1DSYRFS(1) LAPACK routine (version 3.1) DSYRFS(1)
2
6 DSYRFS - 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
9
11 SUBROUTINE DSYRFS( UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB, X,
12 LDX, FERR, BERR, WORK, IWORK, INFO )
13 CHARACTER UPLO
15 INTEGER INFO, LDA, LDAF, LDB, LDX, N, NRHS
17 INTEGER IPIV( * ), IWORK( * )
19 DOUBLE PRECISION A( LDA, * ), AF( LDAF, * ), B( LDB, * ),
21 BERR( * ), FERR( * ), WORK( * ), X( LDX, * )
22
24 DSYRFS improves the computed solution to a system of linear equations
25 when the coefficient matrix is symmetric indefinite, and provides error
26 bounds and backward error estimates for the solution.
27
30 UPLO (input) CHARACTER*1
31 = 'U': Upper triangle of A is stored;
32 = 'L': Lower triangle of A is stored.
33 N (input) INTEGER
35 The order of the matrix A. N >= 0.
36 NRHS (input) INTEGER
38 The number of right hand sides, i.e., the number of columns of
39 the matrices B and X. NRHS >= 0.
40 A (input) DOUBLE PRECISION array, dimension (LDA,N)
42 The symmetric matrix A. If UPLO = 'U', the leading N-by-N
43 upper triangular part of A contains the upper triangular part
44 of the matrix A, and the strictly lower triangular part of A is
45 not referenced. If UPLO = 'L', the leading N-by-N lower trian‐
46 gular part of A contains the lower triangular part of the
47 matrix A, and the strictly upper triangular part of A is not
48 referenced.
49 LDA (input) INTEGER
51 The leading dimension of the array A. LDA >= max(1,N).
52 AF (input) DOUBLE PRECISION array, dimension (LDAF,N)
54 The factored form of the matrix A. AF contains the block diag‐
55 onal matrix D and the multipliers used to obtain the factor U
56 or L from the factorization A = U*D*U**T or A = L*D*L**T as
57 computed by DSYTRF.
58 LDAF (input) INTEGER
60 The leading dimension of the array AF. LDAF >= max(1,N).
61 IPIV (input) INTEGER array, dimension (N)
63 Details of the interchanges and the block structure of D as
64 determined by DSYTRF.
65 B (input) DOUBLE PRECISION array, dimension (LDB,NRHS)
67 The right hand side matrix B.
68 LDB (input) INTEGER
70 The leading dimension of the array B. LDB >= max(1,N).
71 X (input/output) DOUBLE PRECISION array, dimension (LDX,NRHS)
73 On entry, the solution matrix X, as computed by DSYTRS. On
74 exit, the improved solution matrix X.
75 LDX (input) INTEGER
77 The leading dimension of the array X. LDX >= max(1,N).
78 FERR (output) DOUBLE PRECISION array, dimension (NRHS)
80 The estimated forward error bound for each solution vector X(j)
81 (the j-th column of the solution matrix X). If XTRUE is the
82 true solution corresponding to X(j), FERR(j) is an estimated
83 upper bound for the magnitude of the largest element in (X(j) -
84 XTRUE) divided by the magnitude of the largest element in X(j).
85 The estimate is as reliable as the estimate for RCOND, and is
86 almost always a slight overestimate of the true error.
87 BERR (output) DOUBLE PRECISION array, dimension (NRHS)
89 The componentwise relative backward error of each solution vec‐
90 tor X(j) (i.e., the smallest relative change in any element of
91 A or B that makes X(j) an exact solution).
92 WORK (workspace) DOUBLE PRECISION array, dimension (3*N)
94 IWORK (workspace) INTEGER array, dimension (N)
96 INFO (output) INTEGER
98 = 0: successful exit
99 < 0: if INFO = -i, the i-th argument had an illegal value
100
102 ITMAX is the maximum number of steps of iterative refinement.
103 LAPACK routine (version 3.1) November 2006 DSYRFS(1)