1ZGTRFS(1) LAPACK routine (version 3.2) ZGTRFS(1)
2
6 ZGTRFS - improves the computed solution to a system of linear equations
7 when the coefficient matrix is tridiagonal, and provides error bounds
8 and backward error estimates for the solution
9
11 SUBROUTINE ZGTRFS( TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, DU2, IPIV,
12 B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO )
13 CHARACTER TRANS
15 INTEGER INFO, LDB, LDX, N, NRHS
17 INTEGER IPIV( * )
19 DOUBLE PRECISION BERR( * ), FERR( * ), RWORK( * )
21 COMPLEX*16 B( LDB, * ), D( * ), DF( * ), DL( * ), DLF( * ), DU(
23 * ), DU2( * ), DUF( * ), WORK( * ), X( LDX, * )
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26 ZGTRFS improves the computed solution to a system of linear equations
27 when the coefficient matrix is tridiagonal, and provides error bounds
28 and backward error estimates for the solution.
29
31 TRANS (input) CHARACTER*1
32 Specifies the form of the system of equations:
33 = 'N': A * X = B (No transpose)
34 = 'T': A**T * X = B (Transpose)
35 = 'C': A**H * X = B (Conjugate transpose)
36 N (input) INTEGER
38 The order of the matrix A. N >= 0.
39 NRHS (input) INTEGER
41 The number of right hand sides, i.e., the number of columns of
42 the matrix B. NRHS >= 0.
43 DL (input) COMPLEX*16 array, dimension (N-1)
45 The (n-1) subdiagonal elements of A.
46 D (input) COMPLEX*16 array, dimension (N)
48 The diagonal elements of A.
49 DU (input) COMPLEX*16 array, dimension (N-1)
51 The (n-1) superdiagonal elements of A.
52 DLF (input) COMPLEX*16 array, dimension (N-1)
54 The (n-1) multipliers that define the matrix L from the LU fac‐
55 torization of A as computed by ZGTTRF.
56 DF (input) COMPLEX*16 array, dimension (N)
58 The n diagonal elements of the upper triangular matrix U from
59 the LU factorization of A.
60 DUF (input) COMPLEX*16 array, dimension (N-1)
62 The (n-1) elements of the first superdiagonal of U.
63 DU2 (input) COMPLEX*16 array, dimension (N-2)
65 The (n-2) elements of the second superdiagonal of U.
66 IPIV (input) INTEGER array, dimension (N)
68 The pivot indices; for 1 <= i <= n, row i of the matrix was
69 interchanged with row IPIV(i). IPIV(i) will always be either i
70 or i+1; IPIV(i) = i indicates a row interchange was not
71 required.
72 B (input) COMPLEX*16 array, dimension (LDB,NRHS)
74 The right hand side matrix B.
75 LDB (input) INTEGER
77 The leading dimension of the array B. LDB >= max(1,N).
78 X (input/output) COMPLEX*16 array, dimension (LDX,NRHS)
80 On entry, the solution matrix X, as computed by ZGTTRS. On
81 exit, the improved solution matrix X.
82 LDX (input) INTEGER
84 The leading dimension of the array X. LDX >= max(1,N).
85 FERR (output) DOUBLE PRECISION array, dimension (NRHS)
87 The estimated forward error bound for each solution vector X(j)
88 (the j-th column of the solution matrix X). If XTRUE is the
89 true solution corresponding to X(j), FERR(j) is an estimated
90 upper bound for the magnitude of the largest element in (X(j) -
91 XTRUE) divided by the magnitude of the largest element in X(j).
92 The estimate is as reliable as the estimate for RCOND, and is
93 almost always a slight overestimate of the true error.
94 BERR (output) DOUBLE PRECISION array, dimension (NRHS)
96 The componentwise relative backward error of each solution vec‐
97 tor X(j) (i.e., the smallest relative change in any element of
98 A or B that makes X(j) an exact solution).
99 WORK (workspace) COMPLEX*16 array, dimension (2*N)
101 RWORK (workspace) DOUBLE PRECISION array, dimension (N)
103 INFO (output) INTEGER
105 = 0: successful exit
106 < 0: if INFO = -i, the i-th argument had an illegal value
107
109 ITMAX is the maximum number of steps of iterative refinement.
110 LAPACK routine (version 3.2) November 2008 ZGTRFS(1)