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Notes

1.

The appendix consists mainly of indexes giving the nearest LAPACK equivalents of LINPACK and EISPACK routines. These indexes should not be followed blindly or rigidly, especially when two or more LINPACK or EISPACK routines are being used together: in many such cases one of the LAPACK driver routines may be a suitable replacement.

2.

When two or more LAPACK routines are given in a single entry, these routines must be combined to achieve the equivalent function.

3.

For LINPACK, an index is given for equivalents of the real LINPACK routines; these equivalences apply also to the corresponding complex routines. A separate table is included for equivalences of complex Hermitian routines. For EISPACK, an index is given for all real and complex routines, since there is no direct 1-to-1 correspondence between real and complex routines in EISPACK.

4.

A few of the less commonly used routines in LINPACK and EISPACK have no equivalents in Release 1.0 of LAPACK; equivalents for some of these (but not all) are planned for a future release.

5.

For some EISPACK routines, there are LAPACK routines providing similar functionality, but using a significantly different method, or LAPACK routines which provide only part of the functionality; such routines are marked by a $\dag$ . For example, the EISPACK routine ELMHES uses non-orthogonal transformations, whereas the nearest equivalent LAPACK routine, SGEHRD, uses orthogonal transformations.

6.

In some cases the LAPACK equivalents require matrices to be stored in a different storage scheme. For example:

EISPACK routines BANDR, BANDV, BQR and the driver routine RSB require the lower triangle of a symmetric band matrix to be stored in a different storage scheme to that used in LAPACK, which is illustrated in subsection 5.3.3. The corresponding storage scheme used by the EISPACK routines is:

symmetric band matrix A EISPACK band storage

$\left( \begin{array}{ccccc} a_{11} & a_{21} & a_{31} & & \\ a_{21} & a_{22} &... ...a_{43} & a_{44} & a_{54} \\ & & a_{53} & a_{54} & a_{55} \end{array} \right)$ $\begin{array}{ccccc} \ast & \ast & a_{11} \\ \ast & a_{21} & a_{22} \\ a_{... ...& a_{33} \\ a_{42} & a_{43} & a_{44} \\ a_{53} & a_{54} & a_{55} \end{array}$
EISPACK routines TRED1, TRED2, TRED3, HTRID3, HTRIDI, TQL1, TQL2, IMTQL1, IMTQL2, RATQR, TQLRAT and the driver routine RST store the off-diagonal elements of a symmetric tridiagonal matrix in elements 2:n of the array E, whereas LAPACK routines use elements 1:n-1.

7.

The EISPACK and LINPACK routines for the singular value decomposition return the matrix of right singular vectors, V, whereas the corresponding LAPACK routines return the transposed matrix V^T.

8.

In general, the argument lists of the LAPACK routines are different from those of the corresponding EISPACK and LINPACK routines, and the workspace requirements are often different.

LAPACK equivalents of LINPACK routines for real matrices
LINPACK	LAPACK	Function of LINPACK routine
SCHDC		Cholesky factorization with diagonal pivoting option
SCHDD		Rank-1 downdate of a Cholesky factorization or the triangular factor of a QR factorization
SCHEX		Modifies a Cholesky factorization under permutations of the original matrix
SCHUD		Rank-1 update of a Cholesky factorization or the triangular factor of a QR factorization
SGBCO	SLANGB SGBTRF SGBCON	LU factorization and condition estimation of a general band matrix
SGBDI		Determinant of a general band matrix, after factorization by SGBCO or SGBFA
SGBFA	SGBTRF	LU factorization of a general band matrix
SGBSL	SGBTRS	Solves a general band system of linear equations, after factorization by SGBCO or SGBFA
SGECO	SLANGE SGETRF SGECON	LU factorization and condition estimation of a general matrix
SGEDI	SGETRI	Determinant and inverse of a general matrix, after factorization by SGECO or SGEFA
SGEFA	SGETRF	LU factorization of a general matrix
SGESL	SGETRS	Solves a general system of linear equations, after factorization by SGECO or SGEFA
SGTSL	SGTSV	Solves a general tridiagonal system of linear equations
SPBCO	SLANSB SPBTRF SPBCON	Cholesky factorization and condition estimation of a symmetric positive definite band matrix
SPBDI		Determinant of a symmetric positive definite band matrix, after factorization by SPBCO or SPBFA
SPBFA	SPBTRF	Cholesky factorization of a symmetric positive definite band matrix
SPBSL	SPBTRS	Solves a symmetric positive definite band system of linear equations, after factorization by SPBCO or SPBFA
SPOCO	SLANSY SPOTRF SPOCON	Cholesky factorization and condition estimation of a symmetric positive definite matrix
SPODI	SPOTRI	Determinant and inverse of a symmetric positive definite matrix, after factorization by SPOCO or SPOFA
SPOFA	SPOTRF	Cholesky factorization of a symmetric positive definite matrix
SPOSL	SPOTRS	Solves a symmetric positive definite system of linear equations, after factorization by SPOCO or SPOFA
SPPCO	SLANSY SPPTRF SPPCON	Cholesky factorization and condition estimation of a symmetric positive definite matrix (packed storage)

LAPACK equivalents of LINPACK routines for real matrices (continued)

LINPACK LAPACK Function of LINPACK routine

SPPDI SPPTRI Determinant and inverse of a symmetric positive definite matrix, after factorization by SPPCO or SPPFA (packed storage)

SPPFA SPPTRF Cholesky factorization of a symmetric positive definite matrix (packed storage)

SPPSL SPPTRS Solves a symmetric positive definite system of linear equations, after factorization by SPPCO or SPPFA (packed storage)

SPTSL SPTSV Solves a symmetric positive definite tridiagonal system of linear equations

SQRDC SGEQPF or SGEQRF QR factorization with optional column pivoting

SQRSL SORMQR STRSV¹ Solves linear least squares problems after factorization by SQRDC

SSICO SLANSY SSYTRF SSYCON Symmetric indefinite factorization and condition estimation of a symmetric indefinite matrix

SSIDI SSYTRI Determinant, inertia and inverse of a symmetric indefinite matrix, after factorization by SSICO or SSIFA

SSIFA SSYTRF Symmetric indefinite factorization of a symmetric indefinite matrix

SSISL SSYTRS Solves a symmetric indefinite system of linear equations, after factorization by SSICO or SSIFA

SSPCO SLANSP SSPTRF SSPCON Symmetric indefinite factorization and condition estimation of a symmetric indefinite matrix (packed storage)

SSPDI SSPTRI Determinant, inertia and inverse of a symmetric indefinite matrix, after factorization by SSPCO or SSPFA (packed storage)

SSPFA SSPTRF Symmetric indefinite factorization of a symmetric indefinite matrix (packed storage)

SSPSL SSPTRS Solves a symmetric indefinite system of linear equations, after factorization by SSPCO or SSPFA (packed storage)

SSVDC SGESVD All or part of the singular value decomposition of a general matrix

STRCO STRCON Condition estimation of a triangular matrix

STRDI STRTRI Determinant and inverse of a triangular matrix

STRSL STRTRS Solves a triangular system of linear equations

LAPACK equivalents of LINPACK routines for complex Hermitian matrices
LINPACK	LAPACK	Function of LINPACK routine
CHICO	CHECON	Factors a complex Hermitian matrix by elimination with symmetric pivoting and estimates the condition number of the matrix
CHIDI	CHETRI	Computes the determinant, inertia and inverse of a complex Hermitian matrix using the factors from CHIFA
CHIFA	CHETRF	Factors a complex Hermitian matrix by elimination with symmetric pivoting
CHISL	CHETRS	Solves the complex Hermitian system Ax=b using the factors computed by CHIFA
CHPCO	CHPCON	Factors a complex Hermitian matrix stored in packed form by elimination with symmetric pivoting and estimates the condition number of the matrix
CHPDI	CHPTRI	Computes the determinant, intertia and inverse of a complex Hermitian matrix using the factors from CHPFA , where the matrix is stored in packed form
CHPFA	CHPTRF	Factors a complex Hermitian matrix stored in packed form by elimination with symmetric pivoting
CHPSL	CHPTRS	Solves the complex Hermitian system Ax=b using the factors computed by CHPFA

LAPACK equivalents of EISPACK routines
EISPACK	LAPACK	Function of EISPACK routine
BAKVEC		Backtransform eigenvectors after transformation by FIGI
BALANC	SGEBAL	Balance a real matrix
BALBAK	SGEBAK	Backtransform eigenvectors of a real matrix after balancing by BALANC
BANDR	SSBTRD	Reduce a real symmetric band matrix to tridiagonal form
BANDV	SSBEVX SGBSV	Selected eigenvectors of a real band matrix by inverse iteration
BISECT	SSTEBZ	Eigenvalues in a specified interval of a real symmetric tridiagonal matrix
BQR	SSBEVX $\dag$	Some eigenvalues of a real symmetric band matrix
CBABK2	CGEBAK	Backtransform eigenvectors of a complex matrix after balancing by CBAL
CBAL	CGEBAL	Balance a complex matrix
CG	CGEEV	All eigenvalues and optionally eigenvectors of a complex general matrix (driver routine)
CH	CHEEV	All eigenvalues and optionally eigenvectors of a complex Hermitian matrix (driver routine)
CINVIT	CHSEIN	Selected eigenvectors of a complex upper Hessenberg matrix by inverse iteration
COMBAK	CUNMHR $\dag$	Backtransform eigenvectors of a complex matrix after reduction by COMHES
COMHES	CGEHRD $\dag$	Reduce a complex matrix to upper Hessenberg form by a non-unitary transformation
COMLR	CHSEQR $\dag$	All eigenvalues of a complex upper Hessenberg matrix, by the LR algorithm
COMLR2	CUNGHR CHSEQR CTREVC $\dag$	All eigenvalues/vectors of a complex matrix by the LR algorithm, after reduction by COMHES
COMQR	CHSEQR	All eigenvalues of a complex upper Hessenberg matrix by the QR algorithm
COMQR2	CUNGHR CHSEQR CTREVC	All eigenvalues/vectors of a complex matrix by the QR algorithm, after reduction by CORTH
CORTB	CUNMHR	Backtransform eigenvectors of a complex matrix, after reduction by CORTH
CORTH	CGEHRD	Reduce a complex matrix to upper Hessenberg form by a unitary transformation
ELMBAK	SORMHR $\dag$	Backtransform eigenvectors of a real matrix after reduction by ELMHES
ELMHES	SGEHRD $\dag$	Reduce a real matrix to upper Hessenberg form by a non-orthogonal transformation
ELTRAN	SORGHR $\dag$	Generate transformation matrix used by ELMHES

LAPACK equivalents of EISPACK routines (continued)

EISPACK LAPACK Function of EISPACK routine

FIGI Transform a nonsymmetric tridiagonal matrix of special form to a symmetric matrix

FIGI2 As FIGI, with generation of the transformation matrix

HQR SHSEQR All eigenvalues of a complex upper Hessenberg matrix by the QR algorithm

HQR2 SHSEQR STREVC All eigenvalues/vectors of a real upper Hessenberg matrix by the QR algorithm

HTRIB3 CUPMTR Backtransform eigenvectors of a complex Hermitian matrix after reduction by HTRID3

HTRIBK CUNMTR Backtransform eigenvectors of a complex Hermitian matrix after reduction by HTRIDI

HTRID3 CHPTRD Reduce a complex Hermitian matrix to tridiagonal form (packed storage)

HTRIDI CHETRD Reduce a complex Hermitian matrix to tridiagonal form

IMTQL1 SSTEQR or SSTERF $\dag$ All eigenvalues of a symmetric tridiagonal matrix, by the implicit QL algorithm

IMTQL2 SSTEQR or SSTEDC $\dag$ All eigenvalues/vectors of a symmetric tridiagonal matrix, by the implicit QL algorithm

IMTQLV SSTEQR As IMTQL1, preserving the input matrix

INVIT SHSEIN Selected eigenvectors of a real upper Hessenberg matrix, by inverse iteration

MINFIT SGELSS Minimum norm solution of a linear least squares problem, using the singular value decomposition

ORTBAK SORMHR Backtransform eigenvectors of a real matrix after reduction to upper Hessenberg form by ORTHES

ORTHES SGEHRD Reduce a real matrix to upper Hessenberg form by an orthogonal transformation

ORTRAN SORGHR Generate orthogonal transformation matrix used by ORTHES

QZHES SGGHRD Reduce a real generalized eigenproblem $Ax = \lambda Bx$ to a form in which A is upper Hessenberg and B is upper triangular

QZIT SHGEQZ Generalized Schur factorization of a real generalized eigenproblem,

QZVAL after reduction by QZHES

QZVEC STGEVC All eigenvectors of a real generalized eigenproblem from generalized Schur factorization

RATQR SSTEBZ $\dag$ Extreme eigenvalues of a symmetric tridiagonal matrix using the rational QR algorithm with Newton corrections

REBAK STRSM¹ Backtransform eigenvectors of a symmetric definite generalized eigenproblem $Ax = \lambda Bx$ or $ABx=\lambda x$ after reduction by REDUC or REDUC2

REBAKB STRMM² Backtransform eigenvectors of a symmetric definite generalized eigenproblem $BAx=\lambda x$ after reduction by REDUC2

LAPACK equivalents of EISPACK routines (continued)
EISPACK	LAPACK	Function of EISPACK routine
REDUC	SSYGST	Reduce the symmetric definite generalized eigenproblem $Ax = \lambda Bx$ to a standard symmetric eigenproblem
REDUC2	SSYGST	Reduce the symmetric definite generalized eigenproblem $ABx=\lambda x$ or $BAx=\lambda x$ to a standard symmetric eigenproblem
RG	SGEEV	All eigenvalues and optionally eigenvectors of a real general matrix (driver routine)
RGG	SGEGV	All eigenvalues and optionally eigenvectors or a real generalized eigenproblem (driver routine)
RS	SSYEV or SSYEVD $\dag$	All eigenvalues and optionally eigenvectors of a real symmetric matrix (driver routine)
RSB	SSBEV or SSBEVD $\dag$	All eigenvalues and optionally eigenvectors of a real symmetric band matrix (driver routine)
RSG	SSYGV	All eigenvalues and optionally eigenvectors of a real symmetric definite generalized eigenproblem $Ax = \lambda Bx$ (driver routine)
RSGAB	SSYGV	All eigenvalues and optionally eigenvectors of a real symmetric definite generalized eigenproblem $ABx=\lambda x$ (driver routine)
RSGBA	SSYGV	All eigenvalues and optionally eigenvectors of a real symmetric definite generalized eigenproblem $BAx=\lambda x$ (driver routine)
RSM	SSYEVX	Selected eigenvalues and optionally eigenvectors of a real symmetric matrix (driver routine)
RSP	SSPEV or SSPEVD $\dag$	All eigenvalues and optionally eigenvectors of a real symmetric matrix (packed storage) (driver routine)
RST	SSTEV or SSTEVD $\dag$	All eigenvalues and optionally eigenvectors of a real symmetric tridiagonal matrix (driver routine)
RT		All eigenvalues and optionally eigenvectors of a real tridiagonal matrix of special form (driver routine)
SVD	SGESVD	Singular value decomposition of a real matrix
TINVIT	SSTEIN	Selected eigenvectors of a symmetric tridiagonal matrix by inverse iteration
TQL1	SSTEQR $\dag$ or SSTERF $\dag$	All eigenvalues of a symmetric tridiagonal matrix by the explicit QL algorithm
TQL2	SSTEQR $\dag$ or SSTEDC $\dag$	All eigenvalues/vectors of a symmetric tridiagonal matrix by the explicit QL algorithm
TQLRAT	SSTERF	All eigenvalues of a symmetric tridiagonal matrix by a rational variant of the QL algorithm

LAPACK equivalents of EISPACK routines (continued)
EISPACK	LAPACK	Function of EISPACK routine
TRBAK1	SORMTR	Backtransform eigenvectors of a real symmetric matrix after reduction by TRED1
TRBAK3	SOPMTR	Backtransform eigenvectors of a real symmetric matrix after reduction by TRED3 (packed storage)
TRED1	SSYTRD	Reduce a real symmetric matrix to tridiagonal form
TRED2	SSYTRD SORGTR	As TRED1, but also generating the orthogonal transformation matrix
TRED3	SSPTRD	Reduce a real symmetric matrix to tridiagonal form (packed storage)
TRIDIB	SSTEBZ	Eigenvalues between specified indices of a symmetric tridiagonal matrix
TSTURM	SSTEBZ SSTEIN	Eigenvalues in a specified interval of a symmetric tridiagonal matrix, and corresponding eigenvectors by inverse iteration

Next: LAPACK Working Notes Up: Converting from LINPACK or Previous: Converting from LINPACK or Contents Index

Susan Blackford
1999-10-01

symmetric band matrix A	EISPACK band storage
$\left( \begin{array}{ccccc} a_{11} & a_{21} & a_{31} & & \\ a_{21} & a_{22} &... ...a_{43} & a_{44} & a_{54} \\ & & a_{53} & a_{54} & a_{55} \end{array} \right)$	$\begin{array}{ccccc} \ast & \ast & a_{11} \\ \ast & a_{21} & a_{22} \\ a_{... ...& a_{33} \\ a_{42} & a_{43} & a_{44} \\ a_{53} & a_{54} & a_{55} \end{array}$