1ZPPRFS(1) LAPACK routine (version 3.1) ZPPRFS(1)
2
6 ZPPRFS - the computed solution to a system of linear equations when the
7 coefficient matrix is Hermitian positive definite and packed, and pro‐
8 vides error bounds and backward error estimates for the solution
9
11 SUBROUTINE ZPPRFS( UPLO, N, NRHS, AP, AFP, B, LDB, X, LDX, FERR, BERR,
12 WORK, RWORK, INFO )
13 CHARACTER UPLO
15 INTEGER INFO, LDB, LDX, N, NRHS
17 DOUBLE PRECISION BERR( * ), FERR( * ), RWORK( * )
19 COMPLEX*16 AFP( * ), AP( * ), B( LDB, * ), WORK( * ), X( LDX, *
21 )
22
24 ZPPRFS improves the computed solution to a system of linear equations
25 when the coefficient matrix is Hermitian positive definite and packed,
26 and provides error bounds and backward error estimates for the solu‐
27 tion.
28
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*16 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)*(2n-j)/2) =
47 A(i,j) for j<=i<=n.
48 AFP (input) COMPLEX*16 array, dimension (N*(N+1)/2)
50 The triangular factor U or L from the Cholesky factorization A
51 = U**H*U or A = L*L**H, as computed by DPPTRF/ZPPTRF, packed
52 columnwise in a linear array in the same format as A (see AP).
53 B (input) COMPLEX*16 array, dimension (LDB,NRHS)
55 The right hand side matrix B.
56 LDB (input) INTEGER
58 The leading dimension of the array B. LDB >= max(1,N).
59 X (input/output) COMPLEX*16 array, dimension (LDX,NRHS)
61 On entry, the solution matrix X, as computed by ZPPTRS. On
62 exit, the improved solution matrix X.
63 LDX (input) INTEGER
65 The leading dimension of the array X. LDX >= max(1,N).
66 FERR (output) DOUBLE PRECISION array, dimension (NRHS)
68 The estimated forward error bound for each solution vector X(j)
69 (the j-th column of the solution matrix X). If XTRUE is the
70 true solution corresponding to X(j), FERR(j) is an estimated
71 upper bound for the magnitude of the largest element in (X(j) -
72 XTRUE) divided by the magnitude of the largest element in X(j).
73 The estimate is as reliable as the estimate for RCOND, and is
74 almost always a slight overestimate of the true error.
75 BERR (output) DOUBLE PRECISION array, dimension (NRHS)
77 The componentwise relative backward error of each solution vec‐
78 tor X(j) (i.e., the smallest relative change in any element of
79 A or B that makes X(j) an exact solution).
80 WORK (workspace) COMPLEX*16 array, dimension (2*N)
82 RWORK (workspace) DOUBLE PRECISION array, dimension (N)
84 INFO (output) INTEGER
86 = 0: successful exit
87 < 0: if INFO = -i, the i-th argument had an illegal value
88
90 ITMAX is the maximum number of steps of iterative refinement.
91 LAPACK routine (version 3.1) November 2006 ZPPRFS(1)