dtprfs
dtprfs - provide error bounds and backward error estimates for the solution to a system of linear equations with a triangular packed coefficient matrix
SUBROUTINE DTPRFS( UPLO, TRANSA, DIAG, N, NRHS, A, B, LDB, X, LDX,
* FERR, BERR, WORK, WORK2, INFO)
CHARACTER * 1 UPLO, TRANSA, DIAG
INTEGER N, NRHS, LDB, LDX, INFO
INTEGER WORK2(*)
DOUBLE PRECISION A(*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*)
SUBROUTINE DTPRFS_64( UPLO, TRANSA, DIAG, N, NRHS, A, B, LDB, X,
* LDX, FERR, BERR, WORK, WORK2, INFO)
CHARACTER * 1 UPLO, TRANSA, DIAG
INTEGER*8 N, NRHS, LDB, LDX, INFO
INTEGER*8 WORK2(*)
DOUBLE PRECISION A(*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*)
SUBROUTINE TPRFS( UPLO, [TRANSA], DIAG, N, NRHS, A, B, [LDB], X,
* [LDX], FERR, BERR, [WORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: UPLO, TRANSA, DIAG
INTEGER :: N, NRHS, LDB, LDX, INFO
INTEGER, DIMENSION(:) :: WORK2
REAL(8), DIMENSION(:) :: A, FERR, BERR, WORK
REAL(8), DIMENSION(:,:) :: B, X
SUBROUTINE TPRFS_64( UPLO, [TRANSA], DIAG, N, NRHS, A, B, [LDB], X,
* [LDX], FERR, BERR, [WORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: UPLO, TRANSA, DIAG
INTEGER(8) :: N, NRHS, LDB, LDX, INFO
INTEGER(8), DIMENSION(:) :: WORK2
REAL(8), DIMENSION(:) :: A, FERR, BERR, WORK
REAL(8), DIMENSION(:,:) :: B, X
#include <sunperf.h>
void dtprfs(char uplo, char transa, char diag, int n, int nrhs, double *a, double *b, int ldb, double *x, int ldx, double *ferr, double *berr, int *info);
void dtprfs_64(char uplo, char transa, char diag, long n, long nrhs, double *a, double *b, long ldb, double *x, long ldx, double *ferr, double *berr, long *info);
dtprfs provides error bounds and backward error estimates for the
solution to a system of linear equations with a triangular packed
coefficient matrix.
The solution matrix X must be computed by STPTRS or some other
means before entering this routine. STPRFS 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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* 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 matrix A, packed columnwise in
a linear array. The j-th column of A is stored in the array
A as follows:
if UPLO = 'U', A(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', A(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
If DIAG = 'U', the diagonal elements of A are not referenced
and are assumed to be 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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