1ZGTRFS(1) LAPACK routine (version 3.1) ZGTRFS(1)
2
6 ZGTRFS - the computed solution to a system of linear equations when the
7 coefficient matrix is tridiagonal, and provides error bounds and back‐
8 ward error estimates for the solution
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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.
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32 TRANS (input) CHARACTER*1
33 Specifies the form of the system of equations:
34 = 'N': A * X = B (No transpose)
35 = 'T': A**T * X = B (Transpose)
36 = 'C': A**H * X = B (Conjugate transpose)
37 N (input) INTEGER
39 The order of the matrix A. N >= 0.
40 NRHS (input) INTEGER
42 The number of right hand sides, i.e., the number of columns of
43 the matrix B. NRHS >= 0.
44 DL (input) COMPLEX*16 array, dimension (N-1)
46 The (n-1) subdiagonal elements of A.
47 D (input) COMPLEX*16 array, dimension (N)
49 The diagonal elements of A.
50 DU (input) COMPLEX*16 array, dimension (N-1)
52 The (n-1) superdiagonal elements of A.
53 DLF (input) COMPLEX*16 array, dimension (N-1)
55 The (n-1) multipliers that define the matrix L from the LU fac‐
56 torization of A as computed by ZGTTRF.
57 DF (input) COMPLEX*16 array, dimension (N)
59 The n diagonal elements of the upper triangular matrix U from
60 the LU factorization of A.
61 DUF (input) COMPLEX*16 array, dimension (N-1)
63 The (n-1) elements of the first superdiagonal of U.
64 DU2 (input) COMPLEX*16 array, dimension (N-2)
66 The (n-2) elements of the second superdiagonal of U.
67 IPIV (input) INTEGER array, dimension (N)
69 The pivot indices; for 1 <= i <= n, row i of the matrix was
70 interchanged with row IPIV(i). IPIV(i) will always be either i
71 or i+1; IPIV(i) = i indicates a row interchange was not
72 required.
73 B (input) COMPLEX*16 array, dimension (LDB,NRHS)
75 The right hand side matrix B.
76 LDB (input) INTEGER
78 The leading dimension of the array B. LDB >= max(1,N).
79 X (input/output) COMPLEX*16 array, dimension (LDX,NRHS)
81 On entry, the solution matrix X, as computed by ZGTTRS. On
82 exit, the improved solution matrix X.
83 LDX (input) INTEGER
85 The leading dimension of the array X. LDX >= max(1,N).
86 FERR (output) DOUBLE PRECISION array, dimension (NRHS)
88 The estimated forward error bound for each solution vector X(j)
89 (the j-th column of the solution matrix X). If XTRUE is the
90 true solution corresponding to X(j), FERR(j) is an estimated
91 upper bound for the magnitude of the largest element in (X(j) -
92 XTRUE) divided by the magnitude of the largest element in X(j).
93 The estimate is as reliable as the estimate for RCOND, and is
94 almost always a slight overestimate of the true error.
95 BERR (output) DOUBLE PRECISION array, dimension (NRHS)
97 The componentwise relative backward error of each solution vec‐
98 tor X(j) (i.e., the smallest relative change in any element of
99 A or B that makes X(j) an exact solution).
100 WORK (workspace) COMPLEX*16 array, dimension (2*N)
102 RWORK (workspace) DOUBLE PRECISION array, dimension (N)
104 INFO (output) INTEGER
106 = 0: successful exit
107 < 0: if INFO = -i, the i-th argument had an illegal value
108
110 ITMAX is the maximum number of steps of iterative refinement.
111 LAPACK routine (version 3.1) November 2006 ZGTRFS(1)