SYNOPSIS
 SUBROUTINE SGBSV(
 N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO )
 INTEGER INFO, KL, KU, LDAB, LDB, N, NRHS
 INTEGER IPIV( * )
 REAL AB( LDAB, * ), B( LDB, * )
PURPOSE
SGBSV computes the solution to a real system of linear equations A * X = B, where A is a band matrix of order N with KL subdiagonals and KU superdiagonals, and X and B are NbyNRHS matrices. The LU decomposition with partial pivoting and row interchanges is used to factor A as A = L * U, where L is a product of permutation and unit lower triangular matrices with KL subdiagonals, and U is upper triangular with KL+KU superdiagonals. The factored form of A is then used to solve the system of equations A * X = B.ARGUMENTS
 N (input) INTEGER
 The number of linear equations, i.e., 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 matrix B. NRHS >= 0.
 AB (input/output) REAL array, dimension (LDAB,N)
 On entry, the matrix A in band storage, in rows KL+1 to 2*KL+KU+1; rows 1 to KL of the array need not be set. The jth column of A is stored in the jth column of the array AB as follows: AB(KL+KU+1+ij,j) = A(i,j) for max(1,jKU)<=i<=min(N,j+KL) On exit, details of the factorization: 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. See below for further details.
 LDAB (input) INTEGER
 The leading dimension of the array AB. LDAB >= 2*KL+KU+1.
 IPIV (output) INTEGER array, dimension (N)
 The pivot indices that define the permutation matrix P; row i of the matrix was interchanged with row IPIV(i).
 B (input/output) REAL array, dimension (LDB,NRHS)
 On entry, the NbyNRHS right hand side matrix B. On exit, if INFO = 0, the NbyNRHS solution matrix X.
 LDB (input) INTEGER
 The leading dimension of the array B. LDB >= max(1,N).
 INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
> 0: if INFO = i, U(i,i) is exactly zero. The factorization has been completed, but the factor U is exactly singular, and the solution has not been computed.
FURTHER DETAILS
The band storage scheme is illustrated by the following example, when M = N = 6, KL = 2, KU = 1:On entry: On exit:
* * * + + + * * * u14 u25 u36
* * + + + + * * u13 u24 u35 u46
* a12 a23 a34 a45 a56 * u12 u23 u34 u45 u56
a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55 u66
a21 a32 a43 a54 a65 * m21 m32 m43 m54 m65 *
a31 a42 a53 a64 * * m31 m42 m53 m64 * * Array elements marked * are not used by the routine; elements marked + need not be set on entry, but are required by the routine to store elements of U because of fillin resulting from the row interchanges.