1ZSPRFS(1) LAPACK routine (version 3.1) ZSPRFS(1)
2
6 ZSPRFS - the computed solution to a system of linear equations when the
7 coefficient matrix is symmetric indefinite and packed, and provides
8 error bounds and backward error estimates for the solution
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11 SUBROUTINE ZSPRFS( UPLO, N, NRHS, AP, AFP, IPIV, B, LDB, X, LDX, FERR,
12 BERR, WORK, RWORK, INFO )
13 CHARACTER UPLO
15 INTEGER INFO, LDB, LDX, N, NRHS
17 INTEGER IPIV( * )
19 DOUBLE PRECISION BERR( * ), FERR( * ), RWORK( * )
21 COMPLEX*16 AFP( * ), AP( * ), B( LDB, * ), WORK( * ), X( LDX, *
23 )
24
26 ZSPRFS improves the computed solution to a system of linear equations
27 when the coefficient matrix is symmetric indefinite and packed, and
28 provides error 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 AP (input) COMPLEX*16 array, dimension (N*(N+1)/2)
44 The upper or lower triangle of the symmetric matrix A, packed
45 columnwise in a linear array. The j-th column of A is stored
46 in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) =
47 A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) =
48 A(i,j) for j<=i<=n.
49 AFP (input) COMPLEX*16 array, dimension (N*(N+1)/2)
51 The factored form of the matrix A. AFP contains the block
52 diagonal matrix D and the multipliers used to obtain the factor
53 U or L from the factorization A = U*D*U**T or A = L*D*L**T as
54 computed by ZSPTRF, stored as a packed triangular matrix.
55 IPIV (input) INTEGER array, dimension (N)
57 Details of the interchanges and the block structure of D as
58 determined by ZSPTRF.
59 B (input) COMPLEX*16 array, dimension (LDB,NRHS)
61 The right hand side matrix B.
62 LDB (input) INTEGER
64 The leading dimension of the array B. LDB >= max(1,N).
65 X (input/output) COMPLEX*16 array, dimension (LDX,NRHS)
67 On entry, the solution matrix X, as computed by ZSPTRS. On
68 exit, the improved solution matrix X.
69 LDX (input) INTEGER
71 The leading dimension of the array X. LDX >= max(1,N).
72 FERR (output) DOUBLE PRECISION array, dimension (NRHS)
74 The estimated forward error bound for each solution vector X(j)
75 (the j-th column of the solution matrix X). If XTRUE is the
76 true solution corresponding to X(j), FERR(j) is an estimated
77 upper bound for the magnitude of the largest element in (X(j) -
78 XTRUE) divided by the magnitude of the largest element in X(j).
79 The estimate is as reliable as the estimate for RCOND, and is
80 almost always a slight overestimate of the true error.
81 BERR (output) DOUBLE PRECISION array, dimension (NRHS)
83 The componentwise relative backward error of each solution vec‐
84 tor X(j) (i.e., the smallest relative change in any element of
85 A or B that makes X(j) an exact solution).
86 WORK (workspace) COMPLEX*16 array, dimension (2*N)
88 RWORK (workspace) DOUBLE PRECISION array, dimension (N)
90 INFO (output) INTEGER
92 = 0: successful exit
93 < 0: if INFO = -i, the i-th argument had an illegal value
94
96 ITMAX is the maximum number of steps of iterative refinement.
97 LAPACK routine (version 3.1) November 2006 ZSPRFS(1)