1ZTRRFS(1) LAPACK routine (version 3.1) ZTRRFS(1)
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6 ZTRRFS - 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 ZTRRFS( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, X, LDX,
11 FERR, BERR, WORK, RWORK, INFO )
12 CHARACTER DIAG, TRANS, UPLO
14 INTEGER INFO, LDA, LDB, LDX, N, NRHS
16 DOUBLE PRECISION BERR( * ), FERR( * ), RWORK( * )
18 COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * ), X( LDX, * )
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22 ZTRRFS provides error bounds and backward error estimates for the solu‐
23 tion to a system of linear equations with a triangular coefficient
24 matrix.
25 The solution matrix X must be computed by ZTRTRS or some other means
27 before entering this routine. ZTRRFS does not do iterative refinement
28 because doing so cannot improve the backward error.
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32 UPLO (input) CHARACTER*1
33 = 'U': A is upper triangular;
34 = 'L': A is lower triangular.
35 TRANS (input) CHARACTER*1
37 Specifies the form of the system of equations:
38 = 'N': A * X = B (No transpose)
39 = 'T': A**T * X = B (Transpose)
40 = 'C': A**H * X = B (Conjugate transpose)
41 DIAG (input) CHARACTER*1
43 = 'N': A is non-unit triangular;
44 = 'U': A is unit triangular.
45 N (input) INTEGER
47 The order of the matrix A. N >= 0.
48 NRHS (input) INTEGER
50 The number of right hand sides, i.e., the number of columns of
51 the matrices B and X. NRHS >= 0.
52 A (input) COMPLEX*16 array, dimension (LDA,N)
54 The triangular matrix A. If UPLO = 'U', the leading N-by-N
55 upper triangular part of the array A contains the upper trian‐
56 gular matrix, and the strictly lower triangular part of A is
57 not referenced. If UPLO = 'L', the leading N-by-N lower trian‐
58 gular part of the array A contains the lower triangular matrix,
59 and the strictly upper triangular part of A is not referenced.
60 If DIAG = 'U', the diagonal elements of A are also not refer‐
61 enced and are assumed to be 1.
62 LDA (input) INTEGER
64 The leading dimension of the array A. LDA >= max(1,N).
65 B (input) COMPLEX*16 array, dimension (LDB,NRHS)
67 The right hand side matrix B.
68 LDB (input) INTEGER
70 The leading dimension of the array B. LDB >= max(1,N).
71 X (input) COMPLEX*16 array, dimension (LDX,NRHS)
73 The solution matrix X.
74 LDX (input) INTEGER
76 The leading dimension of the array X. LDX >= max(1,N).
77 FERR (output) DOUBLE PRECISION array, dimension (NRHS)
79 The estimated forward error bound for each solution vector X(j)
80 (the j-th column of the solution matrix X). If XTRUE is the
81 true solution corresponding to X(j), FERR(j) is an estimated
82 upper bound for the magnitude of the largest element in (X(j) -
83 XTRUE) divided by the magnitude of the largest element in X(j).
84 The estimate is as reliable as the estimate for RCOND, and is
85 almost always a slight overestimate of the true error.
86 BERR (output) DOUBLE PRECISION array, dimension (NRHS)
88 The componentwise relative backward error of each solution vec‐
89 tor X(j) (i.e., the smallest relative change in any element of
90 A or B that makes X(j) an exact solution).
91 WORK (workspace) COMPLEX*16 array, dimension (2*N)
93 RWORK (workspace) DOUBLE PRECISION array, dimension (N)
95 INFO (output) INTEGER
97 = 0: successful exit
98 < 0: if INFO = -i, the i-th argument had an illegal value
99 LAPACK routine (version 3.1) November 2006 ZTRRFS(1)