1SGBRFS(1) LAPACK routine (version 3.1) SGBRFS(1)
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6 SGBRFS - the computed solution to a system of linear equations when the
7 coefficient matrix is banded, and provides error bounds and backward
8 error estimates for the solution
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11 SUBROUTINE SGBRFS( TRANS, N, KL, KU, NRHS, AB, LDAB, AFB, LDAFB, IPIV,
12 B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO )
13 CHARACTER TRANS
15 INTEGER INFO, KL, KU, LDAB, LDAFB, LDB, LDX, N, NRHS
17 INTEGER IPIV( * ), IWORK( * )
19 REAL AB( LDAB, * ), AFB( LDAFB, * ), B( LDB, * ), BERR( *
21 ), FERR( * ), WORK( * ), X( LDX, * )
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24 SGBRFS improves the computed solution to a system of linear equations
25 when the coefficient matrix is banded, and provides error bounds and
26 backward error estimates for the solution.
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30 TRANS (input) CHARACTER*1
31 Specifies the form of the system of equations:
32 = 'N': A * X = B (No transpose)
33 = 'T': A**T * X = B (Transpose)
34 = 'C': A**H * X = B (Conjugate transpose = Transpose)
35 N (input) INTEGER
37 The order of the matrix A. N >= 0.
38 KL (input) INTEGER
40 The number of subdiagonals within the band of A. KL >= 0.
41 KU (input) INTEGER
43 The number of superdiagonals within the band of A. KU >= 0.
44 NRHS (input) INTEGER
46 The number of right hand sides, i.e., the number of columns of
47 the matrices B and X. NRHS >= 0.
48 AB (input) REAL array, dimension (LDAB,N)
50 The original band matrix A, stored in rows 1 to KL+KU+1. The
51 j-th column of A is stored in the j-th column of the array AB
52 as follows: AB(ku+1+i-j,j) = A(i,j) for max(1,j-
53 ku)<=i<=min(n,j+kl).
54 LDAB (input) INTEGER
56 The leading dimension of the array AB. LDAB >= KL+KU+1.
57 AFB (input) REAL array, dimension (LDAFB,N)
59 Details of the LU factorization of the band matrix A, as com‐
60 puted by SGBTRF. U is stored as an upper triangular band
61 matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and the
62 multipliers used during the factorization are stored in rows
63 KL+KU+2 to 2*KL+KU+1.
64 LDAFB (input) INTEGER
66 The leading dimension of the array AFB. LDAFB >= 2*KL*KU+1.
67 IPIV (input) INTEGER array, dimension (N)
69 The pivot indices from SGBTRF; for 1<=i<=N, row i of the matrix
70 was interchanged with row IPIV(i).
71 B (input) REAL array, dimension (LDB,NRHS)
73 The right hand side matrix B.
74 LDB (input) INTEGER
76 The leading dimension of the array B. LDB >= max(1,N).
77 X (input/output) REAL array, dimension (LDX,NRHS)
79 On entry, the solution matrix X, as computed by SGBTRS. On
80 exit, the improved solution matrix X.
81 LDX (input) INTEGER
83 The leading dimension of the array X. LDX >= max(1,N).
84 FERR (output) REAL array, dimension (NRHS)
86 The estimated forward error bound for each solution vector X(j)
87 (the j-th column of the solution matrix X). If XTRUE is the
88 true solution corresponding to X(j), FERR(j) is an estimated
89 upper bound for the magnitude of the largest element in (X(j) -
90 XTRUE) divided by the magnitude of the largest element in X(j).
91 The estimate is as reliable as the estimate for RCOND, and is
92 almost always a slight overestimate of the true error.
93 BERR (output) REAL array, dimension (NRHS)
95 The componentwise relative backward error of each solution vec‐
96 tor X(j) (i.e., the smallest relative change in any element of
97 A or B that makes X(j) an exact solution).
98 WORK (workspace) REAL array, dimension (3*N)
100 IWORK (workspace) INTEGER array, dimension (N)
102 INFO (output) INTEGER
104 = 0: successful exit
105 < 0: if INFO = -i, the i-th argument had an illegal value
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108 ITMAX is the maximum number of steps of iterative refinement.
109 LAPACK routine (version 3.1) November 2006 SGBRFS(1)