1SGBRFS(1) LAPACK routine (version 3.2) SGBRFS(1)
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6 SGBRFS - 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 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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29 TRANS (input) CHARACTER*1
30 Specifies the form of the system of equations:
31 = 'N': A * X = B (No transpose)
32 = 'T': A**T * X = B (Transpose)
33 = 'C': A**H * X = B (Conjugate transpose = Transpose)
34 N (input) INTEGER
36 The order of the matrix A. N >= 0.
37 KL (input) INTEGER
39 The number of subdiagonals within the band of A. KL >= 0.
40 KU (input) INTEGER
42 The number of superdiagonals within the band of A. KU >= 0.
43 NRHS (input) INTEGER
45 The number of right hand sides, i.e., the number of columns of
46 the matrices B and X. NRHS >= 0.
47 AB (input) REAL array, dimension (LDAB,N)
49 The original band matrix A, stored in rows 1 to KL+KU+1. The
50 j-th column of A is stored in the j-th column of the array AB
51 as follows: AB(ku+1+i-j,j) = A(i,j) for max(1,j-
52 ku)<=i<=min(n,j+kl).
53 LDAB (input) INTEGER
55 The leading dimension of the array AB. LDAB >= KL+KU+1.
56 AFB (input) REAL array, dimension (LDAFB,N)
58 Details of the LU factorization of the band matrix A, as com‐
59 puted by SGBTRF. U is stored as an upper triangular band
60 matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and the
61 multipliers used during the factorization are stored in rows
62 KL+KU+2 to 2*KL+KU+1.
63 LDAFB (input) INTEGER
65 The leading dimension of the array AFB. LDAFB >= 2*KL*KU+1.
66 IPIV (input) INTEGER array, dimension (N)
68 The pivot indices from SGBTRF; for 1<=i<=N, row i of the matrix
69 was interchanged with row IPIV(i).
70 B (input) REAL array, dimension (LDB,NRHS)
72 The right hand side matrix B.
73 LDB (input) INTEGER
75 The leading dimension of the array B. LDB >= max(1,N).
76 X (input/output) REAL array, dimension (LDX,NRHS)
78 On entry, the solution matrix X, as computed by SGBTRS. On
79 exit, the improved solution matrix X.
80 LDX (input) INTEGER
82 The leading dimension of the array X. LDX >= max(1,N).
83 FERR (output) REAL array, dimension (NRHS)
85 The estimated forward error bound for each solution vector X(j)
86 (the j-th column of the solution matrix X). If XTRUE is the
87 true solution corresponding to X(j), FERR(j) is an estimated
88 upper bound for the magnitude of the largest element in (X(j) -
89 XTRUE) divided by the magnitude of the largest element in X(j).
90 The estimate is as reliable as the estimate for RCOND, and is
91 almost always a slight overestimate of the true error.
92 BERR (output) REAL array, dimension (NRHS)
94 The componentwise relative backward error of each solution vec‐
95 tor X(j) (i.e., the smallest relative change in any element of
96 A or B that makes X(j) an exact solution).
97 WORK (workspace) REAL array, dimension (3*N)
99 IWORK (workspace) INTEGER array, dimension (N)
101 INFO (output) INTEGER
103 = 0: successful exit
104 < 0: if INFO = -i, the i-th argument had an illegal value
105
107 ITMAX is the maximum number of steps of iterative refinement.
108 LAPACK routine (version 3.2) November 2008 SGBRFS(1)