1ZSYRFS(1) LAPACK routine (version 3.2) ZSYRFS(1)
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6 ZSYRFS - improves the computed solution to a system of linear equations
7 when the coefficient matrix is symmetric indefinite, and provides error
8 bounds and backward error estimates for the solution
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11 SUBROUTINE ZSYRFS( UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB, X,
12 LDX, FERR, BERR, WORK, RWORK, INFO )
13 CHARACTER UPLO
15 INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS
17 INTEGER IPIV( * )
19 DOUBLE PRECISION BERR( * ), FERR( * ), RWORK( * )
21 COMPLEX*16 A( LDA, * ), AF( LDAF, * ), B( LDB, * ), WORK( * ),
23 X( LDX, * )
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26 ZSYRFS improves the computed solution to a system of linear equations
27 when the coefficient matrix is symmetric indefinite, and provides error
28 bounds and backward error estimates for the solution.
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31 UPLO (input) CHARACTER*1
32 = 'U': Upper triangle of A is stored;
33 = 'L': Lower triangle of A is stored.
34 N (input) INTEGER
36 The order of the matrix A. N >= 0.
37 NRHS (input) INTEGER
39 The number of right hand sides, i.e., the number of columns of
40 the matrices B and X. NRHS >= 0.
41 A (input) COMPLEX*16 array, dimension (LDA,N)
43 The symmetric matrix A. If UPLO = 'U', the leading N-by-N
44 upper triangular part of A contains the upper triangular part
45 of the matrix A, and the strictly lower triangular part of A is
46 not referenced. If UPLO = 'L', the leading N-by-N lower trian‐
47 gular part of A contains the lower triangular part of the
48 matrix A, and the strictly upper triangular part of A is not
49 referenced.
50 LDA (input) INTEGER
52 The leading dimension of the array A. LDA >= max(1,N).
53 AF (input) COMPLEX*16 array, dimension (LDAF,N)
55 The factored form of the matrix A. AF contains the block diag‐
56 onal matrix D and the multipliers used to obtain the factor U
57 or L from the factorization A = U*D*U**T or A = L*D*L**T as
58 computed by ZSYTRF.
59 LDAF (input) INTEGER
61 The leading dimension of the array AF. LDAF >= max(1,N).
62 IPIV (input) INTEGER array, dimension (N)
64 Details of the interchanges and the block structure of D as
65 determined by ZSYTRF.
66 B (input) COMPLEX*16 array, dimension (LDB,NRHS)
68 The right hand side matrix B.
69 LDB (input) INTEGER
71 The leading dimension of the array B. LDB >= max(1,N).
72 X (input/output) COMPLEX*16 array, dimension (LDX,NRHS)
74 On entry, the solution matrix X, as computed by ZSYTRS. On
75 exit, the improved solution matrix X.
76 LDX (input) INTEGER
78 The leading dimension of the array X. LDX >= max(1,N).
79 FERR (output) DOUBLE PRECISION array, dimension (NRHS)
81 The estimated forward error bound for each solution vector X(j)
82 (the j-th column of the solution matrix X). If XTRUE is the
83 true solution corresponding to X(j), FERR(j) is an estimated
84 upper bound for the magnitude of the largest element in (X(j) -
85 XTRUE) divided by the magnitude of the largest element in X(j).
86 The estimate is as reliable as the estimate for RCOND, and is
87 almost always a slight overestimate of the true error.
88 BERR (output) DOUBLE PRECISION array, dimension (NRHS)
90 The componentwise relative backward error of each solution vec‐
91 tor X(j) (i.e., the smallest relative change in any element of
92 A or B that makes X(j) an exact solution).
93 WORK (workspace) COMPLEX*16 array, dimension (2*N)
95 RWORK (workspace) DOUBLE PRECISION array, dimension (N)
97 INFO (output) INTEGER
99 = 0: successful exit
100 < 0: if INFO = -i, the i-th argument had an illegal value
101
103 ITMAX is the maximum number of steps of iterative refinement.
104 LAPACK routine (version 3.2) November 2008 ZSYRFS(1)