1SPORFS(1) LAPACK routine (version 3.2) SPORFS(1)
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6 SPORFS - improves the computed solution to a system of linear equations
7 when the coefficient matrix is symmetric positive definite,
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10 SUBROUTINE SPORFS( UPLO, N, NRHS, A, LDA, AF, LDAF, B, LDB, X, LDX,
11 FERR, BERR, WORK, IWORK, INFO )
12 CHARACTER UPLO
14 INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS
16 INTEGER IWORK( * )
18 REAL A( LDA, * ), AF( LDAF, * ), B( LDB, * ), BERR( * ),
20 FERR( * ), WORK( * ), X( LDX, * )
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23 SPORFS improves the computed solution to a system of linear equations
24 when the coefficient matrix is symmetric positive definite, and pro‐
25 vides error bounds and backward error estimates for the solution.
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28 UPLO (input) CHARACTER*1
29 = 'U': Upper triangle of A is stored;
30 = 'L': Lower triangle of A is stored.
31 N (input) INTEGER
33 The order of the matrix A. N >= 0.
34 NRHS (input) INTEGER
36 The number of right hand sides, i.e., the number of columns of
37 the matrices B and X. NRHS >= 0.
38 A (input) REAL array, dimension (LDA,N)
40 The symmetric matrix A. If UPLO = 'U', the leading N-by-N
41 upper triangular part of A contains the upper triangular part
42 of the matrix A, and the strictly lower triangular part of A is
43 not referenced. If UPLO = 'L', the leading N-by-N lower trian‐
44 gular part of A contains the lower triangular part of the
45 matrix A, and the strictly upper triangular part of A is not
46 referenced.
47 LDA (input) INTEGER
49 The leading dimension of the array A. LDA >= max(1,N).
50 AF (input) REAL array, dimension (LDAF,N)
52 The triangular factor U or L from the Cholesky factorization A
53 = U**T*U or A = L*L**T, as computed by SPOTRF.
54 LDAF (input) INTEGER
56 The leading dimension of the array AF. LDAF >= max(1,N).
57 B (input) REAL array, dimension (LDB,NRHS)
59 The right hand side matrix B.
60 LDB (input) INTEGER
62 The leading dimension of the array B. LDB >= max(1,N).
63 X (input/output) REAL array, dimension (LDX,NRHS)
65 On entry, the solution matrix X, as computed by SPOTRS. On
66 exit, the improved solution matrix X.
67 LDX (input) INTEGER
69 The leading dimension of the array X. LDX >= max(1,N).
70 FERR (output) REAL array, dimension (NRHS)
72 The estimated forward error bound for each solution vector X(j)
73 (the j-th column of the solution matrix X). If XTRUE is the
74 true solution corresponding to X(j), FERR(j) is an estimated
75 upper bound for the magnitude of the largest element in (X(j) -
76 XTRUE) divided by the magnitude of the largest element in X(j).
77 The estimate is as reliable as the estimate for RCOND, and is
78 almost always a slight overestimate of the true error.
79 BERR (output) REAL array, dimension (NRHS)
81 The componentwise relative backward error of each solution vec‐
82 tor X(j) (i.e., the smallest relative change in any element of
83 A or B that makes X(j) an exact solution).
84 WORK (workspace) REAL array, dimension (3*N)
86 IWORK (workspace) INTEGER array, dimension (N)
88 INFO (output) INTEGER
90 = 0: successful exit
91 < 0: if INFO = -i, the i-th argument had an illegal value
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94 ITMAX is the maximum number of steps of iterative refinement.
95 LAPACK routine (version 3.2) November 2008 SPORFS(1)