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porfs(3) LAPACK porfs(3)

NAME

porfs - porfs: iterative refinement

SYNOPSIS

Functions


subroutine cporfs (uplo, n, nrhs, a, lda, af, ldaf, b, ldb, x, ldx, ferr, berr, work, rwork, info)
CPORFS subroutine dporfs (uplo, n, nrhs, a, lda, af, ldaf, b, ldb, x, ldx, ferr, berr, work, iwork, info)
DPORFS subroutine sporfs (uplo, n, nrhs, a, lda, af, ldaf, b, ldb, x, ldx, ferr, berr, work, iwork, info)
SPORFS subroutine zporfs (uplo, n, nrhs, a, lda, af, ldaf, b, ldb, x, ldx, ferr, berr, work, rwork, info)
ZPORFS

Detailed Description

Function Documentation

subroutine cporfs (character uplo, integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldaf, * ) af, integer ldaf, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( ldx, * ) x, integer ldx, real, dimension( * ) ferr, real, dimension( * ) berr, complex, dimension( * ) work, real, dimension( * ) rwork, integer info)

CPORFS

Purpose:



 CPORFS improves the computed solution to a system of linear


 equations when the coefficient matrix is Hermitian positive definite,


 and provides error bounds and backward error estimates for the


 solution.

Parameters

UPLO 



          UPLO is CHARACTER*1


          = 'U':  Upper triangle of A is stored;


          = 'L':  Lower triangle of A is stored.

N



          N is INTEGER


          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 matrices B and X.  NRHS >= 0.

A



          A is COMPLEX array, dimension (LDA,N)


          The Hermitian matrix A.  If UPLO = 'U', the leading N-by-N


          upper triangular part of A contains the upper triangular part


          of the matrix A, and the strictly lower triangular part of A


          is not referenced.  If UPLO = 'L', the leading N-by-N lower


          triangular part of A contains the lower triangular part of


          the matrix A, and the strictly upper triangular part of A is


          not referenced.

LDA



          LDA is INTEGER


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

AF



          AF is COMPLEX array, dimension (LDAF,N)


          The triangular factor U or L from the Cholesky factorization


          A = U**H*U or A = L*L**H, as computed by CPOTRF.

LDAF



          LDAF is INTEGER


          The leading dimension of the array AF.  LDAF >= max(1,N).

B



          B is COMPLEX array, dimension (LDB,NRHS)


          The right hand side matrix B.

LDB



          LDB is INTEGER


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

X



          X is COMPLEX array, dimension (LDX,NRHS)


          On entry, the solution matrix X, as computed by CPOTRS.


          On exit, the improved solution matrix X.

LDX



          LDX is INTEGER


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

FERR



          FERR is REAL array, dimension (NRHS)


          The estimated forward error bound for each solution vector


          X(j) (the j-th column of the solution matrix X).


          If XTRUE is the true solution corresponding to X(j), FERR(j)


          is an estimated upper bound for the magnitude of the largest


          element in (X(j) - XTRUE) divided by the magnitude of the


          largest element in X(j).  The estimate is as reliable as


          the estimate for RCOND, and is almost always a slight


          overestimate of the true error.

BERR



          BERR is REAL array, dimension (NRHS)


          The componentwise relative backward error of each solution


          vector X(j) (i.e., the smallest relative change in


          any element of A or B that makes X(j) an exact solution).

WORK



          WORK is COMPLEX array, dimension (2*N)

RWORK



          RWORK is REAL array, dimension (N)

INFO



          INFO is INTEGER


          = 0:  successful exit


          < 0:  if INFO = -i, the i-th argument had an illegal value

Internal Parameters:



  ITMAX is the maximum number of steps of iterative refinement.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine dporfs (character uplo, integer n, integer nrhs, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldaf, * ) af, integer ldaf, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( ldx, * ) x, integer ldx, double precision, dimension( * ) ferr, double precision, dimension( * ) berr, double precision, dimension( * ) work, integer, dimension( * ) iwork, integer info)

DPORFS

Purpose:



 DPORFS improves the computed solution to a system of linear


 equations when the coefficient matrix is symmetric positive definite,


 and provides error bounds and backward error estimates for the


 solution.

Parameters

UPLO 



          UPLO is CHARACTER*1


          = 'U':  Upper triangle of A is stored;


          = 'L':  Lower triangle of A is stored.

N



          N is INTEGER


          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 matrices B and X.  NRHS >= 0.

A



          A is DOUBLE PRECISION array, dimension (LDA,N)


          The symmetric matrix A.  If UPLO = 'U', the leading N-by-N


          upper triangular part of A contains the upper triangular part


          of the matrix A, and the strictly lower triangular part of A


          is not referenced.  If UPLO = 'L', the leading N-by-N lower


          triangular part of A contains the lower triangular part of


          the matrix A, and the strictly upper triangular part of A is


          not referenced.

LDA



          LDA is INTEGER


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

AF



          AF is DOUBLE PRECISION array, dimension (LDAF,N)


          The triangular factor U or L from the Cholesky factorization


          A = U**T*U or A = L*L**T, as computed by DPOTRF.

LDAF



          LDAF is INTEGER


          The leading dimension of the array AF.  LDAF >= max(1,N).

B



          B is DOUBLE PRECISION array, dimension (LDB,NRHS)


          The 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)


          On entry, the solution matrix X, as computed by DPOTRS.


          On exit, the improved solution matrix X.

LDX



          LDX is INTEGER


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

FERR



          FERR is DOUBLE PRECISION array, dimension (NRHS)


          The estimated forward error bound for each solution vector


          X(j) (the j-th column of the solution matrix X).


          If XTRUE is the true solution corresponding to X(j), FERR(j)


          is an estimated upper bound for the magnitude of the largest


          element in (X(j) - XTRUE) divided by the magnitude of the


          largest element in X(j).  The estimate is as reliable as


          the estimate for RCOND, and is almost always a slight


          overestimate of the true error.

BERR



          BERR is DOUBLE PRECISION array, dimension (NRHS)


          The componentwise relative backward error of each solution


          vector X(j) (i.e., the smallest relative change in


          any element of A or B that makes X(j) an exact solution).

WORK



          WORK is DOUBLE PRECISION array, dimension (3*N)

IWORK



          IWORK is INTEGER array, dimension (N)

INFO



          INFO is INTEGER


          = 0:  successful exit


          < 0:  if INFO = -i, the i-th argument had an illegal value

Internal Parameters:



  ITMAX is the maximum number of steps of iterative refinement.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine sporfs (character uplo, integer n, integer nrhs, real, dimension( lda, * ) a, integer lda, real, dimension( ldaf, * ) af, integer ldaf, real, dimension( ldb, * ) b, integer ldb, real, dimension( ldx, * ) x, integer ldx, real, dimension( * ) ferr, real, dimension( * ) berr, real, dimension( * ) work, integer, dimension( * ) iwork, integer info)

SPORFS

Purpose:



 SPORFS improves the computed solution to a system of linear


 equations when the coefficient matrix is symmetric positive definite,


 and provides error bounds and backward error estimates for the


 solution.

Parameters

UPLO 



          UPLO is CHARACTER*1


          = 'U':  Upper triangle of A is stored;


          = 'L':  Lower triangle of A is stored.

N



          N is INTEGER


          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 matrices B and X.  NRHS >= 0.

A



          A is REAL array, dimension (LDA,N)


          The symmetric matrix A.  If UPLO = 'U', the leading N-by-N


          upper triangular part of A contains the upper triangular part


          of the matrix A, and the strictly lower triangular part of A


          is not referenced.  If UPLO = 'L', the leading N-by-N lower


          triangular part of A contains the lower triangular part of


          the matrix A, and the strictly upper triangular part of A is


          not referenced.

LDA



          LDA is INTEGER


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

AF



          AF is REAL array, dimension (LDAF,N)


          The triangular factor U or L from the Cholesky factorization


          A = U**T*U or A = L*L**T, as computed by SPOTRF.

LDAF



          LDAF is INTEGER


          The leading dimension of the array AF.  LDAF >= max(1,N).

B



          B is REAL array, dimension (LDB,NRHS)


          The right hand side matrix B.

LDB



          LDB is INTEGER


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

X



          X is REAL array, dimension (LDX,NRHS)


          On entry, the solution matrix X, as computed by SPOTRS.


          On exit, the improved solution matrix X.

LDX



          LDX is INTEGER


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

FERR



          FERR is REAL array, dimension (NRHS)


          The estimated forward error bound for each solution vector


          X(j) (the j-th column of the solution matrix X).


          If XTRUE is the true solution corresponding to X(j), FERR(j)


          is an estimated upper bound for the magnitude of the largest


          element in (X(j) - XTRUE) divided by the magnitude of the


          largest element in X(j).  The estimate is as reliable as


          the estimate for RCOND, and is almost always a slight


          overestimate of the true error.

BERR



          BERR is REAL array, dimension (NRHS)


          The componentwise relative backward error of each solution


          vector X(j) (i.e., the smallest relative change in


          any element of A or B that makes X(j) an exact solution).

WORK



          WORK is REAL array, dimension (3*N)

IWORK



          IWORK is INTEGER array, dimension (N)

INFO



          INFO is INTEGER


          = 0:  successful exit


          < 0:  if INFO = -i, the i-th argument had an illegal value

Internal Parameters:



  ITMAX is the maximum number of steps of iterative refinement.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

subroutine zporfs (character uplo, integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldaf, * ) af, integer ldaf, complex*16, dimension( ldb, * ) b, integer ldb, complex*16, dimension( ldx, * ) x, integer ldx, double precision, dimension( * ) ferr, double precision, dimension( * ) berr, complex*16, dimension( * ) work, double precision, dimension( * ) rwork, integer info)

ZPORFS

Purpose:



 ZPORFS improves the computed solution to a system of linear


 equations when the coefficient matrix is Hermitian positive definite,


 and provides error bounds and backward error estimates for the


 solution.

Parameters

UPLO 



          UPLO is CHARACTER*1


          = 'U':  Upper triangle of A is stored;


          = 'L':  Lower triangle of A is stored.

N



          N is INTEGER


          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 matrices B and X.  NRHS >= 0.

A



          A is COMPLEX*16 array, dimension (LDA,N)


          The Hermitian matrix A.  If UPLO = 'U', the leading N-by-N


          upper triangular part of A contains the upper triangular part


          of the matrix A, and the strictly lower triangular part of A


          is not referenced.  If UPLO = 'L', the leading N-by-N lower


          triangular part of A contains the lower triangular part of


          the matrix A, and the strictly upper triangular part of A is


          not referenced.

LDA



          LDA is INTEGER


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

AF



          AF is COMPLEX*16 array, dimension (LDAF,N)


          The triangular factor U or L from the Cholesky factorization


          A = U**H*U or A = L*L**H, as computed by ZPOTRF.

LDAF



          LDAF is INTEGER


          The leading dimension of the array AF.  LDAF >= max(1,N).

B



          B is COMPLEX*16 array, dimension (LDB,NRHS)


          The 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)


          On entry, the solution matrix X, as computed by ZPOTRS.


          On exit, the improved solution matrix X.

LDX



          LDX is INTEGER


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

FERR



          FERR is DOUBLE PRECISION array, dimension (NRHS)


          The estimated forward error bound for each solution vector


          X(j) (the j-th column of the solution matrix X).


          If XTRUE is the true solution corresponding to X(j), FERR(j)


          is an estimated upper bound for the magnitude of the largest


          element in (X(j) - XTRUE) divided by the magnitude of the


          largest element in X(j).  The estimate is as reliable as


          the estimate for RCOND, and is almost always a slight


          overestimate of the true error.

BERR



          BERR is DOUBLE PRECISION array, dimension (NRHS)


          The componentwise relative backward error of each solution


          vector X(j) (i.e., the smallest relative change in


          any element of A or B that makes X(j) an exact solution).

WORK



          WORK is COMPLEX*16 array, dimension (2*N)

RWORK



          RWORK is DOUBLE PRECISION array, dimension (N)

INFO



          INFO is INTEGER


          = 0:  successful exit


          < 0:  if INFO = -i, the i-th argument had an illegal value

Internal Parameters:



  ITMAX is the maximum number of steps of iterative refinement.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Author

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