1ZPTRFS(1) LAPACK routine (version 3.1) ZPTRFS(1)
2
6 ZPTRFS - the computed solution to a system of linear equations when the
7 coefficient matrix is Hermitian positive definite and tridiagonal, and
8 provides error bounds and backward error estimates for the solution
9
11 SUBROUTINE ZPTRFS( UPLO, N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR,
12 BERR, WORK, RWORK, INFO )
13 CHARACTER UPLO
15 INTEGER INFO, LDB, LDX, N, NRHS
17 DOUBLE PRECISION BERR( * ), D( * ), DF( * ), FERR( * ),
19 RWORK( * )
20 COMPLEX*16 B( LDB, * ), E( * ), EF( * ), WORK( * ), X( LDX, * )
22
24 ZPTRFS improves the computed solution to a system of linear equations
25 when the coefficient matrix is Hermitian positive definite and tridiag‐
26 onal, and provides error bounds and backward error estimates for the
27 solution.
28
31 UPLO (input) CHARACTER*1
32 Specifies whether the superdiagonal or the subdiagonal of the
33 tridiagonal matrix A is stored and the form of the factoriza‐
34 tion:
35 = 'U': E is the superdiagonal of A, and A = U**H*D*U;
36 = 'L': E is the subdiagonal of A, and A = L*D*L**H. (The two
37 forms are equivalent if A is real.)
38 N (input) INTEGER
40 The order of the matrix A. N >= 0.
41 NRHS (input) INTEGER
43 The number of right hand sides, i.e., the number of columns of
44 the matrix B. NRHS >= 0.
45 D (input) DOUBLE PRECISION array, dimension (N)
47 The n real diagonal elements of the tridiagonal matrix A.
48 E (input) COMPLEX*16 array, dimension (N-1)
50 The (n-1) off-diagonal elements of the tridiagonal matrix A
51 (see UPLO).
52 DF (input) DOUBLE PRECISION array, dimension (N)
54 The n diagonal elements of the diagonal matrix D from the fac‐
55 torization computed by ZPTTRF.
56 EF (input) COMPLEX*16 array, dimension (N-1)
58 The (n-1) off-diagonal elements of the unit bidiagonal factor U
59 or L from the factorization computed by ZPTTRF (see UPLO).
60 B (input) COMPLEX*16 array, dimension (LDB,NRHS)
62 The right hand side matrix B.
63 LDB (input) INTEGER
65 The leading dimension of the array B. LDB >= max(1,N).
66 X (input/output) COMPLEX*16 array, dimension (LDX,NRHS)
68 On entry, the solution matrix X, as computed by ZPTTRS. On
69 exit, the improved solution matrix X.
70 LDX (input) INTEGER
72 The leading dimension of the array X. LDX >= max(1,N).
73 FERR (output) DOUBLE PRECISION array, dimension (NRHS)
75 The forward error bound for each solution vector X(j) (the j-th
76 column of the solution matrix X). If XTRUE is the true solu‐
77 tion corresponding to X(j), FERR(j) is an estimated upper bound
78 for the magnitude of the largest element in (X(j) - XTRUE)
79 divided by the magnitude of the largest element in X(j).
80 BERR (output) DOUBLE PRECISION 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*16 array, dimension (N)
87 RWORK (workspace) DOUBLE PRECISION 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 3.1) November 2006 ZPTRFS(1)