1CTRRFS(1) LAPACK routine (version 3.2) CTRRFS(1)
2
6 CTRRFS - 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 CTRRFS( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, X, LDX,
12 FERR, BERR, WORK, RWORK, INFO )
13 CHARACTER DIAG, TRANS, UPLO
15 INTEGER INFO, LDA, LDB, LDX, N, NRHS
17 REAL BERR( * ), FERR( * ), RWORK( * )
19 COMPLEX A( LDA, * ), B( LDB, * ), WORK( * ), X( LDX, * )
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23 CTRRFS provides error bounds and backward error estimates for the solu‐
24 tion to a system of linear equations with a triangular coefficient
25 matrix. The solution matrix X must be computed by CTRTRS or some other
26 means before entering this routine. CTRRFS does not do iterative
27 refinement because doing so cannot improve the backward error.
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30 UPLO (input) CHARACTER*1
31 = 'U': A is upper triangular;
32 = 'L': A is lower triangular.
33 TRANS (input) CHARACTER*1
35 Specifies the form of the system of equations:
36 = 'N': A * X = B (No transpose)
37 = 'T': A**T * X = B (Transpose)
38 = 'C': A**H * X = B (Conjugate transpose)
39 DIAG (input) CHARACTER*1
41 = 'N': A is non-unit triangular;
42 = 'U': A is unit triangular.
43 N (input) INTEGER
45 The order of the matrix A. N >= 0.
46 NRHS (input) INTEGER
48 The number of right hand sides, i.e., the number of columns of
49 the matrices B and X. NRHS >= 0.
50 A (input) COMPLEX array, dimension (LDA,N)
52 The triangular matrix A. If UPLO = 'U', the leading N-by-N
53 upper triangular part of the array A contains the upper trian‐
54 gular matrix, and the strictly lower triangular part of A is
55 not referenced. If UPLO = 'L', the leading N-by-N lower trian‐
56 gular part of the array A contains the lower triangular matrix,
57 and the strictly upper triangular part of A is not referenced.
58 If DIAG = 'U', the diagonal elements of A are also not refer‐
59 enced and are assumed to be 1.
60 LDA (input) INTEGER
62 The leading dimension of the array A. LDA >= max(1,N).
63 B (input) COMPLEX array, dimension (LDB,NRHS)
65 The right hand side matrix B.
66 LDB (input) INTEGER
68 The leading dimension of the array B. LDB >= max(1,N).
69 X (input) COMPLEX array, dimension (LDX,NRHS)
71 The solution matrix X.
72 LDX (input) INTEGER
74 The leading dimension of the array X. LDX >= max(1,N).
75 FERR (output) REAL array, dimension (NRHS)
77 The estimated forward error bound for each solution vector X(j)
78 (the j-th column of the solution matrix X). If XTRUE is the
79 true solution corresponding to X(j), FERR(j) is an estimated
80 upper bound for the magnitude of the largest element in (X(j) -
81 XTRUE) divided by the magnitude of the largest element in X(j).
82 The estimate is as reliable as the estimate for RCOND, and is
83 almost always a slight overestimate of the true error.
84 BERR (output) REAL array, dimension (NRHS)
86 The componentwise relative backward error of each solution vec‐
87 tor X(j) (i.e., the smallest relative change in any element of
88 A or B that makes X(j) an exact solution).
89 WORK (workspace) COMPLEX array, dimension (2*N)
91 RWORK (workspace) REAL array, dimension (N)
93 INFO (output) INTEGER
95 = 0: successful exit
96 < 0: if INFO = -i, the i-th argument had an illegal value
97 LAPACK routine (version 3.2) November 2008 CTRRFS(1)