.TH DGBTRS 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) " .SH NAME DGBTRS - a system of linear equations A * X = B or A\(aq * X = B with a general band matrix A using the LU factorization computed by DGBTRF .SH SYNOPSIS .TP 19 SUBROUTINE DGBTRS( TRANS, N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO ) .TP 19 .ti +4 CHARACTER TRANS .TP 19 .ti +4 INTEGER INFO, KL, KU, LDAB, LDB, N, NRHS .TP 19 .ti +4 INTEGER IPIV( * ) .TP 19 .ti +4 DOUBLE PRECISION AB( LDAB, * ), B( LDB, * ) .SH PURPOSE DGBTRS solves a system of linear equations A * X = B or A\(aq * X = B with a general band matrix A using the LU factorization computed by DGBTRF. .SH ARGUMENTS .TP 8 TRANS (input) CHARACTER*1 Specifies the form of the system of equations. = \(aqN\(aq: A * X = B (No transpose) .br = \(aqT\(aq: A\(aq* X = B (Transpose) .br = \(aqC\(aq: A\(aq* X = B (Conjugate transpose = Transpose) .TP 8 N (input) INTEGER The order of the matrix A. N >= 0. .TP 8 KL (input) INTEGER The number of subdiagonals within the band of A. KL >= 0. .TP 8 KU (input) INTEGER The number of superdiagonals within the band of A. KU >= 0. .TP 8 NRHS (input) INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. .TP 8 AB (input) DOUBLE PRECISION array, dimension (LDAB,N) Details of the LU factorization of the band matrix A, as computed by DGBTRF. 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. .TP 8 LDAB (input) INTEGER The leading dimension of the array AB. LDAB >= 2*KL+KU+1. .TP 8 IPIV (input) INTEGER array, dimension (N) The pivot indices; for 1 <= i <= N, row i of the matrix was interchanged with row IPIV(i). .TP 8 B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS) On entry, the right hand side matrix B. On exit, the solution matrix X. .TP 8 LDB (input) INTEGER The leading dimension of the array B. LDB >= max(1,N). .TP 8 INFO (output) INTEGER = 0: successful exit .br < 0: if INFO = -i, the i-th argument had an illegal value