dpprfs
dpprfs - improve the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and packed, and provides error bounds and backward error estimates for the solution
SUBROUTINE DPPRFS( UPLO, N, NRHS, A, AF, B, LDB, X, LDX, FERR, BERR,
* WORK, WORK2, INFO)
CHARACTER * 1 UPLO
INTEGER N, NRHS, LDB, LDX, INFO
INTEGER WORK2(*)
DOUBLE PRECISION A(*), AF(*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*)
SUBROUTINE DPPRFS_64( UPLO, N, NRHS, A, AF, B, LDB, X, LDX, FERR,
* BERR, WORK, WORK2, INFO)
CHARACTER * 1 UPLO
INTEGER*8 N, NRHS, LDB, LDX, INFO
INTEGER*8 WORK2(*)
DOUBLE PRECISION A(*), AF(*), B(LDB,*), X(LDX,*), FERR(*), BERR(*), WORK(*)
SUBROUTINE PPRFS( UPLO, N, [NRHS], A, AF, B, [LDB], X, [LDX], FERR,
* BERR, [WORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: UPLO
INTEGER :: N, NRHS, LDB, LDX, INFO
INTEGER, DIMENSION(:) :: WORK2
REAL(8), DIMENSION(:) :: A, AF, FERR, BERR, WORK
REAL(8), DIMENSION(:,:) :: B, X
SUBROUTINE PPRFS_64( UPLO, N, [NRHS], A, AF, B, [LDB], X, [LDX],
* FERR, BERR, [WORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: UPLO
INTEGER(8) :: N, NRHS, LDB, LDX, INFO
INTEGER(8), DIMENSION(:) :: WORK2
REAL(8), DIMENSION(:) :: A, AF, FERR, BERR, WORK
REAL(8), DIMENSION(:,:) :: B, X
#include <sunperf.h>
void dpprfs(char uplo, int n, int nrhs, double *a, double *af, double *b, int ldb, double *x, int ldx, double *ferr, double *berr, int *info);
void dpprfs_64(char uplo, long n, long nrhs, double *a, double *af, double *b, long ldb, double *x, long ldx, double *ferr, double *berr, long *info);
dpprfs improves the computed solution to a system of linear
equations when the coefficient matrix is symmetric positive definite
and packed, and provides error bounds and backward error estimates
for the solution.
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* UPLO (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 triangle of the symmetric 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)*(2n-j)/2) = A(i,j) for j<=i<=n.
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* AF (input)
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The triangular factor U or L from the Cholesky factorization
A = U**T*U or A = L*L**T, as computed by SPPTRF/CPPTRF,
packed columnwise in a linear array in the same format as A
(see A).
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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 SPPTRS.
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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