1DTBRFS(1) LAPACK routine (version 3.2) DTBRFS(1)
2
6 DTBRFS - 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 DTBRFS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B, LDB, X,
12 LDX, FERR, BERR, WORK, IWORK, INFO )
13 CHARACTER DIAG, TRANS, UPLO
15 INTEGER INFO, KD, LDAB, LDB, LDX, N, NRHS
17 INTEGER IWORK( * )
19 DOUBLE PRECISION AB( LDAB, * ), B( LDB, * ), BERR( * ),
21 FERR( * ), WORK( * ), X( LDX, * )
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24 DTBRFS provides error bounds and backward error estimates for the solu‐
25 tion to a system of linear equations with a triangular band coefficient
26 matrix. The solution matrix X must be computed by DTBTRS or some other
27 means before entering this routine. DTBRFS does not do iterative
28 refinement because doing so cannot improve the backward error.
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31 UPLO (input) CHARACTER*1
32 = 'U': A is upper triangular;
33 = 'L': A is lower triangular.
34 TRANS (input) CHARACTER*1
36 Specifies the form of the system of equations:
37 = 'N': A * X = B (No transpose)
38 = 'T': A**T * X = B (Transpose)
39 = 'C': A**H * X = B (Conjugate transpose = Transpose)
40 DIAG (input) CHARACTER*1
42 = 'N': A is non-unit triangular;
43 = 'U': A is unit triangular.
44 N (input) INTEGER
46 The order of the matrix A. N >= 0.
47 KD (input) INTEGER
49 The number of superdiagonals or subdiagonals of the triangular
50 band matrix A. KD >= 0.
51 NRHS (input) INTEGER
53 The number of right hand sides, i.e., the number of columns of
54 the matrices B and X. NRHS >= 0.
55 AB (input) DOUBLE PRECISION array, dimension (LDAB,N)
57 The upper or lower triangular band matrix A, stored in the
58 first kd+1 rows of the array. The j-th column of A is stored in
59 the j-th column of the array AB as follows: if UPLO = 'U',
60 AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L',
61 AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). If DIAG = 'U',
62 the diagonal elements of A are not referenced and are assumed
63 to be 1.
64 LDAB (input) INTEGER
66 The leading dimension of the array AB. LDAB >= KD+1.
67 B (input) DOUBLE PRECISION array, dimension (LDB,NRHS)
69 The right hand side matrix B.
70 LDB (input) INTEGER
72 The leading dimension of the array B. LDB >= max(1,N).
73 X (input) DOUBLE PRECISION array, dimension (LDX,NRHS)
75 The solution matrix X.
76 LDX (input) INTEGER
78 The leading dimension of the array X. LDX >= max(1,N).
79 FERR (output) DOUBLE PRECISION array, dimension (NRHS)
81 The estimated forward error bound for each solution vector X(j)
82 (the j-th column of the solution matrix X). If XTRUE is the
83 true solution corresponding to X(j), FERR(j) is an estimated
84 upper bound for the magnitude of the largest element in (X(j) -
85 XTRUE) divided by the magnitude of the largest element in X(j).
86 The estimate is as reliable as the estimate for RCOND, and is
87 almost always a slight overestimate of the true error.
88 BERR (output) DOUBLE PRECISION array, dimension (NRHS)
90 The componentwise relative backward error of each solution vec‐
91 tor X(j) (i.e., the smallest relative change in any element of
92 A or B that makes X(j) an exact solution).
93 WORK (workspace) DOUBLE PRECISION array, dimension (3*N)
95 IWORK (workspace) INTEGER array, dimension (N)
97 INFO (output) INTEGER
99 = 0: successful exit
100 < 0: if INFO = -i, the i-th argument had an illegal value
101 LAPACK routine (version 3.2) November 2008 DTBRFS(1)