# sgbsv(3) [centos man page]

sgbsv.f(3) LAPACK sgbsv.f(3)NAME

sgbsv.f-SYNOPSIS

Functions/Subroutines subroutine sgbsv (N, KL, KU, NRHS, AB, LDAB, IPIV, B, LDB, INFO) SGBSV computes the solution to system of linear equations A * X = B for GB matrices (simple driver)Function/Subroutine Documentation subroutine sgbsv (integerN, integerKL, integerKU, integerNRHS, real, dimension( ldab, * )AB, integerLDAB, integer, dimension( * )IPIV, real, dimension( ldb, * )B, integerLDB, integerINFO) SGBSV computes the solution to system of linear equations A * X = B for GB matrices (simple driver) 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 N-by-NRHS 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. Parameters: N N is INTEGER The number of linear equations, i.e., the order of the matrix A. N >= 0. KL KL is INTEGER The number of subdiagonals within the band of A. KL >= 0. KU KU is INTEGER The number of superdiagonals within the band of A. KU >= 0. NRHS NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. AB AB is 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 j-th column of A is stored in the j-th column of the array AB as follows: AB(KL+KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=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 LDAB is INTEGER The leading dimension of the array AB. LDAB >= 2*KL+KU+1. IPIV IPIV is 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 B is REAL array, dimension (LDB,NRHS) On entry, the N-by-NRHS right hand side matrix B. On exit, if INFO = 0, the N-by-NRHS solution matrix X. LDB LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N). INFO INFO is INTEGER = 0: successful exit < 0: if INFO =, the i-th 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. Author: Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. Date: November 2011 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 fill-in resulting from the row interchanges. Definition at line 163 of file sgbsv.f.-iAuthorGenerated automatically by Doxygen for LAPACK from the source code.Version 3.4.2Tue Sep 25 2012 sgbsv.f(3)