Library Functions Manual

NAME¶

trrfs - trrfs: triangular iterative refinement

SYNOPSIS¶

Functions¶

subroutine CTRRFS (uplo, trans, diag, n, nrhs, a, lda, b, ldb, x, ldx, ferr, berr, work, rwork, info)
CTRRFS subroutine DTRRFS (uplo, trans, diag, n, nrhs, a, lda, b, ldb, x, ldx, ferr, berr, work, iwork, info)
DTRRFS subroutine STRRFS (uplo, trans, diag, n, nrhs, a, lda, b, ldb, x, ldx, ferr, berr, work, iwork, info)
STRRFS subroutine ZTRRFS (uplo, trans, diag, n, nrhs, a, lda, b, ldb, x, ldx, ferr, berr, work, rwork, info)
ZTRRFS

Detailed Description¶

Function Documentation¶

subroutine CTRRFS (character uplo, character trans, character diag, integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, 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)¶

CTRRFS

Purpose:

!>
!> CTRRFS provides error bounds and backward error estimates for the
!> solution to a system of linear equations with a triangular
!> coefficient matrix.
!>
!> The solution matrix X must be computed by CTRTRS or some other
!> means before entering this routine.  CTRRFS does not do iterative
!> refinement because doing so cannot improve the backward error.
!>

Parameters

UPLO

!>          UPLO is CHARACTER*1
!>          = 'U':  A is upper triangular;
!>          = 'L':  A is lower triangular.
!>

TRANS

!>          TRANS is CHARACTER*1
!>          Specifies the form of the system of equations:
!>          = 'N':  A * X = B     (No transpose)
!>          = 'T':  A**T * X = B  (Transpose)
!>          = 'C':  A**H * X = B  (Conjugate transpose)
!>

DIAG

!>          DIAG is CHARACTER*1
!>          = 'N':  A is non-unit triangular;
!>          = 'U':  A is unit triangular.
!>

!>          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 is COMPLEX array, dimension (LDA,N)
!>          The triangular matrix A.  If UPLO = 'U', the leading N-by-N
!>          upper triangular part of the array A contains the upper
!>          triangular matrix, and the strictly lower triangular part of
!>          A is not referenced.  If UPLO = 'L', the leading N-by-N lower
!>          triangular part of the array A contains the lower triangular
!>          matrix, and the strictly upper triangular part of A is not
!>          referenced.  If DIAG = 'U', the diagonal elements of A are
!>          also not referenced and are assumed to be 1.
!>

LDA

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

!>          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 is COMPLEX array, dimension (LDX,NRHS)
!>          The 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
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 180 of file ctrrfs.f.

subroutine DTRRFS (character uplo, character trans, character diag, integer n, integer nrhs, double precision, dimension( lda, * ) a, integer lda, 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)¶

DTRRFS

Purpose:

!>
!> DTRRFS provides error bounds and backward error estimates for the
!> solution to a system of linear equations with a triangular
!> coefficient matrix.
!>
!> The solution matrix X must be computed by DTRTRS or some other
!> means before entering this routine.  DTRRFS does not do iterative
!> refinement because doing so cannot improve the backward error.
!>

Parameters

UPLO

!>          UPLO is CHARACTER*1
!>          = 'U':  A is upper triangular;
!>          = 'L':  A is lower triangular.
!>

TRANS

!>          TRANS is CHARACTER*1
!>          Specifies the form of the system of equations:
!>          = 'N':  A * X = B  (No transpose)
!>          = 'T':  A**T * X = B  (Transpose)
!>          = 'C':  A**H * X = B  (Conjugate transpose = Transpose)
!>

DIAG

!>          DIAG is CHARACTER*1
!>          = 'N':  A is non-unit triangular;
!>          = 'U':  A is unit triangular.
!>

!>          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 is DOUBLE PRECISION array, dimension (LDA,N)
!>          The triangular matrix A.  If UPLO = 'U', the leading N-by-N
!>          upper triangular part of the array A contains the upper
!>          triangular matrix, and the strictly lower triangular part of
!>          A is not referenced.  If UPLO = 'L', the leading N-by-N lower
!>          triangular part of the array A contains the lower triangular
!>          matrix, and the strictly upper triangular part of A is not
!>          referenced.  If DIAG = 'U', the diagonal elements of A are
!>          also not referenced and are assumed to be 1.
!>

LDA

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

!>          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 is DOUBLE PRECISION array, dimension (LDX,NRHS)
!>          The 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
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 180 of file dtrrfs.f.

subroutine STRRFS (character uplo, character trans, character diag, integer n, integer nrhs, real, dimension( lda, * ) a, integer lda, 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)¶

STRRFS

Purpose:

!>
!> STRRFS provides error bounds and backward error estimates for the
!> solution to a system of linear equations with a triangular
!> coefficient matrix.
!>
!> The solution matrix X must be computed by STRTRS or some other
!> means before entering this routine.  STRRFS does not do iterative
!> refinement because doing so cannot improve the backward error.
!>

Parameters

UPLO

!>          UPLO is CHARACTER*1
!>          = 'U':  A is upper triangular;
!>          = 'L':  A is lower triangular.
!>

TRANS

!>          TRANS is CHARACTER*1
!>          Specifies the form of the system of equations:
!>          = 'N':  A * X = B  (No transpose)
!>          = 'T':  A**T * X = B  (Transpose)
!>          = 'C':  A**H * X = B  (Conjugate transpose = Transpose)
!>

DIAG

!>          DIAG is CHARACTER*1
!>          = 'N':  A is non-unit triangular;
!>          = 'U':  A is unit triangular.
!>

!>          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 is REAL array, dimension (LDA,N)
!>          The triangular matrix A.  If UPLO = 'U', the leading N-by-N
!>          upper triangular part of the array A contains the upper
!>          triangular matrix, and the strictly lower triangular part of
!>          A is not referenced.  If UPLO = 'L', the leading N-by-N lower
!>          triangular part of the array A contains the lower triangular
!>          matrix, and the strictly upper triangular part of A is not
!>          referenced.  If DIAG = 'U', the diagonal elements of A are
!>          also not referenced and are assumed to be 1.
!>

LDA

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

!>          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 is REAL array, dimension (LDX,NRHS)
!>          The 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
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 180 of file strrfs.f.

subroutine ZTRRFS (character uplo, character trans, character diag, integer n, integer nrhs, complex16, dimension( lda, ) a, integer lda, complex16, dimension( ldb, ) b, integer ldb, complex16, dimension( ldx, ) x, integer ldx, double precision, dimension( * ) ferr, double precision, dimension( * ) berr, complex16, dimension( ) work, double precision, dimension( * ) rwork, integer info)¶

ZTRRFS

Purpose:

!>
!> ZTRRFS provides error bounds and backward error estimates for the
!> solution to a system of linear equations with a triangular
!> coefficient matrix.
!>
!> The solution matrix X must be computed by ZTRTRS or some other
!> means before entering this routine.  ZTRRFS does not do iterative
!> refinement because doing so cannot improve the backward error.
!>

Parameters

UPLO

!>          UPLO is CHARACTER*1
!>          = 'U':  A is upper triangular;
!>          = 'L':  A is lower triangular.
!>

TRANS

!>          TRANS is CHARACTER*1
!>          Specifies the form of the system of equations:
!>          = 'N':  A * X = B     (No transpose)
!>          = 'T':  A**T * X = B  (Transpose)
!>          = 'C':  A**H * X = B  (Conjugate transpose)
!>

DIAG

!>          DIAG is CHARACTER*1
!>          = 'N':  A is non-unit triangular;
!>          = 'U':  A is unit triangular.
!>

!>          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 is COMPLEX*16 array, dimension (LDA,N)
!>          The triangular matrix A.  If UPLO = 'U', the leading N-by-N
!>          upper triangular part of the array A contains the upper
!>          triangular matrix, and the strictly lower triangular part of
!>          A is not referenced.  If UPLO = 'L', the leading N-by-N lower
!>          triangular part of the array A contains the lower triangular
!>          matrix, and the strictly upper triangular part of A is not
!>          referenced.  If DIAG = 'U', the diagonal elements of A are
!>          also not referenced and are assumed to be 1.
!>

LDA

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

!>          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 is COMPLEX*16 array, dimension (LDX,NRHS)
!>          The 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
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 180 of file ztrrfs.f.

Author¶

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