SECTION I. User-callable Routines Category D. Linear Algebra

```D1.  Elementary vector and matrix operations
D1.  Elementary vector and matrix operations
D2.  Solution of systems of linear equations
D3.  Determinants
D4.  Eigenvalues, eigenvectors
D5.  QR decomposition, Gram-Schmidt orthogonalization
D6.  Singular value decomposition
D7.  Update matrix decompositions
D9.  Overdetermined or underdetermined systems of equations, singular systems, pseudo-inverses

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

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

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.

```