SLATEC Common Mathematical Library Version 4.1 Table of Contents 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 which are otherwise equivalent. The names of equivalent routines are listed 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, I integer, H character, L logical, and A is a pseudo-type given to routines 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 directly by library users. They are listed here so that users will be able to avoid duplicating names that are used by the CML and for the benefit of programmers who may be able to use them in the construction of new routines 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 has at least one category. An asterisk (*) immediately preceding a 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). I. Differential and integral equations I1. Ordinary differential equations I1A. Initial value problems I1A1. General, nonstiff or mildly stiff I1A1A. One-step methods (e.g., Runge-Kutta) DERKF-S Solve an initial value problem in ordinary differential DDERKF-D equations using a Runge-Kutta-Fehlberg scheme. I1A1B. Multistep methods (e.g., Adams' predictor-corrector) 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. I1A2. Stiff and mixed algebraic-differential equations 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. I1B. Multipoint boundary value problems I1B1. Linear 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. I2. Partial differential equations I2B. Elliptic boundary value problems I2B1. Linear I2B1A. Second order I2B1A1. Poisson (Laplace) or Helmholz equation I2B1A1A. Rectangular domain (or topologically rectangular in the coordinate 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). I2B1A2. Other separable problems 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. I2B4. Service routines I2B4B. Solution of discretized elliptic equations 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