1CTBRFS(1) LAPACK routine (version 3.2) CTBRFS(1)
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6 CTBRFS - provides error bounds and backward error estimates for the
7 solution to a system of linear equations with a triangular band coeffi‐
8 cient matrix
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11 SUBROUTINE CTBRFS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B, LDB, X,
12 LDX, FERR, BERR, WORK, RWORK, INFO )
13 CHARACTER DIAG, TRANS, UPLO
15 INTEGER INFO, KD, LDAB, LDB, LDX, N, NRHS
17 REAL BERR( * ), FERR( * ), RWORK( * )
19 COMPLEX AB( LDAB, * ), B( LDB, * ), WORK( * ), X( LDX, * )
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23 CTBRFS provides error bounds and backward error estimates for the solu‐
24 tion to a system of linear equations with a triangular band coefficient
25 matrix. The solution matrix X must be computed by CTBTRS or some other
26 means before entering this routine. CTBRFS 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 KD (input) INTEGER
48 The number of superdiagonals or subdiagonals of the triangular
49 band matrix A. KD >= 0.
50 NRHS (input) INTEGER
52 The number of right hand sides, i.e., the number of columns of
53 the matrices B and X. NRHS >= 0.
54 AB (input) COMPLEX array, dimension (LDAB,N)
56 The upper or lower triangular band matrix A, stored in the
57 first kd+1 rows of the array. The j-th column of A is stored in
58 the j-th column of the array AB as follows: if UPLO = 'U',
59 AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L',
60 AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). If DIAG = 'U',
61 the diagonal elements of A are not referenced and are assumed
62 to be 1.
63 LDAB (input) INTEGER
65 The leading dimension of the array AB. LDAB >= KD+1.
66 B (input) COMPLEX 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) COMPLEX 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) REAL 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) REAL 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) COMPLEX array, dimension (2*N)
94 RWORK (workspace) REAL 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 3.2) November 2008 CTBRFS(1)