sgerfs
sgerfs - improve the computed solution to a system of linear equations and provides error bounds and backward error estimates for the solution
SUBROUTINE SGERFS( TRANSA, N, NRHS, A, LDA, AF, LDAF, IPIVOT, B,
* LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)
CHARACTER * 1 TRANSA
INTEGER N, NRHS, LDA, LDAF, LDB, LDX, INFO
INTEGER IPIVOT(*), WORK2(*)
REAL A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*)
SUBROUTINE SGERFS_64( TRANSA, N, NRHS, A, LDA, AF, LDAF, IPIVOT, B,
* LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)
CHARACTER * 1 TRANSA
INTEGER*8 N, NRHS, LDA, LDAF, LDB, LDX, INFO
INTEGER*8 IPIVOT(*), WORK2(*)
REAL A(LDA,*), AF(LDAF,*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*)
SUBROUTINE GERFS( [TRANSA], [N], [NRHS], A, [LDA], AF, [LDAF],
* IPIVOT, B, [LDB], X, [LDX], FERR, BERR, [WORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: TRANSA
INTEGER :: N, NRHS, LDA, LDAF, LDB, LDX, INFO
INTEGER, DIMENSION(:) :: IPIVOT, WORK2
REAL, DIMENSION(:) :: FERR, BERR, WORK
REAL, DIMENSION(:,:) :: A, AF, B, X
SUBROUTINE GERFS_64( [TRANSA], [N], [NRHS], A, [LDA], AF, [LDAF],
* IPIVOT, B, [LDB], X, [LDX], FERR, BERR, [WORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: TRANSA
INTEGER(8) :: N, NRHS, LDA, LDAF, LDB, LDX, INFO
INTEGER(8), DIMENSION(:) :: IPIVOT, WORK2
REAL, DIMENSION(:) :: FERR, BERR, WORK
REAL, DIMENSION(:,:) :: A, AF, B, X
#include <sunperf.h>
void sgerfs(char transa, int n, int nrhs, float *a, int lda, float *af, int ldaf, int *ipivot, float *b, int ldb, float *x, int ldx, float *ferr, float *berr, int *info);
void sgerfs_64(char transa, long n, long nrhs, float *a, long lda, float *af, long ldaf, long *ipivot, float *b, long ldb, float *x, long ldx, float *ferr, float *berr, long *info);
sgerfs improves the computed solution to a system of linear
equations and provides error bounds and backward error estimates for
the solution.
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* TRANSA (input)
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Specifies the form of the system of equations:
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* N (input)
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The order of the matrix A. N >= 0.
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* NRHS (input)
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The number of right hand sides, i.e., the number of columns
of the matrices B and X. NRHS >= 0.
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* A (input)
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The original N-by-N matrix A.
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* LDA (input)
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The leading dimension of the array A. LDA >= max(1,N).
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* AF (input)
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The factors L and U from the factorization A = P*L*U
as computed by SGETRF.
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* LDAF (input)
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The leading dimension of the array AF. LDAF >= max(1,N).
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* IPIVOT (input)
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The pivot indices from SGETRF; for 1<=i<=N, row i of the
matrix was interchanged with row IPIVOT(i).
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* B (input)
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The right hand side matrix B.
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* LDB (input)
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The leading dimension of the array B. LDB >= max(1,N).
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* X (input/output)
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On entry, the solution matrix X, as computed by SGETRS.
On exit, the improved solution matrix X.
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* LDX (input)
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The leading dimension of the array X. LDX >= max(1,N).
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* FERR (output)
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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.
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* BERR (output)
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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).
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* WORK (workspace)
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dimension(2*N)
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* WORK2 (workspace)
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* INFO (output)
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