1DGTRFS(1) LAPACK routine (version 3.2) DGTRFS(1)
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6 DGTRFS - 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
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11 SUBROUTINE DGTRFS( TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF, DU2, IPIV,
12 B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO )
13 CHARACTER TRANS
15 INTEGER INFO, LDB, LDX, N, NRHS
17 INTEGER IPIV( * ), IWORK( * )
19 DOUBLE PRECISION B( LDB, * ), BERR( * ), D( * ), DF( * ),
21 DL( * ), DLF( * ), DU( * ), DU2( * ), DUF( * ),
22 FERR( * ), WORK( * ), X( LDX, * )
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25 DGTRFS improves the computed solution to a system of linear equations
26 when the coefficient matrix is tridiagonal, and provides error bounds
27 and backward error estimates for the solution.
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30 TRANS (input) CHARACTER*1
31 Specifies the form of the system of equations:
32 = 'N': A * X = B (No transpose)
33 = 'T': A**T * X = B (Transpose)
34 = 'C': A**H * X = B (Conjugate transpose = Transpose)
35 N (input) INTEGER
37 The order of the matrix A. N >= 0.
38 NRHS (input) INTEGER
40 The number of right hand sides, i.e., the number of columns of
41 the matrix B. NRHS >= 0.
42 DL (input) DOUBLE PRECISION array, dimension (N-1)
44 The (n-1) subdiagonal elements of A.
45 D (input) DOUBLE PRECISION array, dimension (N)
47 The diagonal elements of A.
48 DU (input) DOUBLE PRECISION array, dimension (N-1)
50 The (n-1) superdiagonal elements of A.
51 DLF (input) DOUBLE PRECISION array, dimension (N-1)
53 The (n-1) multipliers that define the matrix L from the LU fac‐
54 torization of A as computed by DGTTRF.
55 DF (input) DOUBLE PRECISION array, dimension (N)
57 The n diagonal elements of the upper triangular matrix U from
58 the LU factorization of A.
59 DUF (input) DOUBLE PRECISION array, dimension (N-1)
61 The (n-1) elements of the first superdiagonal of U.
62 DU2 (input) DOUBLE PRECISION array, dimension (N-2)
64 The (n-2) elements of the second superdiagonal of U.
65 IPIV (input) INTEGER array, dimension (N)
67 The pivot indices; for 1 <= i <= n, row i of the matrix was
68 interchanged with row IPIV(i). IPIV(i) will always be either i
69 or i+1; IPIV(i) = i indicates a row interchange was not
70 required.
71 B (input) DOUBLE PRECISION array, dimension (LDB,NRHS)
73 The right hand side matrix B.
74 LDB (input) INTEGER
76 The leading dimension of the array B. LDB >= max(1,N).
77 X (input/output) DOUBLE PRECISION array, dimension (LDX,NRHS)
79 On entry, the solution matrix X, as computed by DGTTRS. On
80 exit, the improved solution matrix X.
81 LDX (input) INTEGER
83 The leading dimension of the array X. LDX >= max(1,N).
84 FERR (output) DOUBLE PRECISION array, dimension (NRHS)
86 The estimated forward error bound for each solution vector X(j)
87 (the j-th column of the solution matrix X). If XTRUE is the
88 true solution corresponding to X(j), FERR(j) is an estimated
89 upper bound for the magnitude of the largest element in (X(j) -
90 XTRUE) divided by the magnitude of the largest element in X(j).
91 The estimate is as reliable as the estimate for RCOND, and is
92 almost always a slight overestimate of the true error.
93 BERR (output) DOUBLE PRECISION array, dimension (NRHS)
95 The componentwise relative backward error of each solution vec‐
96 tor X(j) (i.e., the smallest relative change in any element of
97 A or B that makes X(j) an exact solution).
98 WORK (workspace) DOUBLE PRECISION array, dimension (3*N)
100 IWORK (workspace) INTEGER array, dimension (N)
102 INFO (output) INTEGER
104 = 0: successful exit
105 < 0: if INFO = -i, the i-th argument had an illegal value
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108 ITMAX is the maximum number of steps of iterative refinement.
109 LAPACK routine (version 3.2) November 2008 DGTRFS(1)