1DTRRFS(1) LAPACK routine (version 3.2) DTRRFS(1)
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6 DTRRFS - provides error bounds and backward error estimates for the
7 solution to a system of linear equations with a triangular coefficient
8 matrix
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11 SUBROUTINE DTRRFS( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, X, LDX,
12 FERR, BERR, WORK, IWORK, INFO )
13 CHARACTER DIAG, TRANS, UPLO
15 INTEGER INFO, LDA, LDB, LDX, N, NRHS
17 INTEGER IWORK( * )
19 DOUBLE PRECISION A( LDA, * ), B( LDB, * ), BERR( * ), FERR(
21 * ), WORK( * ), X( LDX, * )
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24 DTRRFS provides error bounds and backward error estimates for the solu‐
25 tion to a system of linear equations with a triangular coefficient
26 matrix. The solution matrix X must be computed by DTRTRS or some other
27 means before entering this routine. DTRRFS does not do iterative
28 refinement because doing so cannot improve the backward error.
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31 UPLO (input) CHARACTER*1
32 = 'U': A is upper triangular;
33 = 'L': A is lower triangular.
34 TRANS (input) CHARACTER*1
36 Specifies the form of the system of equations:
37 = 'N': A * X = B (No transpose)
38 = 'T': A**T * X = B (Transpose)
39 = 'C': A**H * X = B (Conjugate transpose = Transpose)
40 DIAG (input) CHARACTER*1
42 = 'N': A is non-unit triangular;
43 = 'U': A is unit triangular.
44 N (input) INTEGER
46 The order of the matrix A. N >= 0.
47 NRHS (input) INTEGER
49 The number of right hand sides, i.e., the number of columns of
50 the matrices B and X. NRHS >= 0.
51 A (input) DOUBLE PRECISION array, dimension (LDA,N)
53 The triangular matrix A. If UPLO = 'U', the leading N-by-N
54 upper triangular part of the array A contains the upper trian‐
55 gular matrix, and the strictly lower triangular part of A is
56 not referenced. If UPLO = 'L', the leading N-by-N lower trian‐
57 gular part of the array A contains the lower triangular matrix,
58 and the strictly upper triangular part of A is not referenced.
59 If DIAG = 'U', the diagonal elements of A are also not refer‐
60 enced and are assumed to be 1.
61 LDA (input) INTEGER
63 The leading dimension of the array A. LDA >= max(1,N).
64 B (input) DOUBLE PRECISION array, dimension (LDB,NRHS)
66 The right hand side matrix B.
67 LDB (input) INTEGER
69 The leading dimension of the array B. LDB >= max(1,N).
70 X (input) DOUBLE PRECISION array, dimension (LDX,NRHS)
72 The solution matrix X.
73 LDX (input) INTEGER
75 The leading dimension of the array X. LDX >= max(1,N).
76 FERR (output) DOUBLE PRECISION array, dimension (NRHS)
78 The estimated forward error bound for each solution vector X(j)
79 (the j-th column of the solution matrix X). If XTRUE is the
80 true solution corresponding to X(j), FERR(j) is an estimated
81 upper bound for the magnitude of the largest element in (X(j) -
82 XTRUE) divided by the magnitude of the largest element in X(j).
83 The estimate is as reliable as the estimate for RCOND, and is
84 almost always a slight overestimate of the true error.
85 BERR (output) DOUBLE PRECISION array, dimension (NRHS)
87 The componentwise relative backward error of each solution vec‐
88 tor X(j) (i.e., the smallest relative change in any element of
89 A or B that makes X(j) an exact solution).
90 WORK (workspace) DOUBLE PRECISION array, dimension (3*N)
92 IWORK (workspace) INTEGER array, dimension (N)
94 INFO (output) INTEGER
96 = 0: successful exit
97 < 0: if INFO = -i, the i-th argument had an illegal value
98 LAPACK routine (version 3.2) November 2008 DTRRFS(1)