sgbrfs (l)  Linux Manuals
sgbrfs: improves the computed solution to a system of linear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solution
NAME
SGBRFS  improves the computed solution to a system of linear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solutionSYNOPSIS
 SUBROUTINE SGBRFS(
 TRANS, N, KL, KU, NRHS, AB, LDAB, AFB, LDAFB, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, IWORK, INFO )
 CHARACTER TRANS
 INTEGER INFO, KL, KU, LDAB, LDAFB, LDB, LDX, N, NRHS
 INTEGER IPIV( * ), IWORK( * )
 REAL AB( LDAB, * ), AFB( LDAFB, * ), B( LDB, * ), BERR( * ), FERR( * ), WORK( * ), X( LDX, * )
PURPOSE
SGBRFS improves the computed solution to a system of linear equations when the coefficient matrix is banded, and provides error bounds and backward error estimates for the solution.ARGUMENTS
 TRANS (input) CHARACTER*1

Specifies the form of the system of equations:
= aqNaq: A * X = B (No transpose)
= aqTaq: A**T * X = B (Transpose)
= aqCaq: A**H * X = B (Conjugate transpose = Transpose)  N (input) INTEGER
 The order of the matrix A. N >= 0.
 KL (input) INTEGER
 The number of subdiagonals within the band of A. KL >= 0.
 KU (input) INTEGER
 The number of superdiagonals within the band of A. KU >= 0.
 NRHS (input) INTEGER
 The number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.
 AB (input) REAL array, dimension (LDAB,N)
 The original band matrix A, stored in rows 1 to KL+KU+1. The jth column of A is stored in the jth column of the array AB as follows: AB(ku+1+ij,j) = A(i,j) for max(1,jku)<=i<=min(n,j+kl).
 LDAB (input) INTEGER
 The leading dimension of the array AB. LDAB >= KL+KU+1.
 AFB (input) REAL array, dimension (LDAFB,N)
 Details of the LU factorization of the band matrix A, as computed by SGBTRF. U is stored as an upper triangular band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and the multipliers used during the factorization are stored in rows KL+KU+2 to 2*KL+KU+1.
 LDAFB (input) INTEGER
 The leading dimension of the array AFB. LDAFB >= 2*KL*KU+1.
 IPIV (input) INTEGER array, dimension (N)
 The pivot indices from SGBTRF; for 1<=i<=N, row i of the matrix was interchanged with row IPIV(i).
 B (input) REAL array, dimension (LDB,NRHS)
 The right hand side matrix B.
 LDB (input) INTEGER
 The leading dimension of the array B. LDB >= max(1,N).
 X (input/output) REAL array, dimension (LDX,NRHS)
 On entry, the solution matrix X, as computed by SGBTRS. On exit, the improved solution matrix X.
 LDX (input) INTEGER
 The leading dimension of the array X. LDX >= max(1,N).
 FERR (output) REAL array, dimension (NRHS)
 The estimated forward error bound for each solution vector X(j) (the jth column of the solution matrix X). If XTRUE is the true solution corresponding to X(j), FERR(j) is an estimated upper bound for the magnitude of the largest element in (X(j)  XTRUE) divided by the magnitude of the largest element in X(j). The estimate is as reliable as the estimate for RCOND, and is almost always a slight overestimate of the true error.
 BERR (output) REAL array, dimension (NRHS)
 The componentwise relative backward error of each solution vector X(j) (i.e., the smallest relative change in any element of A or B that makes X(j) an exact solution).
 WORK (workspace) REAL array, dimension (3*N)
 IWORK (workspace) INTEGER array, dimension (N)
 INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
PARAMETERS
ITMAX is the maximum number of steps of iterative refinement.