1ZPORFS(1) LAPACK routine (version 3.1) ZPORFS(1)
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6 ZPORFS - the computed solution to a system of linear equations when the
7 coefficient matrix is Hermitian positive definite,
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10 SUBROUTINE ZPORFS( UPLO, N, NRHS, A, LDA, AF, LDAF, B, LDB, X, LDX,
11 FERR, BERR, WORK, RWORK, INFO )
12 CHARACTER UPLO
14 INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS
16 DOUBLE PRECISION BERR( * ), FERR( * ), RWORK( * )
18 COMPLEX*16 A( LDA, * ), AF( LDAF, * ), B( LDB, * ), WORK( * ),
20 X( LDX, * )
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23 ZPORFS improves the computed solution to a system of linear equations
24 when the coefficient matrix is Hermitian positive definite, and pro‐
25 vides error bounds and backward error estimates for the solution.
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29 UPLO (input) CHARACTER*1
30 = 'U': Upper triangle of A is stored;
31 = 'L': Lower triangle of A is stored.
32 N (input) INTEGER
34 The order of the matrix A. N >= 0.
35 NRHS (input) INTEGER
37 The number of right hand sides, i.e., the number of columns of
38 the matrices B and X. NRHS >= 0.
39 A (input) COMPLEX*16 array, dimension (LDA,N)
41 The Hermitian matrix A. If UPLO = 'U', the leading N-by-N
42 upper triangular part of A contains the upper triangular part
43 of the matrix A, and the strictly lower triangular part of A is
44 not referenced. If UPLO = 'L', the leading N-by-N lower trian‐
45 gular part of A contains the lower triangular part of the
46 matrix A, and the strictly upper triangular part of A is not
47 referenced.
48 LDA (input) INTEGER
50 The leading dimension of the array A. LDA >= max(1,N).
51 AF (input) COMPLEX*16 array, dimension (LDAF,N)
53 The triangular factor U or L from the Cholesky factorization A
54 = U**H*U or A = L*L**H, as computed by ZPOTRF.
55 LDAF (input) INTEGER
57 The leading dimension of the array AF. LDAF >= max(1,N).
58 B (input) COMPLEX*16 array, dimension (LDB,NRHS)
60 The right hand side matrix B.
61 LDB (input) INTEGER
63 The leading dimension of the array B. LDB >= max(1,N).
64 X (input/output) COMPLEX*16 array, dimension (LDX,NRHS)
66 On entry, the solution matrix X, as computed by ZPOTRS. On
67 exit, the improved solution matrix X.
68 LDX (input) INTEGER
70 The leading dimension of the array X. LDX >= max(1,N).
71 FERR (output) DOUBLE PRECISION array, dimension (NRHS)
73 The estimated forward error bound for each solution vector X(j)
74 (the j-th column of the solution matrix X). If XTRUE is the
75 true solution corresponding to X(j), FERR(j) is an estimated
76 upper bound for the magnitude of the largest element in (X(j) -
77 XTRUE) divided by the magnitude of the largest element in X(j).
78 The estimate is as reliable as the estimate for RCOND, and is
79 almost always a slight overestimate of the true error.
80 BERR (output) DOUBLE PRECISION array, dimension (NRHS)
82 The componentwise relative backward error of each solution vec‐
83 tor X(j) (i.e., the smallest relative change in any element of
84 A or B that makes X(j) an exact solution).
85 WORK (workspace) COMPLEX*16 array, dimension (2*N)
87 RWORK (workspace) DOUBLE PRECISION array, dimension (N)
89 INFO (output) INTEGER
91 = 0: successful exit
92 < 0: if INFO = -i, the i-th argument had an illegal value
93
95 ITMAX is the maximum number of steps of iterative refinement.
96 LAPACK routine (version 3.1) November 2006 ZPORFS(1)