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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 . 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

  - 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 VT.

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 | 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 | Backtransform eigenvectors of a complex matrix after reduction by COMHES
COMHES | CGEHRD | Reduce a complex matrix to upper Hessenberg form by a non-unitary transformation
COMLR | CHSEQR | All eigenvalues of a complex upper Hessenberg matrix, by the LR algorithm
COMLR2 | CUNGHR CHSEQR CTREVC | 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 | Backtransform eigenvectors of a real matrix after reduction by ELMHES
ELMHES | SGEHRD | Reduce a real matrix to upper Hessenberg form by a non-orthogonal transformation
ELTRAN | SORGHR | 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 | All eigenvalues of a symmetric tridiagonal matrix, by the implicit QL algorithm
IMTQL2 | SSTEQR or SSTEDC | 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 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 | 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 or after reduction by REDUC or REDUC2
REBAKB | STRMM2 | Backtransform eigenvectors of a symmetric definite generalized eigenproblem after reduction by REDUC2

LAPACK equivalents of EISPACK routines (continued)
EISPACK | LAPACK | Function of EISPACK routine
REDUC | SSYGST | Reduce the symmetric definite generalized eigenproblem to a standard symmetric eigenproblem
REDUC2 | SSYGST | Reduce the symmetric definite generalized eigenproblem or 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 | All eigenvalues and optionally eigenvectors of a real symmetric matrix (driver routine)
RSB | SSBEV or SSBEVD | 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 (driver routine)
RSGAB | SSYGV | All eigenvalues and optionally eigenvectors of a real symmetric definite generalized eigenproblem (driver routine)
RSGBA | SSYGV | All eigenvalues and optionally eigenvectors of a real symmetric definite generalized eigenproblem (driver routine)
RSM | SSYEVX | Selected eigenvalues and optionally eigenvectors of a real symmetric matrix (driver routine)
RSP | SSPEV or SSPEVD | All eigenvalues and optionally eigenvectors of a real symmetric matrix (packed storage) (driver routine)
RST | SSTEV or SSTEVD | 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 or SSTERF | All eigenvalues of a symmetric tridiagonal matrix by the explicit QL algorithm
TQL2 | SSTEQR or SSTEDC | 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

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