gesv_mixed(3)

NAME
gesv_mixed - gesv: factor and solve, mixed precision

SYNOPSIS

  Functions

subroutine dsgesv (n, nrhs, a, lda, ipiv, b, ldb, x, ldx, work, swork, iter, info)
DSGESV computes the solution to system of linear equations A * X = B for GE matrices (mixed precision with iterative refinement)
subroutine zcgesv (n, nrhs, a, lda, ipiv, b, ldb, x, ldx, work, swork, rwork, iter, info)
ZCGESV computes the solution to system of linear equations A * X = B for GE matrices (mixed precision with iterative refinement)

Detailed Description

Function Documentation

  subroutine dsgesv (integer n, integer nrhs, double precision, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( ldx, * ) x, integer ldx, double precision, dimension( n, * ) work, real, dimension( * ) swork, integer iter, integer info)

DSGESV computes the solution to system of linear equations A * X = B for GE matrices (mixed precision with iterative refinement)

Purpose:

    !>
    !> DSGESV computes the solution to a real system of linear equations
    !>    A * X = B,
    !> where A is an N-by-N matrix and X and B are N-by-NRHS matrices.
    !>
    !> DSGESV first attempts to factorize the matrix in SINGLE PRECISION
    !> and use this factorization within an iterative refinement procedure
    !> to produce a solution with DOUBLE PRECISION normwise backward error
    !> quality (see below). If the approach fails the method switches to a
    !> DOUBLE PRECISION factorization and solve.
    !>
    !> The iterative refinement is not going to be a winning strategy if
    !> the ratio SINGLE PRECISION performance over DOUBLE PRECISION
    !> performance is too small. A reasonable strategy should take the
    !> number of right-hand sides and the size of the matrix into account.
    !> This might be done with a call to ILAENV in the future. Up to now, we
    !> always try iterative refinement.
    !>
    !> The iterative refinement process is stopped if
    !>     ITER > ITERMAX
    !> or for all the RHS we have:
    !>     RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX
    !> where
    !>     o ITER is the number of the current iteration in the iterative
    !>       refinement process
    !>     o RNRM is the infinity-norm of the residual
    !>     o XNRM is the infinity-norm of the solution
    !>     o ANRM is the infinity-operator-norm of the matrix A
    !>     o EPS is the machine epsilon returned by DLAMCH('Epsilon')
    !> The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00
    !> respectively.
    !>

Parameters
    N

    !>          N is INTEGER
    !>          The number of linear equations, i.e., the order of the
    !>          matrix A.  N >= 0.
    !>

    NRHS

    !>          NRHS is INTEGER
    !>          The number of right hand sides, i.e., the number of columns
    !>          of the matrix B.  NRHS >= 0.
    !>

    A

    !>          A is DOUBLE PRECISION array,
    !>          dimension (LDA,N)
    !>          On entry, the N-by-N coefficient matrix A.
    !>          On exit, if iterative refinement has been successfully used
    !>          (INFO = 0 and ITER >= 0, see description below), then A is
    !>          unchanged, if double precision factorization has been used
    !>          (INFO = 0 and ITER < 0, see description below), then the
    !>          array A contains the factors L and U from the factorization
    !>          A = P*L*U; the unit diagonal elements of L are not stored.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= max(1,N).
    !>

    IPIV

    !>          IPIV is INTEGER array, dimension (N)
    !>          The pivot indices that define the permutation matrix P;
    !>          row i of the matrix was interchanged with row IPIV(i).
    !>          Corresponds either to the single precision factorization
    !>          (if INFO = 0 and ITER >= 0) or the double precision
    !>          factorization (if INFO = 0 and ITER < 0).
    !>

    B

    !>          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
    !>          The N-by-NRHS right hand side matrix B.
    !>

    LDB

    !>          LDB is INTEGER
    !>          The leading dimension of the array B.  LDB >= max(1,N).
    !>

    X

    !>          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
    !>          If INFO = 0, the N-by-NRHS solution matrix X.
    !>

    LDX

    !>          LDX is INTEGER
    !>          The leading dimension of the array X.  LDX >= max(1,N).
    !>

    WORK

    !>          WORK is DOUBLE PRECISION array, dimension (N,NRHS)
    !>          This array is used to hold the residual vectors.
    !>

    SWORK

    !>          SWORK is REAL array, dimension (N*(N+NRHS))
    !>          This array is used to use the single precision matrix and the
    !>          right-hand sides or solutions in single precision.
    !>

    ITER

    !>          ITER is INTEGER
    !>          < 0: iterative refinement has failed, double precision
    !>               factorization has been performed
    !>               -1 : the routine fell back to full precision for
    !>                    implementation- or machine-specific reasons
    !>               -2 : narrowing the precision induced an overflow,
    !>                    the routine fell back to full precision
    !>               -3 : failure of SGETRF
    !>               -31: stop the iterative refinement after the 30th
    !>                    iterations
    !>          > 0: iterative refinement has been successfully used.
    !>               Returns the number of iterations
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value
    !>          > 0:  if INFO = i, U(i,i) computed in DOUBLE PRECISION is
    !>                exactly zero.  The factorization has been completed,
    !>                but the factor U is exactly singular, so the solution
    !>                could not be computed.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine zcgesv (integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( ldx, * ) x, integer ldx, complex*16, dimension( n, * ) work, complex, dimension( * ) swork, double precision, dimension( * ) rwork, integer iter, integer info)

ZCGESV computes the solution to system of linear equations A * X = B for GE matrices (mixed precision with iterative refinement)

Purpose:

    !>
    !> ZCGESV computes the solution to a complex system of linear equations
    !>    A * X = B,
    !> where A is an N-by-N matrix and X and B are N-by-NRHS matrices.
    !>
    !> ZCGESV first attempts to factorize the matrix in COMPLEX and use this
    !> factorization within an iterative refinement procedure to produce a
    !> solution with COMPLEX*16 normwise backward error quality (see below).
    !> If the approach fails the method switches to a COMPLEX*16
    !> factorization and solve.
    !>
    !> The iterative refinement is not going to be a winning strategy if
    !> the ratio COMPLEX performance over COMPLEX*16 performance is too
    !> small. A reasonable strategy should take the number of right-hand
    !> sides and the size of the matrix into account. This might be done
    !> with a call to ILAENV in the future. Up to now, we always try
    !> iterative refinement.
    !>
    !> The iterative refinement process is stopped if
    !>     ITER > ITERMAX
    !> or for all the RHS we have:
    !>     RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX
    !> where
    !>     o ITER is the number of the current iteration in the iterative
    !>       refinement process
    !>     o RNRM is the infinity-norm of the residual
    !>     o XNRM is the infinity-norm of the solution
    !>     o ANRM is the infinity-operator-norm of the matrix A
    !>     o EPS is the machine epsilon returned by DLAMCH('Epsilon')
    !> The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00
    !> respectively.
    !>

Parameters
    N

    !>          N is INTEGER
    !>          The number of linear equations, i.e., the order of the
    !>          matrix A.  N >= 0.
    !>

    NRHS

    !>          NRHS is INTEGER
    !>          The number of right hand sides, i.e., the number of columns
    !>          of the matrix B.  NRHS >= 0.
    !>

    A

    !>          A is COMPLEX*16 array,
    !>          dimension (LDA,N)
    !>          On entry, the N-by-N coefficient matrix A.
    !>          On exit, if iterative refinement has been successfully used
    !>          (INFO = 0 and ITER >= 0, see description below), then A is
    !>          unchanged, if double precision factorization has been used
    !>          (INFO = 0 and ITER < 0, see description below), then the
    !>          array A contains the factors L and U from the factorization
    !>          A = P*L*U; the unit diagonal elements of L are not stored.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= max(1,N).
    !>

    IPIV

    !>          IPIV is INTEGER array, dimension (N)
    !>          The pivot indices that define the permutation matrix P;
    !>          row i of the matrix was interchanged with row IPIV(i).
    !>          Corresponds either to the single precision factorization
    !>          (if INFO = 0 and ITER >= 0) or the double precision
    !>          factorization (if INFO = 0 and ITER < 0).
    !>

    B

    !>          B is COMPLEX*16 array, dimension (LDB,NRHS)
    !>          The N-by-NRHS right hand side matrix B.
    !>

    LDB

    !>          LDB is INTEGER
    !>          The leading dimension of the array B.  LDB >= max(1,N).
    !>

    X

    !>          X is COMPLEX*16 array, dimension (LDX,NRHS)
    !>          If INFO = 0, the N-by-NRHS solution matrix X.
    !>

    LDX

    !>          LDX is INTEGER
    !>          The leading dimension of the array X.  LDX >= max(1,N).
    !>

    WORK

    !>          WORK is COMPLEX*16 array, dimension (N,NRHS)
    !>          This array is used to hold the residual vectors.
    !>

    SWORK

    !>          SWORK is COMPLEX array, dimension (N*(N+NRHS))
    !>          This array is used to use the single precision matrix and the
    !>          right-hand sides or solutions in single precision.
    !>

    RWORK

    !>          RWORK is DOUBLE PRECISION array, dimension (N)
    !>

    ITER

    !>          ITER is INTEGER
    !>          < 0: iterative refinement has failed, COMPLEX*16
    !>               factorization has been performed
    !>               -1 : the routine fell back to full precision for
    !>                    implementation- or machine-specific reasons
    !>               -2 : narrowing the precision induced an overflow,
    !>                    the routine fell back to full precision
    !>               -3 : failure of CGETRF
    !>               -31: stop the iterative refinement after the 30th
    !>                    iterations
    !>          > 0: iterative refinement has been successfully used.
    !>               Returns the number of iterations
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value
    !>          > 0:  if INFO = i, U(i,i) computed in COMPLEX*16 is exactly
    !>                zero.  The factorization has been completed, but the
    !>                factor U is exactly singular, so the solution
    !>                could not be computed.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Author

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