions, probability density functions
```
```L5A1E.  Error function, exponential, extreme value
```
```
```
```          ERF-S     Compute the error function.
```
```          DERF-D
```
```
```
```          ERFC-S    Compute the complementary error function.
```
```          DERFC-D
```
```
```
```L6.  Pseudo-random number generation
```
```L6A.  Univariate
```
```L6A14.  Negative binomial, normal
```
```
```
```          RGAUSS-S  Generate a normally distributed (Gaussian) random number.
```
```
```
```L6A21.  Uniform
```
```
```
```          RAND-S    Generate a uniformly distributed random number.
```
```
```
```          RUNIF-S   Generate a uniformly distributed random number.
```
```
```
```L7.  Experimental design, including analysis of variance
```
```L7A.  Univariate
```
```L7A3.  Analysis of covariance
```
```
```
```          CV-S      Evaluate the variance function of the curve obtained
```
```          DCV-D     by the constrained B-spline fitting subprogram FC.
```
```
```
```L8.  Regression (search also classes G, K)
```
```L8A.  Linear least squares (L-2) (search also classes D5, D6, D9)
```
```L8A3.  Piecewise polynomial (i.e. multiphase or spline)
```
```
```
```          EFC-S     Fit a piecewise polynomial curve to discrete data.
```
```          DEFC-D    The piecewise polynomials are represented as B-splines.
```
```                    The fitting is done in a weighted least squares sense.
```
```
```
```          FC-S      Fit a piecewise polynomial curve to discrete data.
```
```          DFC-D     The piecewise polynomials are represented as B-splines.
```
```                    The fitting is done in a weighted least squares sense.
```
```                    Equality and inequality constraints can be imposed on the
```
```                    fitted curve.
```
```
```
```N.  Data handling (search also class L2)
```
```N1.  Input, output
```
```
```
```          SBHIN-S   Read a Sparse Linear System in the Boeing/Harwell Format.
```
```          DBHIN-D   The matrix is read in and if the right hand side is also
```
```                    present in the input file then it too is read in.  The
```
```                    matrix is then modified to be in the SLAP Column format.
```
```
```
```          SCPPLT-S  Printer Plot of SLAP Column Format Matrix.
```
```          DCPPLT-D  Routine to print out a SLAP Column format matrix in a
```
```                    "printer plot" graphical representation.
```
```
```
```          STIN-S    Read in SLAP Triad Format Linear System.
```
```          DTIN-D    Routine to read in a SLAP Triad format matrix and right
```
```                    hand side and solution to the system, if known.
```
```
```
```          STOUT-S   Write out SLAP Triad Format Linear System.
```
```          DTOUT-D   Routine to write out a SLAP Triad format matrix and right
```
```                    hand side and solution to the system, if known.
```
```
```
```N6.  Sorting
```
```N6A.  Internal
```
```N6A1.  Passive (i.e. construct pointer array, rank)
```
```N6A1A.  Integer
```
```
```
```          IPSORT-I  Return the permutation vector generated by sorting a given
```
```          SPSORT-S  array and, optionally, rearrange the elements of the array.
```
```          DPSORT-D  The array may be sorted in increasing or decreasing order.
```
```          HPSORT-H  A slightly modified quicksort algorithm is used.
```
```
```
```N6A1B.  Real
```
```
```
```          SPSORT-S  Return the permutation vector generated by sorting a given
```
```          DPSORT-D  array and, optionally, rearrange the elements of the array.
```
```          IPSORT-I  The array may be sorted in increasing or decreasing order.
```
```          HPSORT-H  A slightly modified quicksort algorithm is used.
```
```
```
```N6A1C.  Character
```
```
```
```          HPSORT-H  Return the permutation vector generated by sorting a
```
```          SPSORT-S  substring within a character array and, optionally,
```
```          DPSORT-D  rearrange the elements of the array.  The array may be
```
```          IPSORT-I  sorted in forward or reverse lexicographical order.  A
```
```                    slightly modified quicksort algorithm is used.
```
```
```
```N6A2.  Active
```
```N6A2A.  Integer
```
```
```
```          IPSORT-I  Return the permutation vector generated by sorting a given
```
```          SPSORT-S  array and, optionally, rearrange the elements of the array.
```
```          DPSORT-D  The array may be sorted in increasing or decreasing order.
```
```          HPSORT-H  A slightly modified quicksort algorithm is used.
```
```
```
```          ISORT-I   Sort an array and optionally make the same interchanges in
```
```          SSORT-S   an auxiliary array.  The array may be sorted in increasing
```
```          DSORT-D   or decreasing order.  A slightly modified QUICKSORT
```
```                    algorithm is used.
```
```
```
```N6A2B.  Real
```
```
```
```          SPSORT-S  Return the permutation vector generated by sorting a given
```
```          DPSORT-D  array and, optionally, rearrange the elements of the array.
```
```          IPSORT-I  The array may be sorted in increasing or decreasing order.
```
```          HPSORT-H  A slightly modified quicksort algorithm is used.
```
```
```
```          SSORT-S   Sort an array and optionally make the same interchanges in
```
```          DSORT-D   an auxiliary array.  The array may be sorted in increasing
```
```          ISORT-I   or decreasing order.  A slightly modified QUICKSORT
```
```                    algorithm is used.
```
```
```
```N6A2C.  Character
```
```
```
```          HPSORT-H  Return the permutation vector generated by sorting a
```
```          SPSORT-S  substring within a character array and, optionally,
```
```          DPSORT-D  rearrange the elements of the array.  The array may be
```
```          IPSORT-I  sorted in forward or reverse lexicographical order.  A
```
```                    slightly modified quicksort algorithm is used.
```
```
```
```N8.  Permuting
```
```
```
```          SPPERM-S  Rearrange a given array according to a prescribed
```
```          DPPERM-D  permutation vector.
```
```          IPPERM-I
```
```          HPPERM-H
```
```
```
```R.  Service routines
```
```R1.  Machine-dependent constants
```
```
```
```          I1MACH-I  Return integer machine dependent constants.
```
```
```
```          R1MACH-S  Return floating point machine dependent constants.
```
```          D1MACH-D
```
```
```
```R2.  Error checking (e.g., check monotonicity)
```
```
```
```          GAMLIM-S  Compute the minimum and maximum bounds for the argument in
```
```          DGAMLM-D  the Gamma function.
```
```
```
```R3.  Error handling
```
```
```
```          FDUMP-A   Symbolic dump (should be locally written).
```
```
```
```R3A.  Set criteria for fatal errors
```
```
```
```          XSETF-A   Set the error control flag.
```
```
```
```R3B.  Set unit number for error messages
```
```
```
```          XSETUA-A  Set logical unit numbers (up to 5) to which error
```
```                    messages are to be sent.
```
```
```
```          XSETUN-A  Set output file to which error messages are to be sent.
```
```
```
```R3C.  Other utility programs
```
```
```
```          NUMXER-I  Return the most recent error number.
```
```
```
```          XERCLR-A  Reset current error number to zero.
```
```
```
```          XERDMP-A  Print the error tables and then clear them.
```
```
```
```          XERMAX-A  Set maximum number of times any error message is to be
```
```                    printed.
```
```
```
```          XERMSG-A  Process error messages for SLATEC and other libraries.
```
```
```
```          XGETF-A   Return the current value of the error control flag.
```
```
```
```          XGETUA-A  Return unit number(s) to which error messages are being
```
```                    sent.
```
```
```
```          XGETUN-A  Return the (first) output file to which error messages
```
```                    are being sent.
```
```
```
```Z.  Other
```
```
```
```          AAAAAA-A  SLATEC Common Mathematical Library disclaimer and version.
```
```
```
```          BSPDOC-A  Documentation for BSPLINE, a package of subprograms for
```
```                    working with piecewise polynomial functions
```
```                    in B-representation.
```
```
```
```          EISDOC-A  Documentation for EISPACK, a collection of subprograms for
```
```                    solving matrix eigen-problems.
```
```
```
```          FFTDOC-A  Documentation for FFTPACK, a collection of Fast Fourier
```
```                    Transform routines.
```
```
```
```          FUNDOC-A  Documentation for FNLIB, a collection of routines for
```
```                    evaluating elementary and special functions.
```
```
```
```          PCHDOC-A  Documentation for PCHIP, a Fortran package for piecewise
```
```                    cubic Hermite interpolation of data.
```
```
```
```          QPDOC-A   Documentation for QUADPACK, a package of subprograms for
```
```                    automatic evaluation of one-dimensional definite integrals.
```
```
```
```          SLPDOC-S  Sparse Linear Algebra Package Version 2.0.2 Documentation.
```
```          DLPDOC-D  Routines to solve large sparse symmetric and nonsymmetric
```
```                    positive definite linear systems, Ax = b, using precondi-
```
```                    tioned iterative methods.
```
```
```
```
```
``` SECTION II. Subsidiary Routines
```
```
```
```          ASYIK     Subsidiary to BESI and BESK
```
```
```
```          ASYJY     Subsidiary to BESJ and BESY
```
```
```
```          BCRH      Subsidiary to CBLKTR
```
```
```
```          BDIFF     Subsidiary to BSKIN
```
```
```
```          BESKNU    Subsidiary to BESK
```
```
```
```          BESYNU    Subsidiary to BESY
```
```
```
```          BKIAS     Subsidiary to BSKIN
```
```
```
```          BKISR     Subsidiary to BSKIN
```
```
```
```          BKSOL     Subsidiary to BVSUP
```
```
```
```          BLKTR1    Subsidiary to BLKTRI
```
```
```
```          BNFAC     Subsidiary to BINT4 and BINTK
```
```
```
```          BNSLV     Subsidiary to BINT4 and BINTK
```
```
```
```          BSGQ8     Subsidiary to BFQAD
```
```
```
```          BSPLVD    Subsidiary to FC
```
```
```
```          BSPLVN    Subsidiary to FC
```
```
```
```          BSRH      Subsidiary to BLKTRI
```
```
```
```          BVDER     Subsidiary to BVSUP
```
```
```
```          BVPOR     Subsidiary to BVSUP
```
```
```
```          C1MERG    Merge two strings of complex numbers.  Each string is
```
```                    ascending by the real part.
```
```
```
```          C9LGMC    Compute the log gamma correction factor so that
```
```                    LOG(CGAMMA(Z)) = 0.5*LOG(2.*PI) + (Z-0.5)*LOG(Z) - Z
```
```                    + C9LGMC(Z).
```
```
```
```          C9LN2R    Evaluate LOG(1+Z) from second order relative accuracy so
```
```                    that  LOG(1+Z) = Z - Z**2/2 + Z**3*C9LN2R(Z).
```
```
```
```          CACAI     Subsidiary to CAIRY
```
```
```
```          CACON     Subsidiary to CBESH and CBESK
```
```
```
```          CASYI     Subsidiary to CBESI and CBESK
```
```
```
```          CBINU     Subsidiary to CAIRY, CBESH, CBESI, CBESJ, CBESK and CBIRY
```
```
```
```          CBKNU     Subsidiary to CAIRY, CBESH, CBESI and CBESK
```
```
```
```          CBLKT1    Subsidiary to CBLKTR
```
```
```
```          CBUNI     Subsidiary to CBESI and CBESK
```
```
```
```          CBUNK     Subsidiary to CBESH and CBESK
```
```
```
```          CCMPB     Subsidiary to CBLKTR
```
```
```
```          CDCOR     Subroutine CDCOR computes corrections to the Y array.
```
```
```
```          CDCST     CDCST sets coefficients used by the core integrator CDSTP.
```
```
```
```          CDIV      Compute the complex quotient of two complex numbers.
```
```
```
```          CDNTL     Subroutine CDNTL is called to set parameters on the first
```
```                    call to CDSTP, on an internal restart, or when the user has
```
```                    altered MINT, MITER, and/or H.
```
```
```
```          CDNTP     Subroutine CDNTP interpolates the K-th derivative of Y at
```
```                    TOUT, using the data in the YH array.  If K has a value
```
```                    greater than NQ, the NQ-th derivative is calculated.
```
```
```
```          CDPSC     Subroutine CDPSC computes the predicted YH values by
```
```                    effectively multiplying the YH array by the Pascal triangle
```
```                    matrix when KSGN is +1, and performs the inverse function
```
```                    when KSGN is -1.
```
```
```
```          CDPST     Subroutine CDPST evaluates the Jacobian matrix of the right
```
```                    hand side of the differential equations.
```
```
```
```          CDSCL     Subroutine CDSCL rescales the YH array whenever the step
```
```                    size is changed.
```
```
```
```          CDSTP     CDSTP performs one step of the integration of an initial
```
```                    value problem for a system of ordinary differential
```
```                    equations.
```
```
```
```          CDZRO     CDZRO searches for a zero of a function F(N, T, Y, IROOT)
```
```                    between the given values B and C until the width of the
```
```                    interval (B, C) has collapsed to within a tolerance
```
```                    specified by the stopping criterion,
```
```                      ABS(B - C) .LE. 2.*(RW*ABS(B) + AE).
```
```
```
```          CFFTB     Compute the unnormalized inverse of CFFTF.
```
```
```
```          CFFTF     Compute the forward transform of a complex, periodic
```
```                    sequence.
```
```
```
```          CFFTI     Initialize a work array for CFFTF and CFFTB.
```
```
```
```          CFOD      Subsidiary to DEBDF
```
```
```
```          CHFCM     Check a single cubic for monotonicity.
```
```
```
```          CHFIE     Evaluates integral of a single cubic for PCHIA
```
```
```
```          CHKPR4    Subsidiary to SEPX4
```
```
```
```          CHKPRM    Subsidiary to SEPELI
```
```
```
```          CHKSN4    Subsidiary to SEPX4
```
```
```
```          CHKSNG    Subsidiary to SEPELI
```
```
```
```          CKSCL     Subsidiary to CBKNU, CUNK1 and CUNK2
```
```
```
```          CMLRI     Subsidiary to CBESI and CBESK
```
```
```
```          CMPCSG    Subsidiary to CMGNBN
```
```
```
```          CMPOSD    Subsidiary to CMGNBN
```
```
```
```          CMPOSN    Subsidiary to CMGNBN
```
```
```
```          CMPOSP    Subsidiary to CMGNBN
```
```
```
```          CMPTR3    Subsidiary to CMGNBN
```
```
```
```          CMPTRX    Subsidiary to CMGNBN
```
```
```
```          COMPB     Subsidiary to BLKTRI
```
```
```
```          COSGEN    Subsidiary to GENBUN
```
```
```
```          COSQB1    Compute the unnormalized inverse of COSQF1.
```
```
```
```          COSQF1    Compute the forward cosine transform with odd wave numbers.
```
```
```
```          CPADD     Subsidiary to CBLKTR
```
```
```
```          CPEVL     Subsidiary to CPZERO
```
```
```
```          CPEVLR    Subsidiary to CPZERO
```
```
```
```          CPROC     Subsidiary to CBLKTR
```
```
```
```          CPROCP    Subsidiary to CBLKTR
```
```
```
```          CPROD     Subsidiary to BLKTRI
```
```
```
```          CPRODP    Subsidiary to BLKTRI
```
```
```
```          CRATI     Subsidiary to CBESH, CBESI and CBESK
```
```
```
```          CS1S2     Subsidiary to CAIRY and CBESK
```
```
```
```          CSCALE    Subsidiary to BVSUP
```
```
```
```          CSERI     Subsidiary to CBESI and CBESK
```
```
```
```          CSHCH     Subsidiary to CBESH and CBESK
```
```
```
```          CSROOT    Compute the complex square root of a complex number.
```
```
```
```          CUCHK     Subsidiary to SERI, CUOIK, CUNK1, CUNK2, CUNI1, CUNI2 and
```
```                    CKSCL
```
```
```
```          CUNHJ     Subsidiary to CBESI and CBESK
```
```
```
```          CUNI1     Subsidiary to CBESI and CBESK
```
```
```
```          CUNI2     Subsidiary to CBESI and CBESK
```
```
```
```          CUNIK     Subsidiary to CBESI and CBESK
```
```
```
```          CUNK1     Subsidiary to CBESK
```
```
```
```          CUNK2     Subsidiary to CBESK
```
```
```
```          CUOIK     Subsidiary to CBESH, CBESI and CBESK
```
```
```
```          CWRSK     Subsidiary to CBESI and CBESK
```
```
```
```          D1MERG    Merge two strings of ascending double precision numbers.
```
```
```
```          D1MPYQ    Subsidiary to DNSQ and DNSQE
```
```
```
```          D1UPDT    Subsidiary to DNSQ and DNSQE
```
```
```
```          D9AIMP    Evaluate the Airy modulus and phase.
```
```
```
```          D9ATN1    Evaluate DATAN(X) from first order relative accuracy so
```
```                    that DATAN(X) = X + X**3*D9ATN1(X).
```
```
```
```          D9B0MP    Evaluate the modulus and phase for the J0 and Y0 Bessel
```
```                    functions.
```
```
```
```          D9B1MP    Evaluate the modulus and phase for the J1 and Y1 Bessel
```
```                    functions.
```
```
```
```          D9CHU     Evaluate for large Z  Z**A * U(A,B,Z) where U is the
```
```                    logarithmic confluent hypergeometric function.
```
```
```
```          D9GMIC    Compute the complementary incomplete Gamma function for A
```
```                    near a negative integer and X small.
```
```
```
```          D9GMIT    Compute Tricomi's incomplete Gamma function for small
```
```                    arguments.
```
```
```
```          D9KNUS    Compute Bessel functions EXP(X)*K-SUB-XNU(X) and EXP(X)*
```
```                    K-SUB-XNU+1(X) for 0.0 .LE. XNU .LT. 1.0.
```
```
```
```          D9LGIC    Compute the log complementary incomplete Gamma function
```
```                    for large X and for A .LE. X.
```
```
```
```          D9LGIT    Compute the logarithm of Tricomi's incomplete Gamma
```
```                    function with Perron's continued fraction for large X and
```
```                    A .GE. X.
```
```
```
```          D9LGMC    Compute the log Gamma correction factor so that
```
```                    LOG(DGAMMA(X)) = LOG(SQRT(2*PI)) + (X-5.)*LOG(X) - X
```
```                    + D9LGMC(X).
```
```
```
```          D9LN2R    Evaluate LOG(1+X) from second order relative accuracy so
```
```                    that LOG(1+X) = X - X**2/2 + X**3*D9LN2R(X)
```
```
```
```          DASYIK    Subsidiary to DBESI and DBESK
```
```
```
```          DASYJY    Subsidiary to DBESJ and DBESY
```
```
```
```          DBDIFF    Subsidiary to DBSKIN
```
```
```
```          DBKIAS    Subsidiary to DBSKIN
```
```
```
```          DBKISR    Subsidiary to DBSKIN
```
```
```
```          DBKSOL    Subsidiary to DBVSUP
```
```
```
```          DBNFAC    Subsidiary to DBINT4 and DBINTK
```
```
```
```          DBNSLV    Subsidiary to DBINT4 and DBINTK
```
```
```
```          DBOLSM    Subsidiary to DBOCLS and DBOLS
```
```
```
```          DBSGQ8    Subsidiary to DBFQAD
```
```
```
```          DBSKNU    Subsidiary to DBESK
```
```
```
```          DBSYNU    Subsidiary to DBESY
```
```
```
```          DBVDER    Subsidiary to DBVSUP
```
```
```
```          DBVPOR    Subsidiary to DBVSUP
```
```
```
```          DCFOD     Subsidiary to DDEBDF
```
```
```
```          DCHFCM    Check a single cubic for monotonicity.
```
```
```
```          DCHFIE    Evaluates integral of a single cubic for DPCHIA
```
```
```
```          DCHKW     SLAP WORK/IWORK Array Bounds Checker.
```
```                    This routine checks the work array lengths and interfaces
```
```                    to the SLATEC error handler if a problem is found.
```
```
```
```          DCOEF     Subsidiary to DBVSUP
```
```
```
```          DCSCAL    Subsidiary to DBVSUP and DSUDS
```
```
```
```          DDAINI    Initialization routine for DDASSL.
```
```
```
```          DDAJAC    Compute the iteration matrix for DDASSL and form the
```
```                    LU-decomposition.
```
```
```
```          DDANRM    Compute vector norm for DDASSL.
```
```
```
```          DDASLV    Linear system solver for DDASSL.
```
```
```
```          DDASTP    Perform one step of the DDASSL integration.
```
```
```
```          DDATRP    Interpolation routine for DDASSL.
```
```
```
```          DDAWTS    Set error weight vector for DDASSL.
```
```
```
```          DDCOR     Subroutine DDCOR computes corrections to the Y array.
```
```
```
```          DDCST     DDCST sets coefficients used by the core integrator DDSTP.
```
```
```
```          DDES      Subsidiary to DDEABM
```
```
```
```          DDNTL     Subroutine DDNTL is called to set parameters on the first
```
```                    call to DDSTP, on an internal restart, or when the user has
```
```                    altered MINT, MITER, and/or H.
```
```
```
```          DDNTP     Subroutine DDNTP interpolates the K-th derivative of Y at
```
```                    TOUT, using the data in the YH array.  If K has a value
```
```                    greater than NQ, the NQ-th derivative is calculated.
```
```
```
```          DDOGLG    Subsidiary to DNSQ and DNSQE
```
```
```
```          DDPSC     Subroutine DDPSC computes the predicted YH values by
```
```                    effectively multiplying the YH array by the Pascal triangle
```
```                    matrix when KSGN is +1, and performs the inverse function
```
```                    when KSGN is -1.
```
```
```
```          DDPST     Subroutine DDPST evaluates the Jacobian matrix of the right
```
```                    hand side of the differential equations.
```
```
```
```          DDSCL     Subroutine DDSCL rescales the YH array whenever the step
```
```                    size is changed.
```
```
```
```          DDSTP     DDSTP performs one step of the integration of an initial
```
```                    value problem for a system of ordinary differential
```
```                    equations.
```
```
```
```          DDZRO     DDZRO searches for a zero of a function F(N, T, Y, IROOT)
```
```                    between the given values B and C until the width of the
```
```                    interval (B, C) has collapsed to within a tolerance
```
```                    specified by the stopping criterion,
```
```                      ABS(B - C) .LE. 2.*(RW*ABS(B) + AE).
```
```
```
```          DEFCMN    Subsidiary to DEFC
```
```
```
```          DEFE4     Subsidiary to SEPX4
```
```
```
```          DEFEHL    Subsidiary to DERKF
```
```
```
```          DEFER     Subsidiary to SEPELI
```
```
```
```          DENORM    Subsidiary to DNSQ and DNSQE
```
```
```
```          DERKFS    Subsidiary to DERKF
```
```
```
```          DES       Subsidiary to DEABM
```
```
```
```          DEXBVP    Subsidiary to DBVSUP
```
```
```
```          DFCMN     Subsidiary to FC
```
```
```
```          DFDJC1    Subsidiary to DNSQ and DNSQE
```
```
```
```          DFDJC3    Subsidiary to DNLS1 and DNLS1E
```
```
```
```          DFEHL     Subsidiary to DDERKF
```
```
```
```          DFSPVD    Subsidiary to DFC
```
```
```
```          DFSPVN    Subsidiary to DFC
```
```
```
```          DFULMT    Subsidiary to DSPLP
```
```
```
```          DGAMLN    Compute the logarithm of the Gamma function
```
```
```
```          DGAMRN    Subsidiary to DBSKIN
```
```
```
```          DH12      Subsidiary to DHFTI, DLSEI and DWNNLS
```
```
```
```          DHELS     Internal routine for DGMRES.
```
```
```
```          DHEQR     Internal routine for DGMRES.
```
```
```
```          DHKSEQ    Subsidiary to DBSKIN
```
```
```
```          DHSTRT    Subsidiary to DDEABM, DDEBDF and DDERKF
```
```
```
```          DHVNRM    Subsidiary to DDEABM, DDEBDF and DDERKF
```
```
```
```          DINTYD    Subsidiary to DDEBDF
```
```
```
```          DJAIRY    Subsidiary to DBESJ and DBESY
```
```
```
```          DLPDP     Subsidiary to DLSEI
```
```
```
```          DLSI      Subsidiary to DLSEI
```
```
```
```          DLSOD     Subsidiary to DDEBDF
```
```
```
```          DLSSUD    Subsidiary to DBVSUP and DSUDS
```
```
```
```          DMACON    Subsidiary to DBVSUP
```
```
```
```          DMGSBV    Subsidiary to DBVSUP
```
```
```
```          DMOUT     Subsidiary to DBOCLS and DFC
```
```
```
```          DMPAR     Subsidiary to DNLS1 and DNLS1E
```
```
```
```          DOGLEG    Subsidiary to SNSQ and SNSQE
```
```
```
```          DOHTRL    Subsidiary to DBVSUP and DSUDS
```
```
```
```          DORTH     Internal routine for DGMRES.
```
```
```
```          DORTHR    Subsidiary to DBVSUP and DSUDS
```
```
```
```          DPCHCE    Set boundary conditions for DPCHIC
```
```
```
```          DPCHCI    Set interior derivatives for DPCHIC
```
```
```
```          DPCHCS    Adjusts derivative values for DPCHIC
```
```
```
```          DPCHDF    Computes divided differences for DPCHCE and DPCHSP
```
```
```
```          DPCHKT    Compute B-spline knot sequence for DPCHBS.
```
```
```
```          DPCHNG    Subsidiary to DSPLP
```
```
```
```          DPCHST    DPCHIP Sign-Testing Routine
```
```
```
```          DPCHSW    Limits excursion from data for DPCHCS
```
```
```
```          DPIGMR    Internal routine for DGMRES.
```
```
```
```          DPINCW    Subsidiary to DSPLP
```
```
```
```          DPINIT    Subsidiary to DSPLP
```
```
```
```          DPINTM    Subsidiary to DSPLP
```
```
```
```          DPJAC     Subsidiary to DDEBDF
```
```
```
```          DPLPCE    Subsidiary to DSPLP
```
```
```
```          DPLPDM    Subsidiary to DSPLP
```
```
```
```          DPLPFE    Subsidiary to DSPLP
```
```
```
```          DPLPFL    Subsidiary to DSPLP
```
```
```
```          DPLPMN    Subsidiary to DSPLP
```
```
```
```          DPLPMU    Subsidiary to DSPLP
```
```
```
```          DPLPUP    Subsidiary to DSPLP
```
```
```
```          DPNNZR    Subsidiary to DSPLP
```
```
```
```          DPOPT     Subsidiary to DSPLP
```
```
```
```          DPPGQ8    Subsidiary to DPFQAD
```
```
```
```          DPRVEC    Subsidiary to DBVSUP
```
```
```
```          DPRWPG    Subsidiary to DSPLP
```
```
```
```          DPRWVR    Subsidiary to DSPLP
```
```
```
```          DPSIXN    Subsidiary to DEXINT
```
```
```
```          DQCHEB    This routine computes the CHEBYSHEV series expansion
```
```                    of degrees 12 and 24 of a function using A
```
```                    FAST FOURIER TRANSFORM METHOD
```
```                    F(X) = SUM(K=1,..,13) (CHEB12(K)*T(K-1,X)),
```
```                    F(X) = SUM(K=1,..,25) (CHEB24(K)*T(K-1,X)),
```
```                    Where T(K,X) is the CHEBYSHEV POLYNOMIAL OF DEGREE K.
```
```
```
```          DQELG     The routine determines the limit of a given sequence of
```
```                    approximations, by means of the Epsilon algorithm of
```
```                    P.Wynn. An estimate of the absolute error is also given.
```
```                    The condensed Epsilon table is computed. Only those
```
```                    elements needed for the computation of the next diagonal
```
```                    are preserved.
```
```
```
```          DQFORM    Subsidiary to DNSQ and DNSQE
```
```
```
```          DQPSRT    This routine maintains the descending ordering in the
```
```                    list of the local error estimated resulting from the
```
```                    interval subdivision process. At each call two error
```
```                    estimates are inserted using the sequential search
```
```                    method, top-down for the largest error estimate and
```
```                    bottom-up for the smallest error estimate.
```
```
```
```          DQRFAC    Subsidiary to DNLS1, DNLS1E, DNSQ and DNSQE
```
```
```
```          DQRSLV    Subsidiary to DNLS1 and DNLS1E
```
```
```
```          DQWGTC    This function subprogram is used together with the
```
```                    routine DQAWC and defines the WEIGHT function.
```
```
```
```          DQWGTF    This function subprogram is used together with the
```
```                    routine DQAWF and defines the WEIGHT function.
```
```
```
```          DQWGTS    This function subprogram is used together with the
```
```                    routine DQAWS and defines the WEIGHT function.
```
```
```
```          DREADP    Subsidiary to DSPLP
```
```
```
```          DREORT    Subsidiary to DBVSUP
```
```
```
```          DRKFAB    Subsidiary to DBVSUP
```
```
```
```          DRKFS     Subsidiary to DDERKF
```
```
```
```          DRLCAL    Internal routine for DGMRES.
```
```
```
```          DRSCO     Subsidiary to DDEBDF
```
```
```
```          DSLVS     Subsidiary to DDEBDF
```
```
```
```          DSOSEQ    Subsidiary to DSOS
```
```
```
```          DSOSSL    Subsidiary to DSOS
```
```
```
```          DSTOD     Subsidiary to DDEBDF
```
```
```
```          DSTOR1    Subsidiary to DBVSUP
```
```
```
```          DSTWAY    Subsidiary to DBVSUP
```
```
```
```          DSUDS     Subsidiary to DBVSUP
```
```
```
```          DSVCO     Subsidiary to DDEBDF
```
```
```
```          DU11LS    Subsidiary to DLLSIA
```
```
```
```          DU11US    Subsidiary to DULSIA
```
```
```
```          DU12LS    Subsidiary to DLLSIA
```
```
```
```          DU12US    Subsidiary to DULSIA
```
```
```
```          DUSRMT    Subsidiary to DSPLP
```
```
```
```          DVECS     Subsidiary to DBVSUP
```
```
```
```          DVNRMS    Subsidiary to DDEBDF
```
```
```
```          DVOUT     Subsidiary to DSPLP
```
```
```
```          DWNLIT    Subsidiary to DWNNLS
```
```
```
```          DWNLSM    Subsidiary to DWNNLS
```
```
```
```          DWNLT1    Subsidiary to WNLIT
```
```
```
```          DWNLT2    Subsidiary to WNLIT
```
```
```
```          DWNLT3    Subsidiary to WNLIT
```
```
```
```          DWRITP    Subsidiary to DSPLP
```
```
```
```          DWUPDT    Subsidiary to DNLS1 and DNLS1E
```
```
```
```          DX        Subsidiary to SEPELI
```
```
```
```          DX4       Subsidiary to SEPX4
```
```
```
```          DXLCAL    Internal routine for DGMRES.
```
```
```
```          DXPMU     To compute the values of Legendre functions for DXLEGF.
```
```                    Method: backward mu-wise recurrence for P(-MU,NU,X) for
```
```                    fixed nu to obtain P(-MU2,NU1,X), P(-(MU2-1),NU1,X), ...,
```
```                    P(-MU1,NU1,X) and store in ascending mu order.
```
```
```
```          DXPMUP    To compute the values of Legendre functions for DXLEGF.
```
```                    This subroutine transforms an array of Legendre functions
```
```                    of the first kind of negative order stored in array PQA
```
```                    into Legendre functions of the first kind of positive
```
```                    order stored in array PQA. The original array is destroyed.
```
```
```
```          DXPNRM    To compute the values of Legendre functions for DXLEGF.
```
```                    This subroutine transforms an array of Legendre functions
```
```                    of the first kind of negative order stored in array PQA
```
```                    into normalized Legendre polynomials stored in array PQA.
```
```                    The original array is destroyed.
```
```
```
```          DXPQNU    To compute the values of Legendre functions for DXLEGF.
```
```                    This subroutine calculates initial values of P or Q using
```
```                    power series, then performs forward nu-wise recurrence to
```
```                    obtain P(-MU,NU,X), Q(0,NU,X), or Q(1,NU,X). The nu-wise
```
```                    recurrence is stable for P for all mu and for Q for mu=0,1.
```
```
```
```          DXPSI     To compute values of the Psi function for DXLEGF.
```
```
```
```          DXQMU     To compute the values of Legendre functions for DXLEGF.
```
```                    Method: forward mu-wise recurrence for Q(MU,NU,X) for fixed
```
```                    nu to obtain Q(MU1,NU,X), Q(MU1+1,NU,X), ..., Q(MU2,NU,X).
```
```
```
```          DXQNU     To compute the values of Legendre functions for DXLEGF.
```
```                    Method: backward nu-wise recurrence for Q(MU,NU,X) for
```
```                    fixed mu to obtain Q(MU1,NU1,X), Q(MU1,NU1+1,X), ...,
```
```                    Q(MU1,NU2,X).
```
```
```
```          DY        Subsidiary to SEPELI
```
```
```
```          DY4       Subsidiary to SEPX4
```
```
```
```          DYAIRY    Subsidiary to DBESJ and DBESY
```
```
```
```          EFCMN     Subsidiary to EFC
```
```
```
```          ENORM     Subsidiary to SNLS1, SNLS1E, SNSQ and SNSQE
```
```
```
```          EXBVP     Subsidiary to BVSUP
```
```
```
```          EZFFT1    EZFFTI calls EZFFT1 with appropriate work array
```
```                    partitioning.
```
```
```
```          FCMN      Subsidiary to FC
```
```
```
```          FDJAC1    Subsidiary to SNSQ and SNSQE
```
```
```
```          FDJAC3    Subsidiary to SNLS1 and SNLS1E
```
```
```
```          FULMAT    Subsidiary to SPLP
```
```
```
```          GAMLN     Compute the logarithm of the Gamma function
```
```
```
```          GAMRN     Subsidiary to BSKIN
```
```
```
```          H12       Subsidiary to HFTI, LSEI and WNNLS
```
```
```
```          HKSEQ     Subsidiary to BSKIN
```
```
```
```          HSTART    Subsidiary to DEABM, DEBDF and DERKF
```
```
```
```          HSTCS1    Subsidiary to HSTCSP
```
```
```
```          HVNRM     Subsidiary to DEABM, DEBDF and DERKF
```
```
```
```          HWSCS1    Subsidiary to HWSCSP
```
```
```
```          HWSSS1    Subsidiary to HWSSSP
```
```
```
```          I1MERG    Merge two strings of ascending integers.
```
```
```
```          IDLOC     Subsidiary to DSPLP
```
```
```
```          INDXA     Subsidiary to BLKTRI
```
```
```
```          INDXB     Subsidiary to BLKTRI
```
```
```
```          INDXC     Subsidiary to BLKTRI
```
```
```
```          INTYD     Subsidiary to DEBDF
```
```
```
```          INXCA     Subsidiary to CBLKTR
```
```
```
```          INXCB     Subsidiary to CBLKTR
```
```
```
```          INXCC     Subsidiary to CBLKTR
```
```
```
```          IPLOC     Subsidiary to SPLP
```
```
```
```          ISDBCG    Preconditioned BiConjugate Gradient Stop Test.
```
```                    This routine calculates the stop test for the BiConjugate
```
```                    Gradient iteration scheme.  It returns a non-zero if the
```
```                    error estimate (the type of which is determined by ITOL)
```
```                    is less than the user specified tolerance TOL.
```
```
```
```          ISDCG     Preconditioned Conjugate Gradient Stop Test.
```
```                    This routine calculates the stop test for the Conjugate
```
```                    Gradient iteration scheme.  It returns a non-zero if the
```
```                    error estimate (the type of which is determined by ITOL)
```
```                    is less than the user specified tolerance TOL.
```
```
```
```          ISDCGN    Preconditioned CG on Normal Equations Stop Test.
```
```                    This routine calculates the stop test for the Conjugate
```
```                    Gradient iteration scheme applied to the normal equations.
```
```                    It returns a non-zero if the error estimate (the type of
```
```                    which is determined by ITOL) is less than the user
```
```                    specified tolerance TOL.
```
```
```
```          ISDCGS    Preconditioned BiConjugate Gradient Squared Stop Test.
```
```                    This routine calculates the stop test for the BiConjugate
```
```                    Gradient Squared iteration scheme.  It returns a non-zero
```
```                    if the error estimate (the type of which is determined by
```
```                    ITOL) is less than the user specified tolerance TOL.
```
```
```
```          ISDGMR    Generalized Minimum Residual Stop Test.
```
```                    This routine calculates the stop test for the Generalized
```
```                    Minimum RESidual (GMRES) iteration scheme.  It returns a
```
```                    non-zero if the error estimate (the type of which is
```
```                    determined by ITOL) is less than the user specified
```
```                    tolerance TOL.
```
```
```
```          ISDIR     Preconditioned Iterative Refinement Stop Test.
```
```                    This routine calculates the stop test for the iterative
```
```                    refinement iteration scheme.  It returns a non-zero if the
```
```                    error estimate (the type of which is determined by ITOL)
```
```                    is less than the user specified tolerance TOL.
```
```
```
```          ISDOMN    Preconditioned Orthomin Stop Test.
```
```                    This routine calculates the stop test for the Orthomin
```
```                    iteration scheme.  It returns a non-zero if the error
```
```                    estimate (the type of which is determined by ITOL) is
```
```                    less than the user specified tolerance TOL.
```
```
```
```          ISSBCG    Preconditioned BiConjugate Gradient Stop Test.
```
```                    This routine calculates the stop test for the BiConjugate
```
```                    Gradient iteration scheme.  It returns a non-zero if the
```
```                    error estimate (the type of which is determined by ITOL)
```
```                    is less than the user specified tolerance TOL.
```
```
```
```          ISSCG     Preconditioned Conjugate Gradient Stop Test.
```
```                    This routine calculates the stop test for the Conjugate
```
```                    Gradient iteration scheme.  It returns a non-zero if the
```
```                    error estimate (the type of which is determined by ITOL)
```
```                    is less than the user specified tolerance TOL.
```
```
```
```          ISSCGN    Preconditioned CG on Normal Equations Stop Test.
```
```                    This routine calculates the stop test for the Conjugate
```
```                    Gradient iteration scheme applied to the normal equations.
```
```                    It returns a non-zero if the error estimate (the type of
```
```                    which is determined by ITOL) is less than the user
```
```                    specified tolerance TOL.
```
```
```
```          ISSCGS    Preconditioned BiConjugate Gradient Squared Stop Test.
```
```                    This routine calculates the stop test for the BiConjugate
```
```                    Gradient Squared iteration scheme.  It returns a non-zero
```
```                    if the error estimate (the type of which is determined by
```
```                    ITOL) is less than the user specified tolerance TOL.
```
```
```
```          ISSGMR    Generalized Minimum Residual Stop Test.
```
```                    This routine calculates the stop test for the Generalized
```
```                    Minimum RESidual (GMRES) iteration scheme.  It returns a
```
```                    non-zero if the error estimate (the type of which is
```
```                    determined by ITOL) is less than the user specified
```
```                    tolerance TOL.
```
```
```
```          ISSIR     Preconditioned Iterative Refinement Stop Test.
```
```                    This routine calculates the stop test for the iterative
```
```                    refinement iteration scheme.  It returns a non-zero if the
```
```                    error estimate (the type of which is determined by ITOL)
```
```                    is less than the user specified tolerance TOL.
```
```
```
```          ISSOMN    Preconditioned Orthomin Stop Test.
```
```                    This routine calculates the stop test for the Orthomin
```
```                    iteration scheme.  It returns a non-zero if the error
```
```                    estimate (the type of which is determined by ITOL) is
```
```                    less than the user specified tolerance TOL.
```
```
```
```          IVOUT     Subsidiary to SPLP
```
```
```
```          J4SAVE    Save or recall global variables needed by error
```
```                    handling routines.
```
```
```
```          JAIRY     Subsidiary to BESJ and BESY
```
```
```
```          LA05AD    Subsidiary to DSPLP
```
```
```
```          LA05AS    Subsidiary to SPLP
```
```
```
```          LA05BD    Subsidiary to DSPLP
```
```
```
```          LA05BS    Subsidiary to SPLP
```
```
```
```          LA05CD    Subsidiary to DSPLP
```
```
```
```          LA05CS    Subsidiary to SPLP
```
```
```
```          LA05ED    Subsidiary to DSPLP
```
```
```
```          LA05ES    Subsidiary to SPLP
```
```
```
```          LMPAR     Subsidiary to SNLS1 and SNLS1E
```
```
```
```          LPDP      Subsidiary to LSEI
```
```
```
```          LSAME     Test two characters to determine if they are the same
```
```                    letter, except for case.
```
```
```
```          LSI       Subsidiary to LSEI
```
```
```
```          LSOD      Subsidiary to DEBDF
```
```
```
```          LSSODS    Subsidiary to BVSUP
```
```
```
```          LSSUDS    Subsidiary to BVSUP
```
```
```
```          MACON     Subsidiary to BVSUP
```
```
```
```          MC20AD    Subsidiary to DSPLP
```
```
```
```          MC20AS    Subsidiary to SPLP
```
```
```
```          MGSBV     Subsidiary to BVSUP
```
```
```
```          MINSO4    Subsidiary to SEPX4
```
```
```
```          MINSOL    Subsidiary to SEPELI
```
```
```
```          MPADD     Subsidiary to DQDOTA and DQDOTI
```
```
```
```          MPADD2    Subsidiary to DQDOTA and DQDOTI
```
```
```
```          MPADD3    Subsidiary to DQDOTA and DQDOTI
```
```
```
```          MPBLAS    Subsidiary to DQDOTA and DQDOTI
```
```
```
```          MPCDM     Subsidiary to DQDOTA and DQDOTI
```
```
```
```          MPCHK     Subsidiary to DQDOTA and DQDOTI
```
```
```
```          MPCMD     Subsidiary to DQDOTA and DQDOTI
```
```
```
```          MPDIVI    Subsidiary to DQDOTA and DQDOTI
```
```
```
```          MPERR     Subsidiary to DQDOTA and DQDOTI
```
```
```
```          MPMAXR    Subsidiary to DQDOTA and DQDOTI
```
```
```
```          MPMLP     Subsidiary to DQDOTA and DQDOTI
```
```
```
```          MPMUL     Subsidiary to DQDOTA and DQDOTI
```
```
```
```          MPMUL2    Subsidiary to DQDOTA and DQDOTI
```
```
```
```          MPMULI    Subsidiary to DQDOTA and DQDOTI
```
```
```
```          MPNZR     Subsidiary to DQDOTA and DQDOTI
```
```
```
```          MPOVFL    Subsidiary to DQDOTA and DQDOTI
```
```
```
```          MPSTR     Subsidiary to DQDOTA and DQDOTI
```
```
```
```          MPUNFL    Subsidiary to DQDOTA and DQDOTI
```
```
```
```          OHTROL    Subsidiary to BVSUP
```
```
```
```          OHTROR    Subsidiary to BVSUP
```
```
```
```          ORTHO4    Subsidiary to SEPX4
```
```
```
```          ORTHOG    Subsidiary to SEPELI
```
```
```
```          ORTHOL    Subsidiary to BVSUP
```
```
```
```          ORTHOR    Subsidiary to BVSUP
```
```
```
```          PASSB     Calculate the fast Fourier transform of subvectors of
```
```                    arbitrary length.
```
```
```
```          PASSB2    Calculate the fast Fourier transform of subvectors of
```
```                    length two.
```
```
```
```          PASSB3    Calculate the fast Fourier transform of subvectors of
```
```                    length three.
```
```
```
```          PASSB4    Calculate the fast Fourier transform of subvectors of
```
```                    length four.
```
```
```
```          PASSB5    Calculate the fast Fourier transform of subvectors of
```
```                    length five.
```
```
```
```          PASSF     Calculate the fast Fourier transform of subvectors of
```
```                    arbitrary length.
```
```
```
```          PASSF2    Calculate the fast Fourier transform of subvectors of
```
```                    length two.
```
```
```
```          PASSF3    Calculate the fast Fourier transform of subvectors of
```
```                    length three.
```
```
```
```          PASSF4    Calculate the fast Fourier transform of subvectors of
```
```                    length four.
```
```
```
```          PASSF5    Calculate the fast Fourier transform of subvectors of
```
```                    length five.
```
```
```
```          PCHCE     Set boundary conditions for PCHIC
```
```
```
```          PCHCI     Set interior derivatives for PCHIC
```
```
```
```          PCHCS     Adjusts derivative values for PCHIC
```
```
```
```          PCHDF     Computes divided differences for PCHCE and PCHSP
```
```
```
```          PCHKT     Compute B-spline knot sequence for PCHBS.
```
```
```
```          PCHNGS    Subsidiary to SPLP
```
```
```
```          PCHST     PCHIP Sign-Testing Routine
```
```
```
```          PCHSW     Limits excursion from data for PCHCS
```
```
```
```          PGSF      Subsidiary to CBLKTR
```
```
```
```          PIMACH    Subsidiary to HSTCSP, HSTSSP and HWSCSP
```
```
```
```          PINITM    Subsidiary to SPLP
```
```
```
```          PJAC      Subsidiary to DEBDF
```
```
```
```          PNNZRS    Subsidiary to SPLP
```
```
```
```          POISD2    Subsidiary to GENBUN
```
```
```
```          POISN2    Subsidiary to GENBUN
```
```
```
```          POISP2    Subsidiary to GENBUN
```
```
```
```          POS3D1    Subsidiary to POIS3D
```
```
```
```          POSTG2    Subsidiary to POISTG
```
```
```
```          PPADD     Subsidiary to BLKTRI
```
```
```
```          PPGQ8     Subsidiary to PFQAD
```
```
```
```          PPGSF     Subsidiary to CBLKTR
```
```
```
```          PPPSF     Subsidiary to CBLKTR
```
```
```
```          PPSGF     Subsidiary to BLKTRI
```
```
```
```          PPSPF     Subsidiary to BLKTRI
```
```
```
```          PROC      Subsidiary to CBLKTR
```
```
```
```          PROCP     Subsidiary to CBLKTR
```
```
```
```          PROD      Subsidiary to BLKTRI
```
```
```
```          PRODP     Subsidiary to BLKTRI
```
```
```
```          PRVEC     Subsidiary to BVSUP
```
```
```
```          PRWPGE    Subsidiary to SPLP
```
```
```
```          PRWVIR    Subsidiary to SPLP
```
```
```
```          PSGF      Subsidiary to BLKTRI
```
```
```
```          PSIXN     Subsidiary to EXINT
```
```
```
```          PYTHAG    Compute the complex square root of a complex number without
```
```                    destructive overflow or underflow.
```
```
```
```          QCHEB     This routine computes the CHEBYSHEV series expansion
```
```                    of degrees 12 and 24 of a function using A
```
```                    FAST FOURIER TRANSFORM METHOD
```
```                    F(X) = SUM(K=1,..,13) (CHEB12(K)*T(K-1,X)),
```
```                    F(X) = SUM(K=1,..,25) (CHEB24(K)*T(K-1,X)),
```
```                    Where T(K,X) is the CHEBYSHEV POLYNOMIAL OF DEGREE K.
```
```
```
```          QELG      The routine determines the limit of a given sequence of
```
```                    approximations, by means of the Epsilon algorithm of
```
```                    P. Wynn. An estimate of the absolute error is also given.
```
```                    The condensed Epsilon table is computed. Only those
```
```                    elements needed for the computation of the next diagonal
```
```                    are preserved.
```
```
```
```          QFORM     Subsidiary to SNSQ and SNSQE
```
```
```
```          QPSRT     Subsidiary to QAGE, QAGIE, QAGPE, QAGSE, QAWCE, QAWOE and
```
```                    QAWSE
```
```
```
```          QRFAC     Subsidiary to SNLS1, SNLS1E, SNSQ and SNSQE
```
```
```
```          QRSOLV    Subsidiary to SNLS1 and SNLS1E
```
```
```
```          QS2I1D    Sort an integer array, moving an integer and DP array.
```
```                    This routine sorts the integer array IA and makes the same
```
```                    interchanges in the integer array JA and the double pre-
```
```                    cision array A.  The array IA may be sorted in increasing
```
```                    order or decreasing order.  A slightly modified QUICKSORT
```
```                    algorithm is used.
```
```
```
```          QS2I1R    Sort an integer array, moving an integer and real array.
```
```                    This routine sorts the integer array IA and makes the same
```
```                    interchanges in the integer array JA and the real array A.
```
```                    The array IA may be sorted in increasing order or decreas-
```
```                    ing order.  A slightly modified QUICKSORT algorithm is
```
```                    used.
```
```
```
```          QWGTC     This function subprogram is used together with the
```
```                    routine QAWC and defines the WEIGHT function.
```
```
```
```          QWGTF     This function subprogram is used together with the
```
```                    routine QAWF and defines the WEIGHT function.
```
```
```
```          QWGTS     This function subprogram is used together with the
```
```                    routine QAWS and defines the WEIGHT function.
```
```
```
```          R1MPYQ    Subsidiary to SNSQ and SNSQE
```
```
```
```          R1UPDT    Subsidiary to SNSQ and SNSQE
```
```
```
```          R9AIMP    Evaluate the Airy modulus and phase.
```
```
```
```          R9ATN1    Evaluate ATAN(X) from first order relative accuracy so that
```
```                    ATAN(X) = X + X**3*R9ATN1(X).
```
```
```
```          R9CHU     Evaluate for large Z  Z**A * U(A,B,Z) where U is the
```
```                    logarithmic confluent hypergeometric function.
```
```
```
```          R9GMIC    Compute the complementary incomplete Gamma function for A
```
```                    near a negative integer and for small X.
```
```
```
```          R9GMIT    Compute Tricomi's incomplete Gamma function for small
```
```                    arguments.
```
```
```
```          R9KNUS    Compute Bessel functions EXP(X)*K-SUB-XNU(X) and EXP(X)*
```
```                    K-SUB-XNU+1(X) for 0.0 .LE. XNU .LT. 1.0.
```
```
```
```          R9LGIC    Compute the log complementary incomplete Gamma function
```
```                    for large X and for A .LE. X.
```
```
```
```          R9LGIT    Compute the logarithm of Tricomi's incomplete Gamma
```
```                    function with Perron's continued fraction for large X and
```
```                    A .GE. X.
```
```
```
```          R9LGMC    Compute the log Gamma correction factor so that
```
```                    LOG(GAMMA(X)) = LOG(SQRT(2*PI)) + (X-.5)*LOG(X) - X
```
```                    + R9LGMC(X).
```
```
```
```          R9LN2R    Evaluate LOG(1+X) from second order relative accuracy so
```
```                    that LOG(1+X) = X - X**2/2 + X**3*R9LN2R(X).
```
```
```
```          RADB2     Calculate the fast Fourier transform of subvectors of
```
```                    length two.
```
```
```
```          RADB3     Calculate the fast Fourier transform of subvectors of
```
```                    length three.
```
```
```
```          RADB4     Calculate the fast Fourier transform of subvectors of
```
```                    length four.
```
```
```
```          RADB5     Calculate the fast Fourier transform of subvectors of
```
```                    length five.
```
```
```
```          RADBG     Calculate the fast Fourier transform of subvectors of
```
```                    arbitrary length.
```
```
```
```          RADF2     Calculate the fast Fourier transform of subvectors of
```
```                    length two.
```
```
```
```          RADF3     Calculate the fast Fourier transform of subvectors of
```
```                    length three.
```
```
```
```          RADF4     Calculate the fast Fourier transform of subvectors of
```
```                    length four.
```
```
```
```          RADF5     Calculate the fast Fourier transform of subvectors of
```
```                    length five.
```
```
```
```          RADFG     Calculate the fast Fourier transform of subvectors of
```
```                    arbitrary length.
```
```
```
```          REORT     Subsidiary to BVSUP
```
```
```
```          RFFTB     Compute the backward fast Fourier transform of a real
```
```                    coefficient array.
```
```
```
```          RFFTF     Compute the forward transform of a real, periodic sequence.
```
```
```
```          RFFTI     Initialize a work array for RFFTF and RFFTB.
```
```
```
```          RKFAB     Subsidiary to BVSUP
```
```
```
```          RSCO      Subsidiary to DEBDF
```
```
```
```          RWUPDT    Subsidiary to SNLS1 and SNLS1E
```
```
```
```          S1MERG    Merge two strings of ascending real numbers.
```
```
```
```          SBOLSM    Subsidiary to SBOCLS and SBOLS
```
```
```
```          SCHKW     SLAP WORK/IWORK Array Bounds Checker.
```
```                    This routine checks the work array lengths and interfaces
```
```                    to the SLATEC error handler if a problem is found.
```
```
```
```          SCLOSM    Subsidiary to SPLP
```
```
```
```          SCOEF     Subsidiary to BVSUP
```
```
```
```          SDAINI    Initialization routine for SDASSL.
```
```
```
```          SDAJAC    Compute the iteration matrix for SDASSL and form the
```
```                    LU-decomposition.
```
```
```
```          SDANRM    Compute vector norm for SDASSL.
```
```
```
```          SDASLV    Linear system solver for SDASSL.
```
```
```
```          SDASTP    Perform one step of the SDASSL integration.
```
```
```
```          SDATRP    Interpolation routine for SDASSL.
```
```
```
```          SDAWTS    Set error weight vector for SDASSL.
```
```
```
```          SDCOR     Subroutine SDCOR computes corrections to the Y array.
```
```
```
```          SDCST     SDCST sets coefficients used by the core integrator SDSTP.
```
```
```
```          SDNTL     Subroutine SDNTL is called to set parameters on the first
```
```                    call to SDSTP, on an internal restart, or when the user has
```
```                    altered MINT, MITER, and/or H.
```
```
```
```          SDNTP     Subroutine SDNTP interpolates the K-th derivative of Y at
```
```                    TOUT, using the data in the YH array.  If K has a value
```
```                    greater than NQ, the NQ-th derivative is calculated.
```
```
```
```          SDPSC     Subroutine SDPSC computes the predicted YH values by
```
```                    effectively multiplying the YH array by the Pascal triangle
```
```                    matrix when KSGN is +1, and performs the inverse function
```
```                    when KSGN is -1.
```
```
```
```          SDPST     Subroutine SDPST evaluates the Jacobian matrix of the right
```
```                    hand side of the differential equations.
```
```
```
```          SDSCL     Subroutine SDSCL rescales the YH array whenever the step
```
```                    size is changed.
```
```
```
```          SDSTP     SDSTP performs one step of the integration of an initial
```
```                    value problem for a system of ordinary differential
```
```                    equations.
```
```
```
```          SDZRO     SDZRO searches for a zero of a function F(N, T, Y, IROOT)
```
```                    between the given values B and C until the width of the
```
```                    interval (B, C) has collapsed to within a tolerance
```
```                    specified by the stopping criterion,
```
```                      ABS(B - C) .LE. 2.*(RW*ABS(B) + AE).
```
```
```
```          SHELS     Internal routine for SGMRES.
```
```
```
```          SHEQR     Internal routine for SGMRES.
```
```
```
```          SLVS      Subsidiary to DEBDF
```
```
```
```          SMOUT     Subsidiary to FC and SBOCLS
```
```
```
```          SODS      Subsidiary to BVSUP
```
```
```
```          SOPENM    Subsidiary to SPLP
```
```
```
```          SORTH     Internal routine for SGMRES.
```
```
```
```          SOSEQS    Subsidiary to SOS
```
```
```
```          SOSSOL    Subsidiary to SOS
```
```
```
```          SPELI4    Subsidiary to SEPX4
```
```
```
```          SPELIP    Subsidiary to SEPELI
```
```
```
```          SPIGMR    Internal routine for SGMRES.
```
```
```
```          SPINCW    Subsidiary to SPLP
```
```
```
```          SPINIT    Subsidiary to SPLP
```
```
```
```          SPLPCE    Subsidiary to SPLP
```
```
```
```          SPLPDM    Subsidiary to SPLP
```
```
```
```          SPLPFE    Subsidiary to SPLP
```
```
```
```          SPLPFL    Subsidiary to SPLP
```
```
```
```          SPLPMN    Subsidiary to SPLP
```
```
```
```          SPLPMU    Subsidiary to SPLP
```
```
```
```          SPLPUP    Subsidiary to SPLP
```
```
```
```          SPOPT     Subsidiary to SPLP
```
```
```
```          SREADP    Subsidiary to SPLP
```
```
```
```          SRLCAL    Internal routine for SGMRES.
```
```
```
```          STOD      Subsidiary to DEBDF
```
```
```
```          STOR1     Subsidiary to BVSUP
```
```
```
```          STWAY     Subsidiary to BVSUP
```
```
```
```          SUDS      Subsidiary to BVSUP
```
```
```
```          SVCO      Subsidiary to DEBDF
```
```
```
```          SVD       Perform the singular value decomposition of a rectangular
```
```                    matrix.
```
```
```
```          SVECS     Subsidiary to BVSUP
```
```
```
```          SVOUT     Subsidiary to SPLP
```
```
```
```          SWRITP    Subsidiary to SPLP
```
```
```
```          SXLCAL    Internal routine for SGMRES.
```
```
```
```          TEVLC     Subsidiary to CBLKTR
```
```
```
```          TEVLS     Subsidiary to BLKTRI
```
```
```
```          TRI3      Subsidiary to GENBUN
```
```
```
```          TRIDQ     Subsidiary to POIS3D
```
```
```
```          TRIS4     Subsidiary to SEPX4
```
```
```
```          TRISP     Subsidiary to SEPELI
```
```
```
```          TRIX      Subsidiary to GENBUN
```
```
```
```          U11LS     Subsidiary to LLSIA
```
```
```
```          U11US     Subsidiary to ULSIA
```
```
```
```          U12LS     Subsidiary to LLSIA
```
```
```
```          U12US     Subsidiary to ULSIA
```
```
```
```          USRMAT    Subsidiary to SPLP
```
```
```
```          VNWRMS    Subsidiary to DEBDF
```
```
```
```          WNLIT     Subsidiary to WNNLS
```
```
```
```          WNLSM     Subsidiary to WNNLS
```
```
```
```          WNLT1     Subsidiary to WNLIT
```
```
```
```          WNLT2     Subsidiary to WNLIT
```
```
```
```          WNLT3     Subsidiary to WNLIT
```
```
```
```          XERBLA    Error handler for the Level 2 and Level 3 BLAS Routines.
```
```
```
```          XERCNT    Allow user control over handling of errors.
```
```
```
```          XERHLT    Abort program execution and print error message.
```
```
```
```          XERPRN    Print error messages processed by XERMSG.
```
```
```
```          XERSVE    Record that an error has occurred.
```
```
```
```          XPMU      To compute the values of Legendre functions for XLEGF.
```
```                    Method: backward mu-wise recurrence for P(-MU,NU,X) for
```
```                    fixed nu to obtain P(-MU2,NU1,X), P(-(MU2-1),NU1,X), ...,
```
```                    P(-MU1,NU1,X) and store in ascending mu order.
```
```
```
```          XPMUP     To compute the values of Legendre functions for XLEGF.
```
```                    This subroutine transforms an array of Legendre functions
```
```                    of the first kind of negative order stored in array PQA
```
```                    into Legendre functions of the first kind of positive
```
```                    order stored in array PQA. The original array is destroyed.
```
```
```
```          XPNRM     To compute the values of Legendre functions for XLEGF.
```
```                    This subroutine transforms an array of Legendre functions
```
```                    of the first kind of negative order stored in array PQA
```
```                    into normalized Legendre polynomials stored in array PQA.
```
```                    The original array is destroyed.
```
```
```
```          XPQNU     To compute the values of Legendre functions for XLEGF.
```
```                    This subroutine calculates initial values of P or Q using
```
```                    power series, then performs forward nu-wise recurrence to
```
```                    obtain P(-MU,NU,X), Q(0,NU,X), or Q(1,NU,X). The nu-wise
```
```                    recurrence is stable for P for all mu and for Q for mu=0,1.
```
```
```
```          XPSI      To compute values of the Psi function for XLEGF.
```
```
```
```          XQMU      To compute the values of Legendre functions for XLEGF.
```
```                    Method: forward mu-wise recurrence for Q(MU,NU,X) for fixed
```
```                    nu to obtain Q(MU1,NU,X), Q(MU1+1,NU,X), ..., Q(MU2,NU,X).
```
```
```
```          XQNU      To compute the values of Legendre functions for XLEGF.
```
```                    Method: backward nu-wise recurrence for Q(MU,NU,X) for
```
```                    fixed mu to obtain Q(MU1,NU1,X), Q(MU1,NU1+1,X), ...,
```
```                    Q(MU1,NU2,X).
```
```
```
```          YAIRY     Subsidiary to BESJ and BESY
```
```
```
```          ZABS      Subsidiary to ZBESH, ZBESI, ZBESJ, ZBESK, ZBESY, ZAIRY and
```
```                    ZBIRY
```
```
```
```          ZACAI     Subsidiary to ZAIRY
```
```
```
```          ZACON     Subsidiary to ZBESH and ZBESK
```
```
```
```          ZASYI     Subsidiary to ZBESI and ZBESK
```
```
```
```          ZBINU     Subsidiary to ZAIRY, ZBESH, ZBESI, ZBESJ, ZBESK and ZBIRY
```
```
```
```          ZBKNU     Subsidiary to ZAIRY, ZBESH, ZBESI and ZBESK
```
```
```
```          ZBUNI     Subsidiary to ZBESI and ZBESK
```
```
```
```          ZBUNK     Subsidiary to ZBESH and ZBESK
```
```
```
```          ZDIV      Subsidiary to ZBESH, ZBESI, ZBESJ, ZBESK, ZBESY, ZAIRY and
```
```                    ZBIRY
```
```
```
```          ZEXP      Subsidiary to ZBESH, ZBESI, ZBESJ, ZBESK, ZBESY, ZAIRY and
```
```                    ZBIRY
```
```
```
```          ZKSCL     Subsidiary to ZBESK
```
```
```
```          ZLOG      Subsidiary to ZBESH, ZBESI, ZBESJ, ZBESK, ZBESY, ZAIRY and
```
```                    ZBIRY
```
```
```
```          ZMLRI     Subsidiary to ZBESI and ZBESK
```
```
```
```          ZMLT      Subsidiary to ZBESH, ZBESI, ZBESJ, ZBESK, ZBESY, ZAIRY and
```
```                    ZBIRY
```
```
```
```          ZRATI     Subsidiary to ZBESH, ZBESI and ZBESK
```
```
```
```          ZS1S2     Subsidiary to ZAIRY and ZBESK
```
```
```
```          ZSERI     Subsidiary to ZBESI and ZBESK
```
```
```
```          ZSHCH     Subsidiary to ZBESH and ZBESK
```
```
```
```          ZSQRT     Subsidiary to ZBESH, ZBESI, ZBESJ, ZBESK, ZBESY, ZAIRY and
```
```                    ZBIRY
```
```
```
```          ZUCHK     Subsidiary to SERI, ZUOIK, ZUNK1, ZUNK2, ZUNI1, ZUNI2 and
```
```                    ZKSCL
```
```
```
```          ZUNHJ     Subsidiary to ZBESI and ZBESK
```
```
```
```          ZUNI1     Subsidiary to ZBESI and ZBESK
```
```
```
```          ZUNI2     Subsidiary to ZBESI and ZBESK
```
```
```
```          ZUNIK     Subsidiary to ZBESI and ZBESK
```
```
```
```          ZUNK1     Subsidiary to ZBESK
```
```
```
```          ZUNK2     Subsidiary to ZBESK
```
```
```
```          ZUOIK     Subsidiary to ZBESH, ZBESI and ZBESK
```
```
```
```          ZWRSK     Subsidiary to ZBESI and ZBESK
```
```
```
```
```
```SECTION III. Alphabetic List of Routines and Categories
```
```             As stated in the introduction, an asterisk (*) immediately
```
```             preceeding a routine name indicates a subsidiary routine.
```
```
```
``` AAAAAA      Z                          ACOSH       C4C
```
``` AI          C10D                       AIE         C10D
```
``` ALBETA      C7B                        ALGAMS      C7A
```
``` ALI         C5                         ALNGAM      C7A
```
``` ALNREL      C4B                        ASINH       C4C
```
```*ASYIK                                 *ASYJY
```
``` ATANH       C4C                        AVINT       H2A1B2
```
``` BAKVEC      D4C4                       BALANC      D4C1A
```
``` BALBAK      D4C4                       BANDR       D4C1B1
```
``` BANDV       D4C3                      *BCRH
```
```*BDIFF                                  BESI        C10B3
```
``` BESI0       C10B1                      BESI0E      C10B1
```
``` BESI1       C10B1                      BESI1E      C10B1
```
``` BESJ        C10A3                      BESJ0       C10A1
```
``` BESJ1       C10A1                      BESK        C10B3
```
``` BESK0       C10B1                      BESK0E      C10B1
```
``` BESK1       C10B1                      BESK1E      C10B1
```
``` BESKES      C10B3                     *BESKNU
```
``` BESKS       C10B3                      BESY        C10A3
```
``` BESY0       C10A1                      BESY1       C10A1
```
```*BESYNU                                 BETA        C7B
```
``` BETAI       C7F                        BFQAD       H2A2A1, E3, K6
```
``` BI          C10D                       BIE         C10D
```
``` BINOM       C1                         BINT4       E1A
```
``` BINTK       E1A                        BISECT      D4A5, D4C2A
```
```*BKIAS                                 *BKISR
```
```*BKSOL                                 *BLKTR1
```
``` BLKTRI      I2B4B                      BNDACC      D9
```
``` BNDSOL      D9                        *BNFAC
```
```*BNSLV                                  BQR         D4A6
```
```*BSGQ8                                  BSKIN       C10F
```
``` BSPDOC      E, E1A, K, Z               BSPDR       E3
```
``` BSPEV       E3, K6                    *BSPLVD
```
```*BSPLVN                                 BSPPP       E3, K6
```
``` BSPVD       E3, K6                     BSPVN       E3, K6
```
``` BSQAD       H2A2A1, E3, K6            *BSRH
```
``` BVALU       E3, K6                    *BVDER
```
```*BVPOR                                  BVSUP       I1B1
```
``` C0LGMC      C7A                       *C1MERG
```
```*C9LGMC      C7A                       *C9LN2R      C4B
```
```*CACAI                                 *CACON
```
``` CACOS       C4A                        CACOSH      C4C
```
``` CAIRY       C10D                       CARG        A4A
```
``` CASIN       C4A                        CASINH      C4C
```
```*CASYI                                  CATAN       C4A
```
``` CATAN2      C4A                        CATANH      C4C
```
``` CAXPY       D1A7                       CBABK2      D4C4
```
``` CBAL        D4C1A                      CBESH       C10A4
```
``` CBESI       C10B4                      CBESJ       C10A4
```
``` CBESK       C10B4                      CBESY       C10A4
```
``` CBETA       C7B                       *CBINU
```
``` CBIRY       C10D                      *CBKNU
```
```*CBLKT1                                 CBLKTR      I2B4B
```
``` CBRT        C2                        *CBUNI
```
```*CBUNK                                  CCBRT       C2
```
``` CCHDC       D2D1B                      CCHDD       D7B
```
``` CCHEX       D7B                        CCHUD       D7B
```
```*CCMPB                                  CCOPY       D1A5
```
``` CCOSH       C4C                        CCOT        C4A
```
``` CDCDOT      D1A4                      *CDCOR
```
```*CDCST                                 *CDIV
```
```*CDNTL                                 *CDNTP
```
``` CDOTC       D1A4                       CDOTU       D1A4
```
```*CDPSC                                 *CDPST
```
``` CDRIV1      I1A2, I1A1B                CDRIV2      I1A2, I1A1B
```
``` CDRIV3      I1A2, I1A1B               *CDSCL
```
```*CDSTP                                 *CDZRO
```
``` CEXPRL      C4B                       *CFFTB       J1A2
```
``` CFFTB1      J1A2                      *CFFTF       J1A2
```
``` CFFTF1      J1A2                      *CFFTI       J1A2
```
``` CFFTI1      J1A2                      *CFOD
```
``` CG          D4A4                       CGAMMA      C7A
```
``` CGAMR       C7A                        CGBCO       D2C2
```
``` CGBDI       D3C2                       CGBFA       D2C2
```
``` CGBMV       D1B4                       CGBSL       D2C2
```
``` CGECO       D2C1                       CGEDI       D2C1, D3C1
```
``` CGEEV       D4A4                       CGEFA       D2C1
```
``` CGEFS       D2C1                       CGEIR       D2C1
```
``` CGEMM       D1B6                       CGEMV       D1B4
```
``` CGERC       D1B4                       CGERU       D1B4
```
``` CGESL       D2C1                       CGTSL       D2C2A
```
``` CH          D4A3                       CHBMV       D1B4
```
``` CHEMM       D1B6                       CHEMV       D1B4
```
``` CHER        D1B4                       CHER2       D1B4
```
``` CHER2K      D1B6                       CHERK       D1B6
```
```*CHFCM                                  CHFDV       E3, H1
```
``` CHFEV       E3                        *CHFIE
```
``` CHICO       D2D1A                      CHIDI       D2D1A, D3D1A
```
``` CHIEV       D4A3                       CHIFA       D2D1A
```
``` CHISL       D2D1A                      CHKDER      F3, G4C
```
```*CHKPR4                                *CHKPRM
```
```*CHKSN4                                *CHKSNG
```
``` CHPCO       D2D1A                      CHPDI       D2D1A, D3D1A
```
``` CHPFA       D2D1A                      CHPMV       D1B4
```
``` CHPR        D1B4                       CHPR2       D1B4
```
``` CHPSL       D2D1A                      CHU         C11
```
``` CINVIT      D4C2B                     *CKSCL
```
``` CLBETA      C7B                        CLNGAM      C7A
```
``` CLNREL      C4B                        CLOG10      C4B
```
``` CMGNBN      I2B4B                     *CMLRI
```
```*CMPCSG                                *CMPOSD
```
```*CMPOSN                                *CMPOSP
```
```*CMPTR3                                *CMPTRX
```
``` CNBCO       D2C2                       CNBDI       D3C2
```
``` CNBFA       D2C2                       CNBFS       D2C2
```
``` CNBIR       D2C2                       CNBSL       D2C2
```
``` COMBAK      D4C4                       COMHES      D4C1B2
```
``` COMLR       D4C2B                      COMLR2      D4C2B
```
```*COMPB                                  COMQR       D4C2B
```
``` COMQR2      D4C2B                      CORTB       D4C4
```
``` CORTH       D4C1B2                     COSDG       C4A
```
```*COSGEN                                 COSQB       J1A3
```
```*COSQB1      J1A3                       COSQF       J1A3
```
```*COSQF1      J1A3                       COSQI       J1A3
```
``` COST        J1A3                       COSTI       J1A3
```
``` COT         C4A                       *CPADD
```
``` CPBCO       D2D2                       CPBDI       D3D2
```
``` CPBFA       D2D2                       CPBSL       D2D2
```
```*CPEVL                                 *CPEVLR
```
``` CPOCO       D2D1B                      CPODI       D2D1B, D3D1B
```
``` CPOFA       D2D1B                      CPOFS       D2D1B
```
``` CPOIR       D2D1B                      CPOSL       D2D1B
```
``` CPPCO       D2D1B                      CPPDI       D2D1B, D3D1B
```
``` CPPFA       D2D1B                      CPPSL       D2D1B
```
``` CPQR79      F1A1B                     *CPROC
```
```*CPROCP                                *CPROD
```
```*CPRODP                                 CPSI        C7C
```
``` CPTSL       D2D2A                      CPZERO      F1A1B
```
``` CQRDC       D5                         CQRSL       D9, D2C1
```
```*CRATI                                  CROTG       D1B10
```
```*CS1S2                                  CSCAL       D1A6
```
```*CSCALE                                *CSERI
```
``` CSEVL       C3A2                      *CSHCH
```
``` CSICO       D2C1                       CSIDI       D2C1, D3C1
```
``` CSIFA       D2C1                       CSINH       C4C
```
``` CSISL       D2C1                       CSPCO       D2C1
```
``` CSPDI       D2C1, D3C1                 CSPFA       D2C1
```
``` CSPSL       D2C1                      *CSROOT
```
``` CSROT       D1B10                      CSSCAL      D1A6
```
``` CSVDC       D6                         CSWAP       D1A5
```
``` CSYMM       D1B6                       CSYR2K      D1B6
```
``` CSYRK       D1B6                       CTAN        C4A
```
``` CTANH       C4C                        CTBMV       D1B4
```
``` CTBSV       D1B4                       CTPMV       D1B4
```
``` CTPSV       D1B4                       CTRCO       D2C3
```
``` CTRDI       D2C3, D3C3                 CTRMM       D1B6
```
``` CTRMV       D1B4                       CTRSL       D2C3
```
``` CTRSM       D1B6                       CTRSV       D1B4
```
```*CUCHK                                 *CUNHJ
```
```*CUNI1                                 *CUNI2
```
```*CUNIK                                 *CUNK1
```
```*CUNK2                                 *CUOIK
```
``` CV          L7A3                      *CWRSK
```
``` D1MACH      R1                        *D1MERG
```
```*D1MPYQ                                *D1UPDT
```
```*D9AIMP      C10D                      *D9ATN1      C4A
```
```*D9B0MP      C10A1                     *D9B1MP      C10A1
```
```*D9CHU       C11                       *D9GMIC      C7E
```
```*D9GMIT      C7E                       *D9KNUS      C10B3
```
```*D9LGIC      C7E                       *D9LGIT      C7E
```
```*D9LGMC      C7E                       *D9LN2R      C4B
```
``` D9PAK       A6B                        D9UPAK      A6B
```
``` DACOSH      C4C                        DAI         C10D
```
``` DAIE        C10D                       DASINH      C4C
```
``` DASUM       D1A3A                     *DASYIK
```
```*DASYJY                                 DATANH      C4C
```
``` DAVINT      H2A1B2                     DAWS        C8C
```
``` DAXPY       D1A7                       DBCG        D2A4, D2B4
```
```*DBDIFF                                 DBESI       C10B3
```
``` DBESI0      C10B1                      DBESI1      C10B1
```
``` DBESJ       C10A3                      DBESJ0      C10A1
```
``` DBESJ1      C10A1                      DBESK       C10B3
```
``` DBESK0      C10B1                      DBESK1      C10B1
```
``` DBESKS      C10B3                      DBESY       C10A3
```
``` DBESY0      C10A1                      DBESY1      C10A1
```
``` DBETA       C7B                        DBETAI      C7F
```
``` DBFQAD      H2A2A1, E3, K6             DBHIN       N1
```
``` DBI         C10D                       DBIE        C10D
```
``` DBINOM      C1                         DBINT4      E1A
```
``` DBINTK      E1A                       *DBKIAS
```
```*DBKISR                                *DBKSOL
```
``` DBNDAC      D9                         DBNDSL      D9
```
```*DBNFAC                                *DBNSLV
```
``` DBOCLS      K1A2A, G2E, G2H1, G2H2     DBOLS       K1A2A, G2E, G2H1, G2H2
```
```*DBOLSM                                *DBSGQ8
```
``` DBSI0E      C10B1                      DBSI1E      C10B1
```
``` DBSK0E      C10B1                      DBSK1E      C10B1
```
``` DBSKES      C10B3                      DBSKIN      C10F
```
```*DBSKNU                                 DBSPDR      E3, K6
```
``` DBSPEV      E3, K6                     DBSPPP      E3, K6
```
``` DBSPVD      E3, K6                     DBSPVN      E3, K6
```
``` DBSQAD      H2A2A1, E3, K6            *DBSYNU
```
``` DBVALU      E3, K6                    *DBVDER
```
```*DBVPOR                                 DBVSUP      I1B1
```
``` DCBRT       C2                         DCDOT       D1A4
```
```*DCFOD                                  DCG         D2B4
```
``` DCGN        D2A4, D2B4                 DCGS        D2A4, D2B4
```
``` DCHDC       D2B1B                      DCHDD       D7B
```
``` DCHEX       D7B                       *DCHFCM
```
``` DCHFDV      E3, H1                     DCHFEV      E3
```
```*DCHFIE                                *DCHKW       R2
```
``` DCHU        C11                        DCHUD       D7B
```
``` DCKDER      F3, G4C                   *DCOEF
```
``` DCOPY       D1A5                       DCOPYM      D1A5
```
``` DCOSDG      C4A                        DCOT        C4A
```
``` DCOV        K1B1                       DCPPLT      N1
```
```*DCSCAL                                 DCSEVL      C3A2
```
``` DCV         L7A3                      *DDAINI
```
```*DDAJAC                                *DDANRM
```
```*DDASLV                                 DDASSL      I1A2
```
```*DDASTP                                *DDATRP
```
``` DDAWS       C8C                       *DDAWTS
```
```*DDCOR                                 *DDCST
```
``` DDEABM      I1A1B                      DDEBDF      I1A2
```
``` DDERKF      I1A1A                     *DDES
```
```*DDNTL                                 *DDNTP
```
```*DDOGLG                                 DDOT        D1A4
```
```*DDPSC                                 *DDPST
```
``` DDRIV1      I1A2, I1A1B                DDRIV2      I1A2, I1A1B
```
``` DDRIV3      I1A2, I1A1B               *DDSCL
```
```*DDSTP                                 *DDZRO
```
``` DE1         C5                         DEABM       I1A1B
```
``` DEBDF       I1A2                       DEFC        K1A1A1, K1A2A, L8A3
```
```*DEFCMN                                *DEFE4
```
```*DEFEHL                                *DEFER
```
``` DEI         C5                        *DENORM
```
``` DERF        C8A, L5A1E                 DERFC       C8A, L5A1E
```
``` DERKF       I1A1A                     *DERKFS
```
```*DES                                   *DEXBVP
```
``` DEXINT      C5                         DEXPRL      C4B
```
``` DFAC        C1                         DFC         K1A1A1, K1A2A, L8A3
```
```*DFCMN                                 *DFDJC1
```
```*DFDJC3                                *DFEHL
```
```*DFSPVD                                *DFSPVN
```
```*DFULMT                                 DFZERO      F1B
```
``` DGAMI       C7E                        DGAMIC      C7E
```
``` DGAMIT      C7E                        DGAMLM      C7A, R2
```
```*DGAMLN      C7A                        DGAMMA      C7A
```
``` DGAMR       C7A                       *DGAMRN
```
``` DGAUS8      H2A1A1                     DGBCO       D2A2
```
``` DGBDI       D3A2                       DGBFA       D2A2
```
``` DGBMV       D1B4                       DGBSL       D2A2
```
``` DGECO       D2A1                       DGEDI       D3A1, D2A1
```
``` DGEFA       D2A1                       DGEFS       D2A1
```
``` DGEMM       D1B6                       DGEMV       D1B4
```
``` DGER        D1B4                       DGESL       D2A1
```
``` DGLSS       D9, D5                     DGMRES      D2A4, D2B4
```
``` DGTSL       D2A2A                     *DH12
```
```*DHELS       D2A4, D2B4                *DHEQR       D2A4, D2B4
```
``` DHFTI       D9                        *DHKSEQ
```
```*DHSTRT                                *DHVNRM
```
``` DINTP       I1A1B                      DINTRV      E3, K6
```
```*DINTYD                                 DIR         D2A4, D2B4
```
```*DJAIRY                                 DLBETA      C7B
```
``` DLGAMS      C7A                        DLI         C5
```
``` DLLSIA      D9, D5                     DLLTI2      D2E
```
``` DLNGAM      C7A                        DLNREL      C4B
```
``` DLPDOC      D2A4, D2B4, Z             *DLPDP
```
``` DLSEI       K1A2A, D9                 *DLSI
```
```*DLSOD                                 *DLSSUD
```
```*DMACON                                *DMGSBV
```
```*DMOUT                                 *DMPAR
```
``` DNBCO       D2A2                       DNBDI       D3A2
```
``` DNBFA       D2A2                       DNBFS       D2A2
```
``` DNBSL       D2A2                       DNLS1       K1B1A1, K1B1A2
```
``` DNLS1E      K1B1A1, K1B1A2             DNRM2       D1A3B
```
``` DNSQ        F2A                        DNSQE       F2A
```
```*DOGLEG                                *DOHTRL
```
``` DOMN        D2A4, D2B4                *DORTH       D2A4, D2B4
```
```*DORTHR                                 DP1VLU      K6
```
``` DPBCO       D2B2                       DPBDI       D3B2
```
``` DPBFA       D2B2                       DPBSL       D2B2
```
``` DPCHBS      E3                        *DPCHCE
```
```*DPCHCI                                 DPCHCM      E3
```
```*DPCHCS                                *DPCHDF
```
``` DPCHFD      E3, H1                     DPCHFE      E3
```
``` DPCHIA      E3, H2A1B2                 DPCHIC      E1A
```
``` DPCHID      E3, H2A1B2                 DPCHIM      E1A
```
```*DPCHKT      E3                        *DPCHNG
```
``` DPCHSP      E1A                       *DPCHST
```
```*DPCHSW                                 DPCOEF      K1A1A2
```
``` DPFQAD      H2A2A1, E3, K6            *DPIGMR      D2A4, D2B4
```
```*DPINCW                                *DPINIT
```
```*DPINTM                                *DPJAC
```
``` DPLINT      E1B                       *DPLPCE
```
```*DPLPDM                                *DPLPFE
```
```*DPLPFL                                *DPLPMN
```
```*DPLPMU                                *DPLPUP
```
```*DPNNZR                                 DPOCH       C1, C7A
```
``` DPOCH1      C1, C7A                    DPOCO       D2B1B
```
``` DPODI       D2B1B, D3B1B               DPOFA       D2B1B
```
``` DPOFS       D2B1B                      DPOLCF      E1B
```
``` DPOLFT      K1A1A2                     DPOLVL      E3
```
```*DPOPT                                  DPOSL       D2B1B
```
``` DPPCO       D2B1B                      DPPDI       D2B1B, D3B1B
```
``` DPPERM      N8                         DPPFA       D2B1B
```
```*DPPGQ8                                 DPPQAD      H2A2A1, E3, K6
```
``` DPPSL       D2B1B                      DPPVAL      E3, K6
```
```*DPRVEC                                *DPRWPG
```
```*DPRWVR                                 DPSI        C7C
```
``` DPSIFN      C7C                       *DPSIXN
```
``` DPSORT      N6A1B, N6A2B               DPTSL       D2B2A
```
``` DQAG        H2A1A1                     DQAGE       H2A1A1
```
``` DQAGI       H2A3A1, H2A4A1             DQAGIE      H2A3A1, H2A4A1
```
``` DQAGP       H2A2A1                     DQAGPE      H2A2A1
```
``` DQAGS       H2A1A1                     DQAGSE      H2A1A1
```
``` DQAWC       H2A2A1, J4                 DQAWCE      H2A2A1, J4
```
``` DQAWF       H2A3A1                     DQAWFE      H2A3A1
```
``` DQAWO       H2A2A1                     DQAWOE      H2A2A1
```
``` DQAWS       H2A2A1                     DQAWSE      H2A2A1
```
``` DQC25C      H2A2A2, J4                 DQC25F      H2A2A2
```
``` DQC25S      H2A2A2                    *DQCHEB
```
``` DQDOTA      D1A4                       DQDOTI      D1A4
```
```*DQELG                                 *DQFORM
```
``` DQK15       H2A1A2                     DQK15I      H2A3A2, H2A4A2
```
``` DQK15W      H2A2A2                     DQK21       H2A1A2
```
``` DQK31       H2A1A2                     DQK41       H2A1A2
```
``` DQK51       H2A1A2                     DQK61       H2A1A2
```
``` DQMOMO      H2A2A1, C3A2               DQNC79      H2A1A1
```
``` DQNG        H2A1A1                    *DQPSRT
```
``` DQRDC       D5                        *DQRFAC
```
``` DQRSL       D9, D2A1                  *DQRSLV
```
```*DQWGTC                                *DQWGTF
```
```*DQWGTS                                 DRC         C14
```
``` DRC3JJ      C19                        DRC3JM      C19
```
``` DRC6J       C19                        DRD         C14
```
```*DREADP                                *DREORT
```
``` DRF         C14                        DRJ         C14
```
```*DRKFAB                                *DRKFS
```
```*DRLCAL      D2A4, D2B4                 DROT        D1A8
```
``` DROTG       D1B10                      DROTM       D1A8
```
``` DROTMG      D1B10                     *DRSCO
```
``` DS2LT       D2E                        DS2Y        D1B9
```
``` DSBMV       D1B4                       DSCAL       D1A6
```
``` DSD2S       D2E                        DSDBCG      D2A4, D2B4
```
``` DSDCG       D2B4                       DSDCGN      D2A4, D2B4
```
``` DSDCGS      D2A4, D2B4                 DSDGMR      D2A4, D2B4
```
``` DSDI        D1B4                       DSDOMN      D2A4, D2B4
```
``` DSDOT       D1A4                       DSDS        D2E
```
``` DSDSCL      D2E                        DSGS        D2A4, D2B4
```
``` DSICCG      D2B4                       DSICO       D2B1A
```
``` DSICS       D2E                        DSIDI       D2B1A, D3B1A
```
``` DSIFA       D2B1A                      DSILUR      D2A4, D2B4
```
``` DSILUS      D2E                        DSINDG      C4A
```
``` DSISL       D2B1A                      DSJAC       D2A4, D2B4
```
``` DSLI        D2A3                       DSLI2       D2A3
```
``` DSLLTI      D2E                        DSLUBC      D2A4, D2B4
```
``` DSLUCN      D2A4, D2B4                 DSLUCS      D2A4, D2B4
```
``` DSLUGM      D2A4, D2B4                 DSLUI       D2E
```
``` DSLUI2      D2E                        DSLUI4      D2E
```
``` DSLUOM      D2A4, D2B4                 DSLUTI      D2E
```
```*DSLVS                                  DSMMI2      D2E
```
``` DSMMTI      D2E                        DSMTV       D1B4
```
``` DSMV        D1B4                       DSORT       N6A2B
```
``` DSOS        F2A                       *DSOSEQ
```
```*DSOSSL                                 DSPCO       D2B1A
```
``` DSPDI       D2B1A, D3B1A               DSPENC      C5
```
``` DSPFA       D2B1A                      DSPLP       G2A2
```
``` DSPMV       D1B4                       DSPR        D1B4
```
``` DSPR2       D1B4                       DSPSL       D2B1A
```
``` DSTEPS      I1A1B                     *DSTOD
```
```*DSTOR1                                *DSTWAY
```
```*DSUDS                                 *DSVCO
```
``` DSVDC       D6                         DSWAP       D1A5
```
``` DSYMM       D1B6                       DSYMV       D1B4
```
``` DSYR        D1B4                       DSYR2       D1B4
```
``` DSYR2K      D1B6                       DSYRK       D1B6
```
``` DTBMV       D1B4                       DTBSV       D1B4
```
``` DTIN        N1                         DTOUT       N1
```
``` DTPMV       D1B4                       DTPSV       D1B4
```
``` DTRCO       D2A3                       DTRDI       D2A3, D3A3
```
``` DTRMM       D1B6                       DTRMV       D1B4
```
``` DTRSL       D2A3                       DTRSM       D1B6
```
``` DTRSV       D1B4                      *DU11LS
```
```*DU11US                                *DU12LS
```
```*DU12US                                 DULSIA      D9
```
```*DUSRMT                                *DVECS
```
```*DVNRMS                                *DVOUT
```
```*DWNLIT                                *DWNLSM
```
```*DWNLT1                                *DWNLT2
```
```*DWNLT3                                 DWNNLS      K1A2A
```
```*DWRITP                                *DWUPDT
```
```*DX                                    *DX4
```
``` DXADD       A3D                        DXADJ       A3D
```
``` DXC210      A3D                        DXCON       A3D
```
```*DXLCAL      D2A4, D2B4                 DXLEGF      C3A2, C9
```
``` DXNRMP      C3A2, C9                  *DXPMU       C3A2, C9
```
```*DXPMUP      C3A2, C9                  *DXPNRM      C3A2, C9
```
```*DXPQNU      C3A2, C9                  *DXPSI       C7C
```
```*DXQMU       C3A2, C9                  *DXQNU       C3A2, C9
```
``` DXRED       A3D                        DXSET       A3D
```
```*DY                                    *DY4
```
```*DYAIRY                                 E1          C5
```
``` EFC         K1A1A1, K1A2A, L8A3       *EFCMN
```
``` EI          C5                         EISDOC      D4, Z
```
``` ELMBAK      D4C4                       ELMHES      D4C1B2
```
``` ELTRAN      D4C4                      *ENORM
```
``` ERF         C8A, L5A1E                 ERFC        C8A, L5A1E
```
```*EXBVP                                  EXINT       C5
```
``` EXPREL      C4B                       *EZFFT1
```
``` EZFFTB      J1A1                       EZFFTF      J1A1
```
``` EZFFTI      J1A1                       FAC         C1
```
``` FC          K1A1A1, K1A2A, L8A3       *FCMN
```
```*FDJAC1                                *FDJAC3
```
``` FDUMP       R3                         FFTDOC      J1, Z
```
``` FIGI        D4C1C                      FIGI2       D4C1C
```
```*FULMAT                                 FUNDOC      C, Z
```
``` FZERO       F1B                        GAMI        C7E
```
``` GAMIC       C7E                        GAMIT       C7E
```
``` GAMLIM      C7A, R2                   *GAMLN       C7A
```
``` GAMMA       C7A                        GAMR        C7A
```
```*GAMRN                                  GAUS8       H2A1A1
```
``` GENBUN      I2B4B                     *H12
```
``` HFTI        D9                        *HKSEQ
```
``` HPPERM      N8                         HPSORT      N6A1C, N6A2C
```
``` HQR         D4C2B                      HQR2        D4C2B
```
```*HSTART                                 HSTCRT      I2B1A1A
```
```*HSTCS1                                 HSTCSP      I2B1A1A
```
``` HSTCYL      I2B1A1A                    HSTPLR      I2B1A1A
```
``` HSTSSP      I2B1A1A                    HTRIB3      D4C4
```
``` HTRIBK      D4C4                       HTRID3      D4C1B1
```
``` HTRIDI      D4C1B1                    *HVNRM
```
``` HW3CRT      I2B1A1A                    HWSCRT      I2B1A1A
```
```*HWSCS1                                 HWSCSP      I2B1A1A
```
``` HWSCYL      I2B1A1A                    HWSPLR      I2B1A1A
```
```*HWSSS1                                 HWSSSP      I2B1A1A
```
``` I1MACH      R1                        *I1MERG
```
``` ICAMAX      D1A2                       ICOPY       D1A5
```
``` IDAMAX      D1A2                      *IDLOC
```
``` IMTQL1      D4A5, D4C2A                IMTQL2      D4A5, D4C2A
```
``` IMTQLV      D4A5, D4C2A               *INDXA
```
```*INDXB                                 *INDXC
```
``` INITDS      C3A2                       INITS       C3A2
```
``` INTRV       E3, K6                    *INTYD
```
``` INVIT       D4C2B                     *INXCA
```
```*INXCB                                 *INXCC
```
```*IPLOC                                  IPPERM      N8
```
``` IPSORT      N6A1A, N6A2A               ISAMAX      D1A2
```
```*ISDBCG      D2A4, D2B4                *ISDCG       D2B4
```
```*ISDCGN      D2A4, D2B4                *ISDCGS      D2A4, D2B4
```
```*ISDGMR      D2A4, D2B4                *ISDIR       D2A4, D2B4
```
```*ISDOMN      D2A4, D2B4                 ISORT       N6A2A
```
```*ISSBCG      D2A4, D2B4                *ISSCG       D2B4
```
```*ISSCGN      D2A4, D2B4                *ISSCGS      D2A4, D2B4
```
```*ISSGMR      D2A4, D2B4                *ISSIR       D2A4, D2B4
```
```*ISSOMN      D2A4, D2B4                 ISWAP       D1A5
```
```*IVOUT                                 *J4SAVE
```
```*JAIRY                                 *LA05AD
```
```*LA05AS                                *LA05BD
```
```*LA05BS                                *LA05CD
```
```*LA05CS                                *LA05ED
```
```*LA05ES                                 LLSIA       D9, D5
```
```*LMPAR                                 *LPDP
```
```*LSAME       R, N3                      LSEI        K1A2A, D9
```
```*LSI                                   *LSOD
```
```*LSSODS                                *LSSUDS
```
```*MACON                                 *MC20AD
```
```*MC20AS                                *MGSBV
```
``` MINFIT      D9                        *MINSO4
```
```*MINSOL                                *MPADD
```
```*MPADD2                                *MPADD3
```
```*MPBLAS                                *MPCDM
```
```*MPCHK                                 *MPCMD
```
```*MPDIVI                                *MPERR
```
```*MPMAXR                                *MPMLP
```
```*MPMUL                                 *MPMUL2
```
```*MPMULI                                *MPNZR
```
```*MPOVFL                                *MPSTR
```
```*MPUNFL                                 NUMXER      R3C
```
```*OHTROL                                *OHTROR
```
``` ORTBAK      D4C4                       ORTHES      D4C1B2
```
```*ORTHO4                                *ORTHOG
```
```*ORTHOL                                *ORTHOR
```
``` ORTRAN      D4C4                      *PASSB
```
```*PASSB2                                *PASSB3
```
```*PASSB4                                *PASSB5
```
```*PASSF                                 *PASSF2
```
```*PASSF3                                *PASSF4
```
```*PASSF5                                 PCHBS       E3
```
```*PCHCE                                 *PCHCI
```
``` PCHCM       E3                        *PCHCS
```
```*PCHDF                                  PCHDOC      E1A, Z
```
``` PCHFD       E3, H1                     PCHFE       E3
```
``` PCHIA       E3, H2A1B2                 PCHIC       E1A
```
``` PCHID       E3, H2A1B2                 PCHIM       E1A
```
```*PCHKT       E3                        *PCHNGS
```
``` PCHSP       E1A                       *PCHST
```
```*PCHSW                                  PCOEF       K1A1A2
```
``` PFQAD       H2A2A1, E3, K6            *PGSF
```
```*PIMACH                                *PINITM
```
```*PJAC                                  *PNNZRS
```
``` POCH        C1, C7A                    POCH1       C1, C7A
```
``` POIS3D      I2B4B                     *POISD2
```
```*POISN2                                *POISP2
```
``` POISTG      I2B4B                      POLCOF      E1B
```
``` POLFIT      K1A1A2                     POLINT      E1B
```
``` POLYVL      E3                        *POS3D1
```
```*POSTG2                                *PPADD
```
```*PPGQ8                                 *PPGSF
```
```*PPPSF                                  PPQAD       H2A2A1, E3, K6
```
```*PPSGF                                 *PPSPF
```
``` PPVAL       E3, K6                    *PROC
```
```*PROCP                                 *PROD
```
```*PRODP                                 *PRVEC
```
```*PRWPGE                                *PRWVIR
```
```*PSGF                                   PSI         C7C
```
``` PSIFN       C7C                       *PSIXN
```
``` PVALUE      K6                        *PYTHAG
```
``` QAG         H2A1A1                     QAGE        H2A1A1
```
``` QAGI        H2A3A1, H2A4A1             QAGIE       H2A3A1, H2A4A1
```
``` QAGP        H2A2A1                     QAGPE       H2A2A1
```
``` QAGS        H2A1A1                     QAGSE       H2A1A1
```
``` QAWC        H2A2A1, J4                 QAWCE       H2A2A1, J4
```
``` QAWF        H2A3A1                     QAWFE       H2A3A1
```
``` QAWO        H2A2A1                     QAWOE       H2A2A1
```
``` QAWS        H2A2A1                     QAWSE       H2A2A1
```
``` QC25C       H2A2A2, J4                 QC25F       H2A2A2
```
``` QC25S       H2A2A2                    *QCHEB
```
```*QELG                                  *QFORM
```
``` QK15        H2A1A2                     QK15I       H2A3A2, H2A4A2
```
``` QK15W       H2A2A2                     QK21        H2A1A2
```
``` QK31        H2A1A2                     QK41        H2A1A2
```
``` QK51        H2A1A2                     QK61        H2A1A2
```
``` QMOMO       H2A2A1, C3A2               QNC79       H2A1A1
```
``` QNG         H2A1A1                     QPDOC       H2, Z
```
```*QPSRT                                 *QRFAC
```
```*QRSOLV                                *QS2I1D      N6A2A
```
```*QS2I1R      N6A2A                     *QWGTC
```
```*QWGTF                                 *QWGTS
```
``` QZHES       D4C1B3                     QZIT        D4C1B3
```
``` QZVAL       D4C2C                      QZVEC       D4C3
```
``` R1MACH      R1                        *R1MPYQ
```
```*R1UPDT                                *R9AIMP      C10D
```
```*R9ATN1      C4A                       *R9CHU       C11
```
```*R9GMIC      C7E                       *R9GMIT      C7E
```
```*R9KNUS      C10B3                     *R9LGIC      C7E
```
```*R9LGIT      C7E                       *R9LGMC      C7E
```
```*R9LN2R      C4B                        R9PAK       A6B
```
``` R9UPAK      A6B                       *RADB2
```
```*RADB3                                 *RADB4
```
```*RADB5                                 *RADBG
```
```*RADF2                                 *RADF3
```
```*RADF4                                 *RADF5
```
```*RADFG                                  RAND        L6A21
```
``` RATQR       D4A5, D4C2A                RC          C14
```
``` RC3JJ       C19                        RC3JM       C19
```
``` RC6J        C19                        RD          C14
```
``` REBAK       D4C4                       REBAKB      D4C4
```
``` REDUC       D4C1C                      REDUC2      D4C1C
```
```*REORT                                  RF          C14
```
```*RFFTB       J1A1                       RFFTB1      J1A1
```
```*RFFTF       J1A1                       RFFTF1      J1A1
```
```*RFFTI       J1A1                       RFFTI1      J1A1
```
``` RG          D4A2                       RGAUSS      L6A14
```
``` RGG         D4B2                       RJ          C14
```
```*RKFAB                                  RPQR79      F1A1A
```
``` RPZERO      F1A1A                      RS          D4A1
```
``` RSB         D4A6                      *RSCO
```
``` RSG         D4B1                       RSGAB       D4B1
```
``` RSGBA       D4B1                       RSP         D4A1
```
``` RST         D4A5                       RT          D4A5
```
``` RUNIF       L6A21                     *RWUPDT
```
```*S1MERG                                 SASUM       D1A3A
```
``` SAXPY       D1A7                       SBCG        D2A4, D2B4
```
``` SBHIN       N1                         SBOCLS      K1A2A, G2E, G2H1, G2H2
```
``` SBOLS       K1A2A, G2E, G2H1, G2H2    *SBOLSM
```
``` SCASUM      D1A3A                      SCG         D2B4
```
``` SCGN        D2A4, D2B4                 SCGS        D2A4, D2B4
```
``` SCHDC       D2B1B                      SCHDD       D7B
```
``` SCHEX       D7B                       *SCHKW       R2
```
``` SCHUD       D7B                       *SCLOSM
```
``` SCNRM2      D1A3B                     *SCOEF
```
``` SCOPY       D1A5                       SCOPYM      D1A5
```
``` SCOV        K1B1                       SCPPLT      N1
```
```*SDAINI                                *SDAJAC
```
```*SDANRM                                *SDASLV
```
``` SDASSL      I1A2                      *SDASTP
```
```*SDATRP                                *SDAWTS
```
```*SDCOR                                 *SDCST
```
```*SDNTL                                 *SDNTP
```
``` SDOT        D1A4                      *SDPSC
```
```*SDPST                                  SDRIV1      I1A2, I1A1B
```
``` SDRIV2      I1A2, I1A1B                SDRIV3      I1A2, I1A1B
```
```*SDSCL                                  SDSDOT      D1A4
```
```*SDSTP                                 *SDZRO
```
``` SEPELI      I2B1A2                     SEPX4       I2B1A2
```
``` SGBCO       D2A2                       SGBDI       D3A2
```
``` SGBFA       D2A2                       SGBMV       D1B4
```
``` SGBSL       D2A2                       SGECO       D2A1
```
``` SGEDI       D2A1, D3A1                 SGEEV       D4A2
```
``` SGEFA       D2A1                       SGEFS       D2A1
```
``` SGEIR       D2A1                       SGEMM       D1B6
```
``` SGEMV       D1B4                       SGER        D1B4
```
``` SGESL       D2A1                       SGLSS       D9, D5
```
``` SGMRES      D2A4, D2B4                 SGTSL       D2A2A
```
```*SHELS       D2A4, D2B4                *SHEQR       D2A4, D2B4
```
``` SINDG       C4A                        SINQB       J1A3
```
``` SINQF       J1A3                       SINQI       J1A3
```
``` SINT        J1A3                       SINTI       J1A3
```
``` SINTRP      I1A1B                      SIR         D2A4, D2B4
```
``` SLLTI2      D2E                        SLPDOC      D2A4, D2B4, Z
```
```*SLVS                                  *SMOUT
```
``` SNBCO       D2A2                       SNBDI       D3A2
```
``` SNBFA       D2A2                       SNBFS       D2A2
```
``` SNBIR       D2A2                       SNBSL       D2A2
```
``` SNLS1       K1B1A1, K1B1A2             SNLS1E      K1B1A1, K1B1A2
```
``` SNRM2       D1A3B                      SNSQ        F2A
```
``` SNSQE       F2A                       *SODS
```
``` SOMN        D2A4, D2B4                *SOPENM
```
```*SORTH       D2A4, D2B4                 SOS         F2A
```
```*SOSEQS                                *SOSSOL
```
``` SPBCO       D2B2                       SPBDI       D3B2
```
``` SPBFA       D2B2                       SPBSL       D2B2
```
```*SPELI4                                *SPELIP
```
``` SPENC       C5                        *SPIGMR      D2A4, D2B4
```
```*SPINCW                                *SPINIT
```
``` SPLP        G2A2                      *SPLPCE
```
```*SPLPDM                                *SPLPFE
```
```*SPLPFL                                *SPLPMN
```
```*SPLPMU                                *SPLPUP
```
``` SPOCO       D2B1B                      SPODI       D2B1B, D3B1B
```
``` SPOFA       D2B1B                      SPOFS       D2B1B
```
``` SPOIR       D2B1B                     *SPOPT
```
``` SPOSL       D2B1B                      SPPCO       D2B1B
```
``` SPPDI       D2B1B, D3B1B               SPPERM      N8
```
``` SPPFA       D2B1B                      SPPSL       D2B1B
```
``` SPSORT      N6A1B, N6A2B               SPTSL       D2B2A
```
``` SQRDC       D5                         SQRSL       D9, D2A1
```
```*SREADP                                *SRLCAL      D2A4, D2B4
```
``` SROT        D1A8                       SROTG       D1B10
```
``` SROTM       D1A8                       SROTMG      D1B10
```
``` SS2LT       D2E                        SS2Y        D1B9
```
``` SSBMV       D1B4                       SSCAL       D1A6
```
``` SSD2S       D2E                        SSDBCG      D2A4, D2B4
```
``` SSDCG       D2B4                       SSDCGN      D2A4, D2B4
```
``` SSDCGS      D2A4, D2B4                 SSDGMR      D2A4, D2B4
```
``` SSDI        D1B4                       SSDOMN      D2A4, D2B4
```
``` SSDS        D2E                        SSDSCL      D2E
```
``` SSGS        D2A4, D2B4                 SSICCG      D2B4
```
``` SSICO       D2B1A                      SSICS       D2E
```
``` SSIDI       D2B1A, D3B1A               SSIEV       D4A1
```
``` SSIFA       D2B1A                      SSILUR      D2A4, D2B4
```
``` SSILUS      D2E                        SSISL       D2B1A
```
``` SSJAC       D2A4, D2B4                 SSLI        D2A3
```
``` SSLI2       D2A3                       SSLLTI      D2E
```
``` SSLUBC      D2A4, D2B4                 SSLUCN      D2A4, D2B4
```
``` SSLUCS      D2A4, D2B4                 SSLUGM      D2A4, D2B4
```
``` SSLUI       D2E                        SSLUI2      D2E
```
``` SSLUI4      D2E                        SSLUOM      D2A4, D2B4
```
``` SSLUTI      D2E                        SSMMI2      D2E
```
``` SSMMTI      D2E                        SSMTV       D1B4
```
``` SSMV        D1B4                       SSORT       N6A2B
```
``` SSPCO       D2B1A                      SSPDI       D2B1A, D3B1A
```
``` SSPEV       D4A1                       SSPFA       D2B1A
```
``` SSPMV       D1B4                       SSPR        D1B4
```
``` SSPR2       D1B4                       SSPSL       D2B1A
```
``` SSVDC       D6                         SSWAP       D1A5
```
``` SSYMM       D1B6                       SSYMV       D1B4
```
``` SSYR        D1B4                       SSYR2       D1B4
```
``` SSYR2K      D1B6                       SSYRK       D1B6
```
``` STBMV       D1B4                       STBSV       D1B4
```
``` STEPS       I1A1B                      STIN        N1
```
```*STOD                                  *STOR1
```
``` STOUT       N1                         STPMV       D1B4
```
``` STPSV       D1B4                       STRCO       D2A3
```
``` STRDI       D2A3, D3A3                 STRMM       D1B6
```
``` STRMV       D1B4                       STRSL       D2A3
```
``` STRSM       D1B6                       STRSV       D1B4
```
```*STWAY                                 *SUDS
```
```*SVCO                                  *SVD
```
```*SVECS                                 *SVOUT
```
```*SWRITP                                *SXLCAL      D2A4, D2B4
```
```*TEVLC                                 *TEVLS
```
``` TINVIT      D4C3                       TQL1        D4A5, D4C2A
```
``` TQL2        D4A5, D4C2A                TQLRAT      D4A5, D4C2A
```
``` TRBAK1      D4C4                       TRBAK3      D4C4
```
``` TRED1       D4C1B1                     TRED2       D4C1B1
```
``` TRED3       D4C1B1                    *TRI3
```
``` TRIDIB      D4A5, D4C2A               *TRIDQ
```
```*TRIS4                                 *TRISP
```
```*TRIX                                   TSTURM      D4A5, D4C2A
```
```*U11LS                                 *U11US
```
```*U12LS                                 *U12US
```
``` ULSIA       D9                        *USRMAT
```
```*VNWRMS                                *WNLIT
```
```*WNLSM                                 *WNLT1
```
```*WNLT2                                 *WNLT3
```
``` WNNLS       K1A2A                      XADD        A3D
```
``` XADJ        A3D                        XC210       A3D
```
``` XCON        A3D                       *XERBLA      R3
```
``` XERCLR      R3C                       *XERCNT      R3C
```
``` XERDMP      R3C                       *XERHLT      R3C
```
``` XERMAX      R3C                        XERMSG      R3C
```
```*XERPRN      R3C                       *XERSVE      R3
```
``` XGETF       R3C                        XGETUA      R3C
```
``` XGETUN      R3C                        XLEGF       C3A2, C9
```
``` XNRMP       C3A2, C9                  *XPMU        C3A2, C9
```
```*XPMUP       C3A2, C9                  *XPNRM       C3A2, C9
```
```*XPQNU       C3A2, C9                  *XPSI        C7C
```
```*XQMU        C3A2, C9                  *XQNU        C3A2, C9
```
``` XRED        A3D                        XSET        A3D
```
``` XSETF       R3A                        XSETUA      R3B
```
``` XSETUN      R3B                       *YAIRY
```
```*ZABS                                  *ZACAI
```
```*ZACON                                  ZAIRY       C10D
```
```*ZASYI                                  ZBESH       C10A4
```
``` ZBESI       C10B4                      ZBESJ       C10A4
```
``` ZBESK       C10B4                      ZBESY       C10A4
```
```*ZBINU                                  ZBIRY       C10D
```
```*ZBKNU                                 *ZBUNI
```
```*ZBUNK                                 *ZDIV
```
```*ZEXP                                  *ZKSCL
```
```*ZLOG                                  *ZMLRI
```
```*ZMLT                                  *ZRATI
```
```*ZS1S2                                 *ZSERI
```
```*ZSHCH                                 *ZSQRT
```
```*ZUCHK                                 *ZUNHJ
```
```*ZUNI1                                 *ZUNI2
```
```*ZUNIK                                 *ZUNK1
```
```*ZUNK2                                 *ZUOIK
```
```*ZWRSK
```

```.
```