1DTRRFS(1) LAPACK routine (version 3.1) DTRRFS(1)
2
6 DTRRFS - error bounds and backward error estimates for the solution to
7 a system of linear equations with a triangular coefficient matrix
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10 SUBROUTINE DTRRFS( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, X, LDX,
11 FERR, BERR, WORK, IWORK, INFO )
12 CHARACTER DIAG, TRANS, UPLO
14 INTEGER INFO, LDA, LDB, LDX, N, NRHS
16 INTEGER IWORK( * )
18 DOUBLE PRECISION A( LDA, * ), B( LDB, * ), BERR( * ), FERR(
20 * ), WORK( * ), X( LDX, * )
21
23 DTRRFS provides error bounds and backward error estimates for the solu‐
24 tion to a system of linear equations with a triangular coefficient
25 matrix.
26 The solution matrix X must be computed by DTRTRS or some other means
28 before entering this routine. DTRRFS does not do iterative refinement
29 because doing so cannot improve the backward error.
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33 UPLO (input) CHARACTER*1
34 = 'U': A is upper triangular;
35 = 'L': A is lower triangular.
36 TRANS (input) CHARACTER*1
38 Specifies the form of the system of equations:
39 = 'N': A * X = B (No transpose)
40 = 'T': A**T * X = B (Transpose)
41 = 'C': A**H * X = B (Conjugate transpose = Transpose)
42 DIAG (input) CHARACTER*1
44 = 'N': A is non-unit triangular;
45 = 'U': A is unit triangular.
46 N (input) INTEGER
48 The order of the matrix A. N >= 0.
49 NRHS (input) INTEGER
51 The number of right hand sides, i.e., the number of columns of
52 the matrices B and X. NRHS >= 0.
53 A (input) DOUBLE PRECISION array, dimension (LDA,N)
55 The triangular matrix A. If UPLO = 'U', the leading N-by-N
56 upper triangular part of the array A contains the upper trian‐
57 gular matrix, and the strictly lower triangular part of A is
58 not referenced. If UPLO = 'L', the leading N-by-N lower trian‐
59 gular part of the array A contains the lower triangular matrix,
60 and the strictly upper triangular part of A is not referenced.
61 If DIAG = 'U', the diagonal elements of A are also not refer‐
62 enced and are assumed to be 1.
63 LDA (input) INTEGER
65 The leading dimension of the array A. LDA >= max(1,N).
66 B (input) DOUBLE PRECISION array, dimension (LDB,NRHS)
68 The right hand side matrix B.
69 LDB (input) INTEGER
71 The leading dimension of the array B. LDB >= max(1,N).
72 X (input) DOUBLE PRECISION array, dimension (LDX,NRHS)
74 The solution matrix X.
75 LDX (input) INTEGER
77 The leading dimension of the array X. LDX >= max(1,N).
78 FERR (output) DOUBLE PRECISION array, dimension (NRHS)
80 The estimated forward error bound for each solution vector X(j)
81 (the j-th column of the solution matrix X). If XTRUE is the
82 true solution corresponding to X(j), FERR(j) is an estimated
83 upper bound for the magnitude of the largest element in (X(j) -
84 XTRUE) divided by the magnitude of the largest element in X(j).
85 The estimate is as reliable as the estimate for RCOND, and is
86 almost always a slight overestimate of the true error.
87 BERR (output) DOUBLE PRECISION array, dimension (NRHS)
89 The componentwise relative backward error of each solution vec‐
90 tor X(j) (i.e., the smallest relative change in any element of
91 A or B that makes X(j) an exact solution).
92 WORK (workspace) DOUBLE PRECISION array, dimension (3*N)
94 IWORK (workspace) INTEGER array, dimension (N)
96 INFO (output) INTEGER
98 = 0: successful exit
99 < 0: if INFO = -i, the i-th argument had an illegal value
100 LAPACK routine (version 3.1) November 2006 DTRRFS(1)