stbrfs
stbrfs - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular band coefficient matrix
SUBROUTINE STBRFS( UPLO, TRANSA, DIAG, N, NDIAG, NRHS, A, LDA, B,
* LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)
CHARACTER * 1 UPLO, TRANSA, DIAG
INTEGER N, NDIAG, NRHS, LDA, LDB, LDX, INFO
INTEGER WORK2(*)
REAL A(LDA,*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*)
SUBROUTINE STBRFS_64( UPLO, TRANSA, DIAG, N, NDIAG, NRHS, A, LDA, B,
* LDB, X, LDX, FERR, BERR, WORK, WORK2, INFO)
CHARACTER * 1 UPLO, TRANSA, DIAG
INTEGER*8 N, NDIAG, NRHS, LDA, LDB, LDX, INFO
INTEGER*8 WORK2(*)
REAL A(LDA,*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*)
SUBROUTINE TBRFS( UPLO, [TRANSA], DIAG, N, NDIAG, NRHS, A, [LDA], B,
* [LDB], X, [LDX], FERR, BERR, [WORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: UPLO, TRANSA, DIAG
INTEGER :: N, NDIAG, NRHS, LDA, LDB, LDX, INFO
INTEGER, DIMENSION(:) :: WORK2
REAL, DIMENSION(:) :: FERR, BERR, WORK
REAL, DIMENSION(:,:) :: A, B, X
SUBROUTINE TBRFS_64( UPLO, [TRANSA], DIAG, N, NDIAG, NRHS, A, [LDA],
* B, [LDB], X, [LDX], FERR, BERR, [WORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: UPLO, TRANSA, DIAG
INTEGER(8) :: N, NDIAG, NRHS, LDA, LDB, LDX, INFO
INTEGER(8), DIMENSION(:) :: WORK2
REAL, DIMENSION(:) :: FERR, BERR, WORK
REAL, DIMENSION(:,:) :: A, B, X
#include <sunperf.h>
void stbrfs(char uplo, char transa, char diag, int n, int ndiag, int nrhs, float *a, int lda, float *b, int ldb, float *x, int ldx, float *ferr, float *berr, int *info);
void stbrfs_64(char uplo, char transa, char diag, long n, long ndiag, long nrhs, float *a, long lda, float *b, long ldb, float *x, long ldx, float *ferr, float *berr, long *info);
stbrfs provides error bounds and backward error estimates for the
solution to a system of linear equations with a triangular band
coefficient matrix.
The solution matrix X must be computed by STBTRS or some other
means before entering this routine. STBRFS does not do iterative
refinement because doing so cannot improve the backward error.
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* UPLO (input)
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* TRANSA (input)
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Specifies the form of the system of equations:
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* DIAG (input)
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* N (input)
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The order of the matrix A. N >= 0.
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* NDIAG (input)
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The number of superdiagonals or subdiagonals of the
triangular band matrix A. NDIAG >= 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 upper or lower triangular band matrix A, stored in the
first kd+1 rows of the array. The j-th column of A is stored
in the j-th column of the array A as follows:
if UPLO = 'U', A(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', A(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
If DIAG = 'U', the diagonal elements of A are not referenced
and are assumed to be 1.
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* LDA (input)
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The leading dimension of the array A. LDA >= NDIAG+1.
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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)
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The 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(3*N)
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* WORK2 (workspace)
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* INFO (output)
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