1CGBRFS(1) LAPACK routine (version 3.2) CGBRFS(1)
2
6 CGBRFS - improves the computed solution to a system of linear equations
7 when the coefficient matrix is banded, and provides error bounds and
8 backward error estimates for the solution
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11 SUBROUTINE CGBRFS( TRANS, N, KL, KU, NRHS, AB, LDAB, AFB, LDAFB, IPIV,
12 B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO )
13 CHARACTER TRANS
15 INTEGER INFO, KL, KU, LDAB, LDAFB, LDB, LDX, N, NRHS
17 INTEGER IPIV( * )
19 REAL BERR( * ), FERR( * ), RWORK( * )
21 COMPLEX AB( LDAB, * ), AFB( LDAFB, * ), B( LDB, * ), WORK( *
23 ), X( LDX, * )
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26 CGBRFS improves the computed solution to a system of linear equations
27 when the coefficient matrix is banded, and provides error bounds and
28 backward error estimates for the solution.
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31 TRANS (input) CHARACTER*1
32 Specifies the form of the system of equations:
33 = 'N': A * X = B (No transpose)
34 = 'T': A**T * X = B (Transpose)
35 = 'C': A**H * X = B (Conjugate transpose)
36 N (input) INTEGER
38 The order of the matrix A. N >= 0.
39 KL (input) INTEGER
41 The number of subdiagonals within the band of A. KL >= 0.
42 KU (input) INTEGER
44 The number of superdiagonals within the band of A. KU >= 0.
45 NRHS (input) INTEGER
47 The number of right hand sides, i.e., the number of columns of
48 the matrices B and X. NRHS >= 0.
49 AB (input) COMPLEX array, dimension (LDAB,N)
51 The original band matrix A, stored in rows 1 to KL+KU+1. The
52 j-th column of A is stored in the j-th column of the array AB
53 as follows: AB(ku+1+i-j,j) = A(i,j) for max(1,j-
54 ku)<=i<=min(n,j+kl).
55 LDAB (input) INTEGER
57 The leading dimension of the array AB. LDAB >= KL+KU+1.
58 AFB (input) COMPLEX array, dimension (LDAFB,N)
60 Details of the LU factorization of the band matrix A, as com‐
61 puted by CGBTRF. U is stored as an upper triangular band
62 matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and the
63 multipliers used during the factorization are stored in rows
64 KL+KU+2 to 2*KL+KU+1.
65 LDAFB (input) INTEGER
67 The leading dimension of the array AFB. LDAFB >= 2*KL*KU+1.
68 IPIV (input) INTEGER array, dimension (N)
70 The pivot indices from CGBTRF; for 1<=i<=N, row i of the matrix
71 was interchanged with row IPIV(i).
72 B (input) COMPLEX array, dimension (LDB,NRHS)
74 The right hand side matrix B.
75 LDB (input) INTEGER
77 The leading dimension of the array B. LDB >= max(1,N).
78 X (input/output) COMPLEX array, dimension (LDX,NRHS)
80 On entry, the solution matrix X, as computed by CGBTRS. On
81 exit, the improved solution matrix X.
82 LDX (input) INTEGER
84 The leading dimension of the array X. LDX >= max(1,N).
85 FERR (output) REAL array, dimension (NRHS)
87 The estimated forward error bound for each solution vector X(j)
88 (the j-th column of the solution matrix X). If XTRUE is the
89 true solution corresponding to X(j), FERR(j) is an estimated
90 upper bound for the magnitude of the largest element in (X(j) -
91 XTRUE) divided by the magnitude of the largest element in X(j).
92 The estimate is as reliable as the estimate for RCOND, and is
93 almost always a slight overestimate of the true error.
94 BERR (output) REAL array, dimension (NRHS)
96 The componentwise relative backward error of each solution vec‐
97 tor X(j) (i.e., the smallest relative change in any element of
98 A or B that makes X(j) an exact solution).
99 WORK (workspace) COMPLEX array, dimension (2*N)
101 RWORK (workspace) REAL array, dimension (N)
103 INFO (output) INTEGER
105 = 0: successful exit
106 < 0: if INFO = -i, the i-th argument had an illegal value
107
109 ITMAX is the maximum number of steps of iterative refinement.
110 LAPACK routine (version 3.2) November 2008 CGBRFS(1)