# lapack/single

# --------------------------------------------------------
# Available SIMPLE and DIVIDE AND CONQUER DRIVER routines:
# --------------------------------------------------------

file sgesv.f  sgesv.f plus dependencies
prec single
for  Solves a general system of linear equations AX=B.
gams d2a1

file sgbsv.f  sgbsv.f plus dependencies
prec single
for  Solves a general banded system of linear equations AX=B.
gams d2a2

file sgtsv.f  sgtsv.f plus dependencies
prec single
for  Solves a general tridiagonal system of linear equations AX=B.
gams d2a2a

file sposv.f  sposv.f plus dependencies
prec single
for  Solves a symmetric positive definite system of linear
,    equations AX=B.
gams d2b1b

file sppsv.f  sppsv.f plus dependencies
prec single
for  Solves a symmetric positive definite system of linear
,    equations AX=B, where A is held in packed storage.
gams d2b1b

file spbsv.f  spbsv.f plus dependencies
prec single
for  Solves a symmetric positive definite banded system
,    of linear equations AX=B.
gams d2b2

file sptsv.f  sptsv.f plus dependencies
prec single
for  Solves a symmetric positive definite tridiagonal system
,    of linear equations AX=B.
gams d2b2a

file ssysv.f  ssysv.f plus dependencies
prec single
for  Solves a real symmetric indefinite system of linear equations AX=B.
gams d2b1a

file sspsv.f  sspsv.f plus dependencies
prec single
for  Solves a real symmetric indefinite system of linear equations AX=B,
,    where A is held in packed storage.
gams d2b1a

file sgels.f  sgels.f plus dependencies
prec single
for  Computes the least squares solution to an over-determined system
,    of linear equations, A X=B or A**H X=B,  or the minimum norm
,    solution of an under-determined system, where A is a general
,    rectangular matrix of full rank,  using a QR or LQ factorization
,    of A.
gams d9a1

file sgelsd.f  sgelsd.f plus dependencies
prec single
for  Computes the least squares solution to an over-determined system
,    of linear equations, A X=B or A**H X=B,  or the minimum norm
,    solution of an under-determined system, using a divide and conquer
,    method, where A is a general rectangular matrix of full rank,
,    using a QR or LQ factorization of A.
gams d9a1

file sgglse.f  sgglse.f plus dependencies
prec single
for  Solves the LSE (Constrained Linear Least Squares Problem) using
,    the GRQ (Generalized RQ) factorization
gams d9b1

file sggglm.f  sggglm.f plus dependencies
prec single
for  Solves the GLM (Generalized Linear Regression Model) using
,    the GQR (Generalized QR) factorization

file ssyev.f  ssyev.f plus dependencies
prec single
for  Computes all eigenvalues, and optionally, eigenvectors of a real
,    symmetric matrix.
gams d4a1

file ssyevd.f  ssyevd.f plus dependencies
prec single
for  Computes all eigenvalues, and optionally, eigenvectors of a real
,    symmetric matrix.  If eigenvectors are desired, it uses a divide
,    and conquer algorithm.
gams d4a1

file sspev.f  sspev.f plus dependencies
prec single
for  Computes all eigenvalues, and optionally, eigenvectors of a real
,    symmetric matrix in packed storage.
gams d4a1

file sspevd.f  sspevd.f plus dependencies
prec single
for  Computes all eigenvalues, and optionally, eigenvectors of a real
,    symmetric matrix in packed storage.  If eigenvectors are desired,
,    it uses a divide and conquer algorithm.
gams d4a1

file ssbev.f  ssbev.f plus dependencies
prec single
for  Computes all eigenvalues, and optionally, eigenvectors of a real
,    symmetric band matrix.
gams d4a1, d4a6

file ssbevd.f  ssbevd.f plus dependencies
prec single
for  Computes all eigenvalues, and optionally, eigenvectors of a real
,    symmetric band matrix.  If eigenvectors are desired, it uses a
,    divide and conquer algorithm.
gams d4a1, d4a6

file sstev.f  sstev.f plus dependencies
prec single
for  Computes all eigenvalues, and optionally, eigenvectors of a real
,    symmetric tridiagonal matrix.
gams d4a1, d4a5

file sstevd.f  sstevd.f plus dependencies
prec single
for  Computes all eigenvalues, and optionally, eigenvectors of a real
,    symmetric tridiagonal matrix.  If eigenvectors are desired, it uses
,    a divide and conquer algorithm.
gams d4a1, d4a5

file sgees.f  sgees.f plus dependencies
prec single
for  Computes the eigenvalues and Schur factorization of a general
,    matrix, and orders the factorization so that selected eigenvalues
,    are at the top left of the Schur form.
gams d4a2

file sgeev.f  sgeev.f plus dependencies
prec single
for  Computes the eigenvalues and left and right eigenvectors of
,    a general matrix.
gams d4a2

file sgesvd.f  sgesvd.f plus dependencies
prec single
for  Computes the singular value decomposition (SVD) of a general
,    rectangular matrix.
gams d6

file sgesdd.f  sgesdd.f plus dependencies
prec single
for  Computes the singular value decomposition (SVD) of a general
,    rectangular matrix using divide-and-conquer.
gams d6

file ssygv.f  ssygv.f plus dependencies
prec single
for  Computes all eigenvalues and the eigenvectors of  a generalized
,    symmetric-definite generalized eigenproblem,
,    Ax= lambda Bx,  ABx= lambda x,  or BAx= lambda x.
gams d4b1

file ssygvd.f  ssygvd.f plus dependencies
prec single
for  Computes all eigenvalues and the eigenvectors of  a generalized
,    symmetric-definite generalized eigenproblem,
,    Ax= lambda Bx,  ABx= lambda x,  or BAx= lambda x.
,    If eigenvectors are desired, it uses a divide and conquer algorithm.
gams d4b1

file sspgv.f  sspgv.f plus dependencies
prec single
for  Computes all eigenvalues and eigenvectors of  a generalized
,    symmetric-definite generalized eigenproblem,  Ax= lambda
,    Bx,  ABx= lambda x,  or BAx= lambda x, where A and B are in packed
,    storage.
gams d4b1

file sspgvd.f  sspgvd.f plus dependencies
prec single
for  Computes all eigenvalues and eigenvectors of  a generalized
,    symmetric-definite generalized eigenproblem,  Ax= lambda
,    Bx,  ABx= lambda x,  or BAx= lambda x, where A and B are in packed
,    storage.
,    If eigenvectors are desired, it uses a divide and conquer algorithm.
gams d4b1

file ssbgv.f  ssbgv.f plus dependencies
prec single
for  Computes all the eigenvalues, and optionally, the eigenvectors
,    of a real generalized symmetric-definite banded eigenproblem, of
,    the form A*x=(lambda)*B*x.  A and B are assumed to be symmetric
,    and banded, and B is also positive definite.

file ssbgvd.f  ssbgvd.f plus dependencies
prec single
for  Computes all the eigenvalues, and optionally, the eigenvectors
,    of a real generalized symmetric-definite banded eigenproblem, of
,    the form A*x=(lambda)*B*x.  A and B are assumed to be symmetric
,    and banded, and B is also positive definite.
,    If eigenvectors are desired, it uses a divide and conquer algorithm.

file sgegs.f  sgegs.f plus dependencies
prec single
for  Computes the generalized eigenvalues, Schur form, and left and/or
,    right Schur vectors for a pair of nonsymmetric matrices

file sgges.f  sgges.f plus dependencies
prec single
for  Computes the generalized eigenvalues, Schur form, and left and/or
,    right Schur vectors for a pair of nonsymmetric matrices

file sgegv.f  sgegv.f plus dependencies
prec single
for  Computes the generalized eigenvalues, and left and/or right
,    generalized eigenvectors for a pair of nonsymmetric matrices

file sggev.f  sggev.f plus dependencies
prec single
for  Computes the generalized eigenvalues, and left and/or right
,    generalized eigenvectors for a pair of nonsymmetric matrices

file sggsvd.f  sggsvd.f plus dependencies
prec single
for  Computes the Generalized Singular Value Decomposition

# -----------------------------------------
# Available EXPERT and RRR DRIVER routines:
# -----------------------------------------

file sgesvx.f  sgesvx.f plus dependencies
prec single
for  Solves a general system of linear equations AX=B, A**T X=B
,    or A**H X=B, and provides an estimate of the condition number
,    and error bounds on the solution.
gams d2a1

file sgbsvx.f  sgbsvx.f plus dependencies
prec single
for  Solves a general banded system of linear equations AX=B,
,    A**T X=B or A**H X=B, and provides an estimate of the condition
,    number and error bounds on the solution.
gams d2a2

file sgtsvx.f  sgtsvx.f plus dependencies
prec single
for  Solves a general tridiagonal system of linear equations AX=B,
,    A**T X=B or A**H X=B, and provides an estimate of the condition
,    number  and error bounds on the solution.
gams d2a2a

file sposvx.f  sposvx.f plus dependencies
prec single
for  Solves a symmetric positive definite system of linear
,    equations AX=B, and provides an estimate of the condition number
,    and error bounds on the solution.
gams d2b1b

file sppsvx.f  sppsvx.f plus dependencies
prec single
for  Solves a symmetric positive definite system of linear
,    equations AX=B, where A is held in packed storage, and provides
,    an estimate of the condition number and error bounds on the
,    solution.
gams d2b1b

file spbsvx.f  spbsvx.f plus dependencies
prec single
for  Solves a symmetric positive definite banded system
,    of linear equations AX=B, and provides an estimate of the condition
,    number and error bounds on the solution.
gams d2b2

file sptsvx.f  sptsvx.f plus dependencies
prec single
for  Solves a symmetric positive definite tridiagonal
,    system of linear equations AX=B, and provides an estimate of
,    the condition number and error bounds on the solution.
gams d2b2a

file ssysvx.f  ssysvx.f plus dependencies
prec single
for  Solves a real symmetric
,    indefinite system  of linear equations AX=B, and provides an
,    estimate of the condition number and error bounds on the solution.
gams d2b1a

file sspsvx.f  sspsvx.f plus dependencies
prec single
for  Solves a real symmetric
,    indefinite system of linear equations AX=B, where A is held
,    in packed storage, and provides an estimate of the condition
,    number and error bounds on the solution.
gams d2b1a

file sgelsx.f  sgelsx.f plus dependencies
prec single
for  Computes the minimum norm least squares solution to an over-
,    or under-determined system of linear equations A X=B, using a
,    complete orthogonal factorization of A.
gams d9a1

file sgelsy.f  sgelsy.f plus dependencies
prec single
for  Computes the minimum norm least squares solution to an over-
,    or under-determined system of linear equations A X=B, using a
,    complete orthogonal factorization of A.
gams d9a1

file sgelss.f  sgelss.f plus dependencies
prec single
for  Computes the minimum norm least squares solution to an over-
,    or under-determined system of linear equations A X=B,  using
,    the singular value decomposition of A.
gams d9a1

file ssyevx.f  ssyevx.f plus dependencies
prec single
for  Computes selected eigenvalues and eigenvectors of a symmetric matrix.
gams d4a1

file ssyevr.f  ssyevr.f plus dependencies
prec single
for  Computes selected eigenvalues, and optionally, eigenvectors of a real
,    symmetric matrix.  Eigenvalues are computed by the dqds
,    algorithm, and eigenvectors are computed from various "good" LDL^T
,    representations (also known as Relatively Robust Representations).
gams d4a1, d4a5

file ssygvx.f  ssygvx.f plus dependencies
prec single
for  Computes selected eigenvalues, and optionally, the eigenvectors of
,    a generalized symmetric-definite generalized eigenproblem,
,    Ax= lambda Bx,  ABx= lambda x,  or BAx= lambda x.
gams d4b1

file sspevx.f  sspevx.f plus dependencies
prec single
for  Computes selected eigenvalues and eigenvectors of a
,    symmetric matrix in packed storage.
gams d4a1

file sspgvx.f  sspgvx.f plus dependencies
prec single
for  Computes selected eigenvalues, and optionally, eigenvectors of
,    a generalized symmetric-definite generalized eigenproblem,  Ax= lambda
,    Bx,  ABx= lambda x,  or BAx= lambda x, where A and B are in packed
,    storage.
gams d4b1

file ssbevx.f  ssbevx.f plus dependencies
prec single
for  Computes selected eigenvalues and eigenvectors of a
,    symmetric band matrix.
gams d4a1, d4a6

file ssbgvx.f  ssbgvx.f plus dependencies
prec single
for  Computes selected eigenvalues, and optionally, the eigenvectors
,    of a real generalized symmetric-definite banded eigenproblem, of
,    the form A*x=(lambda)*B*x.  A and B are assumed to be symmetric
,    and banded, and B is also positive definite.

file sstevx.f  sstevx.f plus dependencies
prec single
for  Computes selected eigenvalues and eigenvectors of a real
,    symmetric tridiagonal matrix.
gams d4a1, d4a5

file sstevr.f  sstevr.f plus dependencies
prec single
for  Computes selected eigenvalues, and optionally, eigenvectors of a real
,    symmetric tridiagonal matrix.  Eigenvalues are computed by the dqds
,    algorithm, and eigenvectors are computed from various "good" LDL^T
,    representations (also known as Relatively Robust Representations).
gams d4a1, d4a5

file sgeesx.f  sgeesx.f plus dependencies
prec single
for  Computes the eigenvalues and Schur factorization of a general
,    matrix, orders the factorization so that selected eigenvalues
,    are at the top left of the Schur form, and computes reciprocal
,    condition numbers for the average of the selected eigenvalues,
,    and for the associated right invariant subspace.
gams d4a2

file sggesx.f  sggesx.f plus dependencies
prec single
for  Computes the generalized eigenvalues, the real Schur form, and,
,    optionally, the left and/or right matrices of Schur vectors.

file sgeevx.f  sgeevx.f plus dependencies
prec single
for  Computes the eigenvalues and left and right eigenvectors of
,    a general matrix,  with preliminary balancing of the matrix,
,    and computes reciprocal condition numbers for the eigenvalues
,    and right eigenvectors.
gams d4a2

file sggevx.f  sggevx.f plus dependencies
prec single
for  Computes the generalized eigenvalues, and optionally, the left
,    and/or right generalized eigenvectors.

# ---------------------------------
# Available COMPUTATIONAL routines:
# ---------------------------------

file sbdsdc.f  sbdsdc.f plus dependencies
prec single
for  Computes the singular value decomposition (SVD) of a real bidiagonal
,    matrix, using a divide and conquer method.
gams d6

file sbdsqr.f  sbdsqr.f plus dependencies
prec single
for  Computes the singular value decomposition (SVD) of a real bidiagonal
,    matrix, using the bidiagonal QR algorithm.
gams d6

file sdisna.f  sdisna.f plus dependencies
prec single
for  Computes the reciprocal condition numbers for the eigenvectors of a
,    real symmetric or complex Hermitian matrix or for the left or right
,    singular vectors of a general matrix.

file sgbbrd.f  sgbbrd.f plus dependencies
prec single
,    Reduces a general band matrix to real upper bidiagonal form
,    by an orthogonal transformation.

file sgbcon.f  sgbcon.f plus dependencies
prec single
for  Estimates the reciprocal of the condition number of a general
,    band matrix, in either the 1-norm or the infinity-norm, using
,    the LU factorization computed by SGBTRF.
gams d2a2

file sgbequ.f  sgbequ.f plus dependencies
prec single
for  Computes row and column scalings to equilibrate a general band
,    matrix and reduce its condition number.
gams d2a2

file sgbrfs.f  sgbrfs.f plus dependencies
prec single
for  Improves the computed solution to a general banded system of
,    linear equations AX=B, A**T X=B or A**H X=B, and provides forward
,    and backward error bounds for the solution.
gams d2a2

file sgbtrf.f  sgbtrf.f plus dependencies
prec single
for  Computes an LU factorization of a general band matrix, using
,    partial pivoting with row interchanges.
gams d2a2

file sgbtrs.f  sgbtrs.f plus dependencies
prec single
for  Solves a general banded system of linear equations AX=B,
,    A**T X=B or A**H X=B, using the LU factorization computed
,    by SGBTRF.
gams d2a2

file sgebak.f  sgebak.f plus dependencies
prec single
for  Transforms eigenvectors of a balanced matrix to those of the
,    original matrix supplied to SGEBAL.
gams d4c4

file sgebal.f  sgebal.f plus dependencies
prec single
for  Balances a general matrix in order to improve the accuracy
,    of computed eigenvalues.
gams d4c1a

file sgebrd.f  sgebrd.f plus dependencies
prec single
for  Reduces a general rectangular matrix to real bidiagonal form
,    by an orthogonal transformation.
gams d6

file sgecon.f  sgecon.f plus dependencies
prec single
for  Estimates the reciprocal of the condition number of a general
,    matrix, in either the 1-norm or the infinity-norm, using the
,    LU factorization computed by SGETRF.
gams d2a1

file sgeequ.f  sgeequ.f plus dependencies
prec single
for  Computes row and column scalings to equilibrate a general
,    rectangular matrix and reduce its condition number.
gams d2a1

file sgehrd.f  sgehrd.f plus dependencies
prec single
for  Reduces a general matrix to upper Hessenberg form by an
,    orthogonal similarity transformation.
gams d4c1b2

file sgelqf.f  sgelqf.f plus dependencies
prec single
for  Computes an LQ factorization of a general rectangular matrix.
gams d5

file sgeqlf.f  sgeqlf.f plus dependencies
prec single
for  Computes a QL factorization of a general rectangular matrix.
gams d5

file sgeqp3.f  sgeqp3.f plus dependencies
prec single
for  Computes a QR factorization with column pivoting of a general
,    rectangular matrix using Level 3 BLAS.
gams d5

file sgeqpf.f  sgeqpf.f plus dependencies
prec single
for  Computes a QR factorization with column pivoting of a general
,    rectangular matrix.
gams d5

file sgeqrf.f  sgeqrf.f plus dependencies
prec single
for  Computes a QR factorization of a general rectangular matrix.
gams d5

file sgerfs.f  sgerfs.f plus dependencies
prec single
for  Improves the computed solution to a general system of linear
,    equations AX=B, A**T X=B or A**H X=B, and provides forward and
,    backward error bounds for the solution.
gams d2a1

file sgerqf.f  sgerqf.f plus dependencies
prec single
for  Computes an RQ factorization of a general rectangular matrix.
gams d5

file sgetrf.f  sgetrf.f plus dependencies
prec single
for  Computes an LU factorization of a general matrix, using partial
,    pivoting with row interchanges.
gams d2a1

file sgetri.f  sgetri.f plus dependencies
prec single
for  Computes the inverse of a general matrix, using the LU factorization
,    computed by SGETRF.
gams d2a1

file sgetrs.f  sgetrs.f plus dependencies
prec single
for  Solves a general system of linear equations AX=B, A**T X=B
,    or A**H X=B, using the LU factorization computed by SGETRF.
gams d2a1

file sggbak.f  sggbak.f plus dependencies
prec single
For  Forms the right or left eigenvectors of the generalized eigenvalue
,    problem by backward transformation on the computed eigenvectors of
,    the balanced pair of matrices output by SGGBAL.

file sggbal.f  sggbal.f plus dependencies
prec single
For  Balances a pair of general real matrices for the generalized
,    eigenvalue problem A x = lambda B x.

file sgghrd.f  sgghrd.f plus dependencies
prec single
for  Reduces a pair of real matrices to generalized upper
,    Hessenberg form using orthogonal transformations

file sggqrf.f  sggqrf.f plus dependencies
prec single
for  Computes a generalized QR factorization of a pair of matrices.

file sggrqf.f  sggrqf.f plus dependencies
prec single
for  Computes a generalized RQ factorization of a pair of matrices.

file sggsvp.f  sggsvp.f plus dependencies
prec single
for  Computes orthogonal matrices as a preprocessing step
,    for computing the generalized singular value decomposition

file sgtcon.f  sgtcon.f plus dependencies
prec single
for  Estimates the reciprocal of the condition number of a general
,    tridiagonal matrix, in either the 1-norm or the infinity-norm,
,    using the LU factorization computed by SGTTRF.
gams d2a2a

file sgtrfs.f  sgtrfs.f plus dependencies
prec single
for  Improves the computed solution to a general tridiagonal system
,    of linear equations AX=B, A**T X=B or A**H X=B, and provides
,    forward and backward error bounds for the solution.
gams d2a2a

file sgttrf.f  sgttrf.f plus dependencies
prec single
for  Computes an LU factorization of a general tridiagonal matrix,
,    using partial pivoting with row interchanges.
gams d2a2a

file sgttrs.f  sgttrs.f plus dependencies
prec single
for  Solves a general tridiagonal system of linear equations AX=B,
,    A**T X=B or A**H X=B, using the LU factorization computed by
,    SGTTRF.
gams d2a2a

file shgeqz.f  shgeqz.f plus dependencies
prec single
for  Implements a single-/double-shift version of the QZ method for
,    finding the generalized eigenvalues of the equation
,    det(A - w(i) B) = 0

file shsein.f  shsein.f plus dependencies
prec single
for  Computes specified right and/or left eigenvectors of an upper
,    Hessenberg matrix by inverse iteration.
gams d4c3

file shseqr.f  shseqr.f plus dependencies
prec single
for  Computes the eigenvalues and Schur factorization of an upper
,    Hessenberg matrix, using the multishift QR algorithm.
gams d4c2b

file sopgtr.f  sopgtr.f plus dependencies
prec single
for  Generates the orthogonal transformation matrix from
,    a reduction to tridiagonal form determined by SSPTRD.
gams d4c1b1

file sopmtr.f  sopmtr.f plus dependencies
prec single
for  Multiplies a general matrix by the orthogonal
,    transformation matrix from a reduction to tridiagonal form
,    determined by SSPTRD.
gams d4c4

file sorgbr.f  sorgbr.f plus dependencies
prec single
for  Generates the orthogonal transformation matrices from
,    a reduction to bidiagonal form determined by SGEBRD.
gams d6

file sorghr.f  sorghr.f plus dependencies
prec single
for  Generates the orthogonal transformation matrix from
,    a reduction to Hessenberg form determined by SGEHRD.
gams d4c1b2

file sorglq.f  sorglq.f plus dependencies
prec single
for  Generates all or part of the orthogonal matrix Q from
,    an LQ factorization determined by SGELQF.
gams d5

file sorgql.f  sorgql.f plus dependencies
prec single
for  Generates all or part of the orthogonal matrix Q from
,    a QL factorization determined by SGEQLF.
gams d5

file sorgqr.f  sorgqr.f plus dependencies
prec single
for  Generates all or part of the orthogonal matrix Q from
,    a QR factorization determined by SGEQRF.
gams d5

file sorgrq.f  sorgrq.f plus dependencies
prec single
for  Generates all or part of the orthogonal matrix Q from
,    an RQ factorization determined by SGERQF.
gams d5

file sorgtr.f  sorgtr.f plus dependencies
prec single
for  Generates the orthogonal transformation matrix from
,    a reduction to tridiagonal form determined by SSYTRD.
gams d4c1b1

file sormbr.f  sormbr.f plus dependencies
prec single
for  Multiplies a general matrix by one of the orthogonal
,    transformation  matrices from a reduction to bidiagonal form
,    determined by SGEBRD.
gams d6

file sormhr.f  sormhr.f plus dependencies
prec single
for  Multiplies a general matrix by the orthogonal transformation
,    matrix from a reduction to Hessenberg form determined by SGEHRD.
gams d4c4

file sormlq.f  sormlq.f plus dependencies
prec single
for  Multiplies a general matrix by the orthogonal matrix
,    from an LQ factorization determined by SGELQF.
gams d5

file sormql.f  sormql.f plus dependencies
prec single
for  Multiplies a general matrix by the orthogonal matrix
,    from a QL factorization determined by SGEQLF.
gams d5

file sormqr.f  sormqr.f plus dependencies
prec single
for  Multiplies a general matrix by the orthogonal matrix
,    from a QR factorization determined by SGEQRF.
gams d5

file sormr3.f  sormr3.f plus dependencies
prec single
for  Multiples a general matrix by the orthogonal matrix
,    from an RZ factorization determined by STZRZF.

file sormrq.f  sormrq.f plus dependencies
prec single
for  Multiplies a general matrix by the orthogonal matrix
,    from an RQ factorization determined by SGERQF.
gams d5

file sormrz.f  sormrz.f plus dependencies
prec single
for  Multiples a general matrix by the orthogonal matrix
,    from an RZ factorization determined by STZRZF.

file sormtr.f  sormtr.f plus dependencies
prec single
for  Multiplies a general matrix by the orthogonal
,    transformation matrix from a reduction to tridiagonal form
,    determined by SSYTRD.
gams d4c4

file spbcon.f  spbcon.f plus dependencies
prec single
for  Estimates the reciprocal of the condition number of a
,    symmetric positive definite band matrix, using the
,    Cholesky factorization computed by SPBTRF.
gams d2b2

file spbequ.f  spbequ.f plus dependencies
prec single
for  Computes row and column scalings to equilibrate a symmetric
,    positive definite band matrix and reduce its condition number.
gams d2b2

file spbrfs.f  spbrfs.f plus dependencies
prec single
for  Improves the computed solution to a symmetric positive
,    definite banded system of linear equations AX=B, and provides
,    forward and backward error bounds for the solution.
gams d2b2

file spbstf.f  spbstf.f plus dependencies
prec single
for  Computes a split Cholesky factorization of a real symmetric positive
,    definite band matrix.

file spbtrf.f  spbtrf.f plus dependencies
prec single
for  Computes the Cholesky factorization of a symmetric
,    positive definite band matrix.
gams d2b2

file spbtrs.f  spbtrs.f plus dependencies
prec single
for  Solves a symmetric positive definite banded system
,    of linear equations AX=B, using the Cholesky factorization
,    computed by SPBTRF.
gams d2b2

file spocon.f  spocon.f plus dependencies
prec single
for  Estimates the reciprocal of the condition number of a
,    symmetric positive definite matrix, using the
,    Cholesky factorization computed by SPOTRF.
gams d2b1b

file spoequ.f  spoequ.f plus dependencies
prec single
for  Computes row and column scalings to equilibrate a symmetric
,    positive definite matrix and reduce its condition number.
gams d2b1b

file sporfs.f  sporfs.f plus dependencies
prec single
for  Improves the computed solution to a symmetric positive
,    definite system of linear equations AX=B, and provides forward
,    and backward error bounds for the solution.
gams d2b1b

file spotrf.f  spotrf.f plus dependencies
prec single
for  Computes the Cholesky factorization of a symmetric
,    positive definite matrix.
gams d2b1b

file spotri.f  spotri.f plus dependencies
prec single
for  Computes the inverse of a symmetric positive definite
,    matrix, using the Cholesky factorization computed by SPOTRF.
gams d2b1b

file spotrs.f  spotrs.f plus dependencies
prec single
for  Solves a symmetric positive definite system of linear
,    equations AX=B, using the Cholesky factorization computed by
,    SPOTRF.
gams d2b1b

file sppcon.f  sppcon.f plus dependencies
prec single
for  Estimates the reciprocal of the condition number of a
,    symmetric positive definite matrix in packed storage,
,    using the Cholesky factorization computed by SPPTRF.
gams d2b1b

file sppequ.f  sppequ.f plus dependencies
prec single
for  Computes row and column scalings to equilibrate a symmetric
,    positive definite matrix in packed storage and reduce its condition
,    number.
gams d2b1b

file spprfs.f  spprfs.f plus dependencies
prec single
for  Improves the computed solution to a symmetric positive
,    definite system of linear equations AX=B, where A is held in
,    packed storage, and provides forward and backward error bounds
,    for the solution.
gams d2b1b

file spptrf.f  spptrf.f plus dependencies
prec single
for  Computes the Cholesky factorization of a symmetric
,    positive definite matrix in packed storage.
gams d2b1b

file spptri.f  spptri.f plus dependencies
prec single
for  Computes the inverse of a symmetric positive definite
,    matrix in packed storage, using the Cholesky factorization computed
,    by SPPTRF.
gams d2b1b

file spptrs.f  spptrs.f plus dependencies
prec single
for  Solves a symmetric positive definite system of linear
,    equations AX=B, where A is held in packed storage, using the
,    Cholesky factorization computed by SPPTRF.
gams d2b1b

file sptcon.f  sptcon.f plus dependencies
prec single
for  Computes the reciprocal of the condition number of a
,    symmetric positive definite tridiagonal matrix,
,    using the LDL**H factorization computed by SPTTRF.
gams d2b2a

file spteqr.f  spteqr.f plus dependencies
prec single
for  Computes all eigenvalues and eigenvectors of a real symmetric
,    positive definite tridiagonal matrix, by computing the SVD of
,    its bidiagonal Cholesky factor.
gams d4c2a

file sptrfs.f  sptrfs.f plus dependencies
prec single
for  Improves the computed solution to a symmetric positive
,    definite tridiagonal system of linear equations AX=B, and provides
,    forward and backward error bounds for the solution.
gams d2b2a

file spttrf.f  spttrf.f plus dependencies
prec single
for  Computes the LDL**H factorization of a symmetric
,    positive definite tridiagonal matrix.
gams d2b2a

file spttrs.f  spttrs.f plus dependencies
prec single
for  Solves a symmetric positive definite tridiagonal
,    system of linear equations, using the LDL**H factorization
,    computed by SPTTRF.
gams d2b2a

file ssbgst.f  ssbgst.f plus dependencies
prec single
for  Reduces a real symmetric-definite banded generalized eigenproblem
,    A x = lambda B x to standard form, where B has been factorized by
,    SPBSTF (Crawford's algorithm).

file ssbtrd.f  ssbtrd.f plus dependencies
prec single
for  Reduces a symmetric band matrix to real symmetric
,    tridiagonal form by an orthogonal similarity transformation.
gams d4c1b1

file sspcon.f  sspcon.f plus dependencies
prec single
for  Estimates the reciprocal of the condition number of a
,    real symmetric indefinite
,    matrix in packed storage, using the factorization computed
,    by SSPTRF.
gams d2b1a

file sspgst.f  sspgst.f plus dependencies
prec single
for  Reduces a symmetric-definite generalized eigenproblem
,    Ax= lambda Bx,  ABx= lambda x,  or BAx= lambda x, to standard
,    form,  where A and B are held in packed storage, and B has been
,    factorized by SPPTRF.
gams d4c1c

file ssprfs.f  ssprfs.f plus dependencies
prec single
for  Improves the computed solution to a real
,    symmetric indefinite system of linear equations
,    AX=B, where A is held in packed storage, and provides forward
,    and backward error bounds for the solution.
gams d2b1a

file ssptrd.f  ssptrd.f plus dependencies
prec single
for  Reduces a symmetric matrix in packed storage to real
,    symmetric tridiagonal form by an orthogonal similarity
,    transformation.
gams d4c1b1

file ssptrf.f  ssptrf.f plus dependencies
prec single
for  Computes the factorization of a real
,    symmetric-indefinite matrix in packed storage,
,    using the diagonal pivoting method.
gams d2b1a

file ssptri.f  ssptri.f plus dependencies
prec single
for  Computes the inverse of a real symmetric
,    indefinite matrix in packed storage, using the factorization
,    computed by SSPTRF.
gams d2b1a

file ssptrs.f  ssptrs.f plus dependencies
prec single
for  Solves a real symmetric
,    indefinite system of linear equations AX=B, where A is held
,    in packed storage, using the factorization computed
,    by SSPTRF.
gams d2b1a

file sstebz.f  sstebz.f plus dependencies
prec single
for  Computes selected eigenvalues of a real symmetric tridiagonal
,    matrix by bisection.
gams d4c2a

file sstedc.f  sstedc.f plus dependencies
prec single
for  Computes all eigenvalues and, optionally, eigenvectors of a
,    symmetric tridiagonal matrix using the divide and conquer algorithm.

file sstegr.f  sstegr.f plus dependencies
prec single
for  Computes selected eigenvalues and, optionally, eigenvectors of a
,    symmetric tridiagonal matrix.  The eigenvalues are computed by the
,    dqds algorithm, while eigenvectors are computed from various "good"
,    LDL^T representations (also known as Relatively Robust Representations.)

file sstein.f  sstein.f plus dependencies
prec single
for  Computes selected eigenvectors of a real symmetric tridiagonal
,    matrix by inverse iteration.
gams d4c3

file ssteqr.f  ssteqr.f plus dependencies
prec single
for  Computes all eigenvalues and eigenvectors of a real symmetric
,    tridiagonal matrix, using the implicit QL or QR algorithm.
gams d4a1, d4a5, d4c2a

file ssterf.f  ssterf.f plus dependencies
prec single
for  Computes all eigenvalues of a real symmetric tridiagonal matrix,
,    using a root-free variant of the QL or QR algorithm.
gams d4c2a

file ssycon.f  ssycon.f plus dependencies
prec single
for  Estimates the reciprocal of the condition number of a
,    real symmetric indefinite matrix,
,    using the factorization computed by SSYTRF.
gams d2b1a

file ssygst.f  ssygst.f plus dependencies
prec single
for  Reduces a symmetric-definite generalized eigenproblem
,    Ax= lambda Bx,  ABx= lambda x,  or BAx= lambda x, to standard
,    form, where B has been factorized by SPOTRF.
gams d4c1c

file ssyrfs.f  ssyrfs.f plus dependencies
prec single
for  Improves the computed solution to a real
,    symmetric indefinite system of linear equations
,    AX=B, and provides forward and backward error bounds for the
,    solution.
gams d2b1a

file ssytrd.f  ssytrd.f plus dependencies
prec single
for  Reduces a symmetric matrix to real symmetric tridiagonal
,    form by an orthogonal similarity transformation.
gams d4c1b1

file ssytrf.f  ssytrf.f plus dependencies
prec single
for  Computes the factorization of a real symmetric-indefinite matrix,
,    using the diagonal pivoting method.
gams d2b1a

file ssytri.f  ssytri.f plus dependencies
prec single
for  Computes the inverse of a real symmetric indefinite matrix,
,    using the factorization computed by SSYTRF.
gams d2b1a

file ssytrs.f  ssytrs.f plus dependencies
prec single
for  Solves a real symmetric indefinite system of linear equations AX=B,
,    using the factorization computed by SSPTRF.
gams d2b1a

file stbcon.f  stbcon.f plus dependencies
prec single
for  Estimates the reciprocal of the condition number of a triangular
,    band matrix, in either the 1-norm or the infinity-norm.
gams d2a2, d2a3

file stbrfs.f  stbrfs.f plus dependencies
prec single
for  Provides forward and backward error bounds for the solution
,    of a triangular banded system of linear equations AX=B,
,    A**T X=B or A**H X=B.
gams d2a2, d2a3

file stbtrs.f  stbtrs.f plus dependencies
prec single
for  Solves a triangular banded system of linear equations AX=B,
,    A**T X=B or A**H X=B.
gams d2a2, d2a3

file stgevc.f  stgevc.f plus dependencies
prec single
for  Computes some or all of the right and/or left generalized eigenvectors
,    of a pair of upper triangular matrices.
gams d4b2

file stgexc.f  stgexc.f plus dependencies
prec single
for  Reorders the generalized real Schur decomposition of a real
,    matrix pair (A,B) using an orthogonal equivalence transformation
,    so that the diagonal block of (A,B) with row index IFST is moved
,    to row ILST.

file stgsen.f  stgsen.f plus dependencies
prec single
for  Reorders the generalized real Schur decomposition of a real
,    matrix pair (A, B) so that a selected cluster of eigenvalues
,    appears in the leading diagonal blocks of the upper quasi-triangular
,    matrix A and the upper triangular B.

file stgsja.f  stgsja.f plus dependencies
prec single
for  Computes the generalized singular value decomposition of two real
,    upper triangular (or trapezoidal) matrices as output by SGGSVP.
gams d6

file stgsna.f  stgsna.f plus dependencies
prec single
for  Estimates reciprocal condition numbers for specified
,    eigenvalues and/or eigenvectors of a matrix pair (A, B) in
,    generalized real Schur canonical form, as returned by SGGES.

file stgsyl.f  stgsyl.f plus dependencies
prec single
for  Solves the generalized Sylvester equation.

file stpcon.f  stpcon.f plus dependencies
prec single
for  Estimates the reciprocal of the condition number of a triangular
,    matrix in packed storage, in either the 1-norm or the infinity-norm.
gams d2a3

file stprfs.f  stprfs.f plus dependencies
prec single
for  Provides forward and backward error bounds for the solution
,    of a triangular system of linear equations AX=B, A**T X=B or
,    A**H X=B, where A is held in packed storage.
gams d2a3

file stptri.f  stptri.f plus dependencies
prec single
for   Computes the inverse of a triangular matrix in packed storage.
gams d2a3

file stptrs.f  stptrs.f plus dependencies
prec single
for  Solves a triangular system of linear equations AX=B,
,    A**T X=B or A**H X=B, where A is held in packed storage.
gams d2a3

file strcon.f  strcon.f plus dependencies
prec single
for  Estimates the reciprocal of the condition number of a triangular
,    matrix, in either the 1-norm or the infinity-norm.
gams d2a3

file strevc.f  strevc.f plus dependencies
prec single
for  Computes some or all of the right and/or left eigenvectors of
,    an upper quasi-triangular matrix.
gams d4c3

file strexc.f  strexc.f plus dependencies
prec single
for  Reorders the Schur factorization of a matrix by an orthogonal
,    similarity transformation.
gams d4c

file strrfs.f  strrfs.f plus dependencies
prec single
for  Provides forward and backward error bounds for the solution
,    of a triangular system of linear equations A X=B, A**T X=B or
,    A**H X=B.
gams d2a3

file strsen.f  strsen.f plus dependencies
prec single
for  Reorders the Schur factorization of a matrix in order to find
,    an orthonormal basis of a right invariant subspace corresponding
,    to selected eigenvalues, and returns reciprocal condition numbers
,    (sensitivities) of the average of the cluster of eigenvalues
,    and of the invariant subspace.
gams d4c

file strsna.f  strsna.f plus dependencies
prec single
for  Estimates the reciprocal condition numbers (sensitivities)
,    of selected eigenvalues and eigenvectors of an upper
,    quasi-triangular matrix.
gams d4c

file strsyl.f  strsyl.f plus dependencies
prec single
for  Solves the Sylvester matrix equation A X +/- X B=C where A
,    and B are upper quasi-triangular, and may be transposed.
gams d8

file strtri.f  strtri.f plus dependencies
prec single
for  Computes the inverse of a triangular matrix.
gams d2a3

file strtrs.f  strtrs.f plus dependencies
prec single
for  Solves a triangular system of linear equations AX=B,
,    A**T X=B or A**H X=B.
gams d2a3

file stzrqf.f  stzrqf.f plus dependencies
prec single
for  Computes an RQ factorization of an upper trapezoidal matrix.
gams d5

file stzrzf.f  stzrzf.f plus dependencies
prec single
for  Computes an RZ factorization of an upper trapezoidal matrix
,    (blocked version of STZRQF).