1CSYRFS(1) LAPACK routine (version 3.1) CSYRFS(1)
2
6 CSYRFS - the computed solution to a system of linear equations when the
7 coefficient matrix is symmetric indefinite, and provides error bounds
8 and backward error estimates for the solution
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11 SUBROUTINE CSYRFS( 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 REAL BERR( * ), FERR( * ), RWORK( * )
21 COMPLEX A( LDA, * ), AF( LDAF, * ), B( LDB, * ), WORK( * ),
23 X( LDX, * )
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26 CSYRFS 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.
29
32 UPLO (input) CHARACTER*1
33 = 'U': Upper triangle of A is stored;
34 = 'L': Lower triangle of A is stored.
35 N (input) INTEGER
37 The order of the matrix A. N >= 0.
38 NRHS (input) INTEGER
40 The number of right hand sides, i.e., the number of columns of
41 the matrices B and X. NRHS >= 0.
42 A (input) COMPLEX array, dimension (LDA,N)
44 The symmetric matrix A. If UPLO = 'U', the leading N-by-N
45 upper triangular part of A contains the upper triangular part
46 of the matrix A, and the strictly lower triangular part of A is
47 not referenced. If UPLO = 'L', the leading N-by-N lower trian‐
48 gular part of A contains the lower triangular part of the
49 matrix A, and the strictly upper triangular part of A is not
50 referenced.
51 LDA (input) INTEGER
53 The leading dimension of the array A. LDA >= max(1,N).
54 AF (input) COMPLEX array, dimension (LDAF,N)
56 The factored form of the matrix A. AF contains the block diag‐
57 onal matrix D and the multipliers used to obtain the factor U
58 or L from the factorization A = U*D*U**T or A = L*D*L**T as
59 computed by CSYTRF.
60 LDAF (input) INTEGER
62 The leading dimension of the array AF. LDAF >= max(1,N).
63 IPIV (input) INTEGER array, dimension (N)
65 Details of the interchanges and the block structure of D as
66 determined by CSYTRF.
67 B (input) COMPLEX array, dimension (LDB,NRHS)
69 The right hand side matrix B.
70 LDB (input) INTEGER
72 The leading dimension of the array B. LDB >= max(1,N).
73 X (input/output) COMPLEX array, dimension (LDX,NRHS)
75 On entry, the solution matrix X, as computed by CSYTRS. On
76 exit, the improved solution matrix X.
77 LDX (input) INTEGER
79 The leading dimension of the array X. LDX >= max(1,N).
80 FERR (output) REAL array, dimension (NRHS)
82 The estimated forward error bound for each solution vector X(j)
83 (the j-th column of the solution matrix X). If XTRUE is the
84 true solution corresponding to X(j), FERR(j) is an estimated
85 upper bound for the magnitude of the largest element in (X(j) -
86 XTRUE) divided by the magnitude of the largest element in X(j).
87 The estimate is as reliable as the estimate for RCOND, and is
88 almost always a slight overestimate of the true error.
89 BERR (output) REAL array, dimension (NRHS)
91 The componentwise relative backward error of each solution vec‐
92 tor X(j) (i.e., the smallest relative change in any element of
93 A or B that makes X(j) an exact solution).
94 WORK (workspace) COMPLEX array, dimension (2*N)
96 RWORK (workspace) REAL array, dimension (N)
98 INFO (output) INTEGER
100 = 0: successful exit
101 < 0: if INFO = -i, the i-th argument had an illegal value
102
104 ITMAX is the maximum number of steps of iterative refinement.
105 LAPACK routine (version 3.1) November 2006 CSYRFS(1)