#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int sgbsv_(integer *n, integer *kl, integer *ku, integer * nrhs, real *ab, integer *ldab, integer *ipiv, real *b, integer *ldb, integer *info) { /* -- LAPACK driver routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 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. 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 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 (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 N-by-NRHS right hand side matrix B. On exit, if INFO = 0, the N-by-NRHS 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 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. 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. ===================================================================== Test the input parameters. Parameter adjustments */ /* System generated locals */ integer ab_dim1, ab_offset, b_dim1, b_offset, i__1; /* Local variables */ extern /* Subroutine */ int xerbla_(char *, integer *), sgbtrf_( integer *, integer *, integer *, integer *, real *, integer *, integer *, integer *), sgbtrs_(char *, integer *, integer *, integer *, integer *, real *, integer *, integer *, real *, integer *, integer *); ab_dim1 = *ldab; ab_offset = 1 + ab_dim1; ab -= ab_offset; --ipiv; b_dim1 = *ldb; b_offset = 1 + b_dim1; b -= b_offset; /* Function Body */ *info = 0; if (*n < 0) { *info = -1; } else if (*kl < 0) { *info = -2; } else if (*ku < 0) { *info = -3; } else if (*nrhs < 0) { *info = -4; } else if (*ldab < (*kl << 1) + *ku + 1) { *info = -6; } else if (*ldb < max(*n,1)) { *info = -9; } if (*info != 0) { i__1 = -(*info); xerbla_("SGBSV ", &i__1); return 0; } /* Compute the LU factorization of the band matrix A. */ sgbtrf_(n, n, kl, ku, &ab[ab_offset], ldab, &ipiv[1], info); if (*info == 0) { /* Solve the system A*X = B, overwriting B with X. */ sgbtrs_("No transpose", n, kl, ku, nrhs, &ab[ab_offset], ldab, &ipiv[ 1], &b[b_offset], ldb, info); } return 0; /* End of SGBSV */ } /* sgbsv_ */