SPORFS(3F) SPORFS(3F)
SPORFS  improve the computed solution to a system of linear equations
when the coefficient matrix is symmetric positive definite,
SUBROUTINE SPORFS( UPLO, N, NRHS, A, LDA, AF, LDAF, B, LDB, X, LDX, FERR,
BERR, WORK, IWORK, INFO )
CHARACTER UPLO
INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS
INTEGER IWORK( * )
REAL A( LDA, * ), AF( LDAF, * ), B( LDB, * ), BERR( * ),
FERR( * ), WORK( * ), X( LDX, * )
SPORFS improves the computed solution to a system of linear equations
when the coefficient matrix is symmetric positive definite, and provides
error bounds and backward error estimates for the solution.
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns of
the matrices B and X. NRHS >= 0.
A (input) REAL array, dimension (LDA,N)
The symmetric matrix A. If UPLO = 'U', the leading NbyN upper
triangular part of A contains the upper triangular part of the
matrix A, and the strictly lower triangular part of A is not
referenced. If UPLO = 'L', the leading NbyN lower triangular
part of A contains the lower triangular part of the matrix A, and
the strictly upper triangular part of A is not referenced.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
AF (input) REAL array, dimension (LDAF,N)
The triangular factor U or L from the Cholesky factorization A =
U**T*U or A = L*L**T, as computed by SPOTRF.
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SPORFS(3F) SPORFS(3F)
LDAF (input) INTEGER
The leading dimension of the array AF. LDAF >= max(1,N).
B (input) REAL array, dimension (LDB,NRHS)
The right hand side matrix B.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
X (input/output) REAL array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by SPOTRS. On exit,
the improved solution matrix X.
LDX (input) INTEGER
The leading dimension of the array X. LDX >= max(1,N).
FERR (output) REAL array, dimension (NRHS)
The estimated forward error bound for each solution vector X(j)
(the jth 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 (output) 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 (workspace) REAL array, dimension (3*N)
IWORK (workspace) INTEGER array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
ITMAX is the maximum number of steps of iterative refinement.
SPORFS(3F) SPORFS(3F)
SPORFS  improve the computed solution to a system of linear equations
when the coefficient matrix is symmetric positive definite,
SUBROUTINE SPORFS( UPLO, N, NRHS, A, LDA, AF, LDAF, B, LDB, X, LDX, FERR,
BERR, WORK, IWORK, INFO )
CHARACTER UPLO
INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS
INTEGER IWORK( * )
REAL A( LDA, * ), AF( LDAF, * ), B( LDB, * ), BERR( * ),
FERR( * ), WORK( * ), X( LDX, * )
SPORFS improves the computed solution to a system of linear equations
when the coefficient matrix is symmetric positive definite, and provides
error bounds and backward error estimates for the solution.
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns of
the matrices B and X. NRHS >= 0.
A (input) REAL array, dimension (LDA,N)
The symmetric matrix A. If UPLO = 'U', the leading NbyN upper
triangular part of A contains the upper triangular part of the
matrix A, and the strictly lower triangular part of A is not
referenced. If UPLO = 'L', the leading NbyN lower triangular
part of A contains the lower triangular part of the matrix A, and
the strictly upper triangular part of A is not referenced.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
AF (input) REAL array, dimension (LDAF,N)
The triangular factor U or L from the Cholesky factorization A =
U**T*U or A = L*L**T, as computed by SPOTRF.
Page 1
SPORFS(3F) SPORFS(3F)
LDAF (input) INTEGER
The leading dimension of the array AF. LDAF >= max(1,N).
B (input) REAL array, dimension (LDB,NRHS)
The right hand side matrix B.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
X (input/output) REAL array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by SPOTRS. On exit,
the improved solution matrix X.
LDX (input) INTEGER
The leading dimension of the array X. LDX >= max(1,N).
FERR (output) REAL array, dimension (NRHS)
The estimated forward error bound for each solution vector X(j)
(the jth 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 (output) 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 (workspace) REAL array, dimension (3*N)
IWORK (workspace) INTEGER array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
ITMAX is the maximum number of steps of iterative refinement.
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