1CHPRFS(1) LAPACK routine (version 3.2) CHPRFS(1)
2
6 CHPRFS - improves the computed solution to a system of linear equations
7 when the coefficient matrix is Hermitian indefinite and packed, and
8 provides error bounds and backward error estimates for the solution
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11 SUBROUTINE CHPRFS( 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 REAL BERR( * ), FERR( * ), RWORK( * )
21 COMPLEX AFP( * ), AP( * ), B( LDB, * ), WORK( * ), X( LDX, *
23 )
24
26 CHPRFS improves the computed solution to a system of linear equations
27 when the coefficient matrix is Hermitian indefinite and packed, and
28 provides error bounds and backward error estimates for the solution.
29
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 AP (input) COMPLEX array, dimension (N*(N+1)/2)
43 The upper or lower triangle of the Hermitian matrix A, packed
44 columnwise in a linear array. The j-th column of A is stored
45 in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) =
46 A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) =
47 A(i,j) for j<=i<=n.
48 AFP (input) COMPLEX array, dimension (N*(N+1)/2)
50 The factored form of the matrix A. AFP contains the block
51 diagonal matrix D and the multipliers used to obtain the factor
52 U or L from the factorization A = U*D*U**H or A = L*D*L**H as
53 computed by CHPTRF, stored as a packed triangular matrix.
54 IPIV (input) INTEGER array, dimension (N)
56 Details of the interchanges and the block structure of D as
57 determined by CHPTRF.
58 B (input) COMPLEX 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 array, dimension (LDX,NRHS)
66 On entry, the solution matrix X, as computed by CHPTRS. 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) REAL 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) REAL 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 array, dimension (2*N)
87 RWORK (workspace) REAL 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 3.2) November 2008 CHPRFS(1)