1DTBRFS(1) LAPACK routine (version 3.1) DTBRFS(1)
2
6 DTBRFS - error bounds and backward error estimates for the solution to
7 a system of linear equations with a triangular band coefficient matrix
8
10 SUBROUTINE DTBRFS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B, LDB, X,
11 LDX, FERR, BERR, WORK, IWORK, INFO )
12 CHARACTER DIAG, TRANS, UPLO
14 INTEGER INFO, KD, LDAB, LDB, LDX, N, NRHS
16 INTEGER IWORK( * )
18 DOUBLE PRECISION AB( LDAB, * ), B( LDB, * ), BERR( * ),
20 FERR( * ), WORK( * ), X( LDX, * )
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23 DTBRFS 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.
26 The solution matrix X must be computed by DTBTRS or some other means
28 before entering this routine. DTBRFS does not do iterative refinement
29 because doing so cannot improve the backward error.
30
33 UPLO (input) CHARACTER*1
34 = 'U': A is upper triangular;
35 = 'L': A is lower triangular.
36 TRANS (input) CHARACTER*1
38 Specifies the form of the system of equations:
39 = 'N': A * X = B (No transpose)
40 = 'T': A**T * X = B (Transpose)
41 = 'C': A**H * X = B (Conjugate transpose = Transpose)
42 DIAG (input) CHARACTER*1
44 = 'N': A is non-unit triangular;
45 = 'U': A is unit triangular.
46 N (input) INTEGER
48 The order of the matrix A. N >= 0.
49 KD (input) INTEGER
51 The number of superdiagonals or subdiagonals of the triangular
52 band matrix A. KD >= 0.
53 NRHS (input) INTEGER
55 The number of right hand sides, i.e., the number of columns of
56 the matrices B and X. NRHS >= 0.
57 AB (input) DOUBLE PRECISION array, dimension (LDAB,N)
59 The upper or lower triangular band matrix A, stored in the
60 first kd+1 rows of the array. The j-th column of A is stored in
61 the j-th column of the array AB as follows: if UPLO = 'U',
62 AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L',
63 AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). If DIAG = 'U',
64 the diagonal elements of A are not referenced and are assumed
65 to be 1.
66 LDAB (input) INTEGER
68 The leading dimension of the array AB. LDAB >= KD+1.
69 B (input) DOUBLE PRECISION array, dimension (LDB,NRHS)
71 The right hand side matrix B.
72 LDB (input) INTEGER
74 The leading dimension of the array B. LDB >= max(1,N).
75 X (input) DOUBLE PRECISION array, dimension (LDX,NRHS)
77 The solution matrix X.
78 LDX (input) INTEGER
80 The leading dimension of the array X. LDX >= max(1,N).
81 FERR (output) DOUBLE PRECISION array, dimension (NRHS)
83 The estimated forward error bound for each solution vector X(j)
84 (the j-th column of the solution matrix X). If XTRUE is the
85 true solution corresponding to X(j), FERR(j) is an estimated
86 upper bound for the magnitude of the largest element in (X(j) -
87 XTRUE) divided by the magnitude of the largest element in X(j).
88 The estimate is as reliable as the estimate for RCOND, and is
89 almost always a slight overestimate of the true error.
90 BERR (output) DOUBLE PRECISION array, dimension (NRHS)
92 The componentwise relative backward error of each solution vec‐
93 tor X(j) (i.e., the smallest relative change in any element of
94 A or B that makes X(j) an exact solution).
95 WORK (workspace) DOUBLE PRECISION array, dimension (3*N)
97 IWORK (workspace) INTEGER array, dimension (N)
99 INFO (output) INTEGER
101 = 0: successful exit
102 < 0: if INFO = -i, the i-th argument had an illegal value
103 LAPACK routine (version 3.1) November 2006 DTBRFS(1)