1CTBRFS(1) LAPACK routine (version 3.1) CTBRFS(1)
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6 CTBRFS - error bounds and backward error estimates for the solution to
7 a system of linear equations with a triangular band coefficient matrix
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10 SUBROUTINE CTBRFS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B, LDB, X,
11 LDX, FERR, BERR, WORK, RWORK, INFO )
12 CHARACTER DIAG, TRANS, UPLO
14 INTEGER INFO, KD, LDAB, LDB, LDX, N, NRHS
16 REAL BERR( * ), FERR( * ), RWORK( * )
18 COMPLEX AB( LDAB, * ), B( LDB, * ), WORK( * ), X( LDX, * )
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22 CTBRFS provides error bounds and backward error estimates for the solu‐
23 tion to a system of linear equations with a triangular band coefficient
24 matrix.
25 The solution matrix X must be computed by CTBTRS or some other means
27 before entering this routine. CTBRFS 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 KD (input) INTEGER
50 The number of superdiagonals or subdiagonals of the triangular
51 band matrix A. KD >= 0.
52 NRHS (input) INTEGER
54 The number of right hand sides, i.e., the number of columns of
55 the matrices B and X. NRHS >= 0.
56 AB (input) COMPLEX array, dimension (LDAB,N)
58 The upper or lower triangular band matrix A, stored in the
59 first kd+1 rows of the array. The j-th column of A is stored in
60 the j-th column of the array AB as follows: if UPLO = 'U',
61 AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L',
62 AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). If DIAG = 'U',
63 the diagonal elements of A are not referenced and are assumed
64 to be 1.
65 LDAB (input) INTEGER
67 The leading dimension of the array AB. LDAB >= KD+1.
68 B (input) COMPLEX array, dimension (LDB,NRHS)
70 The right hand side matrix B.
71 LDB (input) INTEGER
73 The leading dimension of the array B. LDB >= max(1,N).
74 X (input) COMPLEX array, dimension (LDX,NRHS)
76 The solution matrix X.
77 LDX (input) INTEGER
79 The leading dimension of the array X. LDX >= max(1,N).
80 FERR (output) REAL array, dimension (NRHS)
82 The estimated forward error bound for each solution vector X(j)
83 (the j-th column of the solution matrix X). If XTRUE is the
84 true solution corresponding to X(j), FERR(j) is an estimated
85 upper bound for the magnitude of the largest element in (X(j) -
86 XTRUE) divided by the magnitude of the largest element in X(j).
87 The estimate is as reliable as the estimate for RCOND, and is
88 almost always a slight overestimate of the true error.
89 BERR (output) REAL array, dimension (NRHS)
91 The componentwise relative backward error of each solution vec‐
92 tor X(j) (i.e., the smallest relative change in any element of
93 A or B that makes X(j) an exact solution).
94 WORK (workspace) COMPLEX array, dimension (2*N)
96 RWORK (workspace) REAL array, dimension (N)
98 INFO (output) INTEGER
100 = 0: successful exit
101 < 0: if INFO = -i, the i-th argument had an illegal value
102 LAPACK routine (version 3.1) November 2006 CTBRFS(1)