dgbsv - compute 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
SUBROUTINE DGBSV(N, KL, KU, NRHS, A, LDA, IPIVOT, B, LDB, INFO) INTEGER N, KL, KU, NRHS, LDA, LDB, INFO INTEGER IPIVOT(*) DOUBLE PRECISION A(LDA,*), B(LDB,*) SUBROUTINE DGBSV_64(N, KL, KU, NRHS, A, LDA, IPIVOT, B, LDB, INFO) INTEGER*8 N, KL, KU, NRHS, LDA, LDB, INFO INTEGER*8 IPIVOT(*) DOUBLE PRECISION A(LDA,*), B(LDB,*) F95 INTERFACE SUBROUTINE GBSV(N, KL, KU, NRHS, A, LDA, IPIVOT, B, LDB, INFO) INTEGER :: N, KL, KU, NRHS, LDA, LDB, INFO INTEGER, DIMENSION(:) :: IPIVOT REAL(8), DIMENSION(:,:) :: A, B SUBROUTINE GBSV_64(N, KL, KU, NRHS, A, LDA, IPIVOT, B, LDB, INFO) INTEGER(8) :: N, KL, KU, NRHS, LDA, LDB, INFO INTEGER(8), DIMENSION(:) :: IPIVOT REAL(8), DIMENSION(:,:) :: A, B C INTERFACE #include <sunperf.h> void dgbsv(int n, int kl, int ku, int nrhs, double *a, int lda, int *ipivot, double *b, int ldb, int *info); void dgbsv_64(long n, long kl, long ku, long nrhs, double *a, long lda, long *ipivot, double *b, long ldb, long *info);
Oracle Solaris Studio Performance Library dgbsv(3P) NAME dgbsv - compute 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 SYNOPSIS SUBROUTINE DGBSV(N, KL, KU, NRHS, A, LDA, IPIVOT, B, LDB, INFO) INTEGER N, KL, KU, NRHS, LDA, LDB, INFO INTEGER IPIVOT(*) DOUBLE PRECISION A(LDA,*), B(LDB,*) SUBROUTINE DGBSV_64(N, KL, KU, NRHS, A, LDA, IPIVOT, B, LDB, INFO) INTEGER*8 N, KL, KU, NRHS, LDA, LDB, INFO INTEGER*8 IPIVOT(*) DOUBLE PRECISION A(LDA,*), B(LDB,*) F95 INTERFACE SUBROUTINE GBSV(N, KL, KU, NRHS, A, LDA, IPIVOT, B, LDB, INFO) INTEGER :: N, KL, KU, NRHS, LDA, LDB, INFO INTEGER, DIMENSION(:) :: IPIVOT REAL(8), DIMENSION(:,:) :: A, B SUBROUTINE GBSV_64(N, KL, KU, NRHS, A, LDA, IPIVOT, B, LDB, INFO) INTEGER(8) :: N, KL, KU, NRHS, LDA, LDB, INFO INTEGER(8), DIMENSION(:) :: IPIVOT REAL(8), DIMENSION(:,:) :: A, B C INTERFACE #include <sunperf.h> void dgbsv(int n, int kl, int ku, int nrhs, double *a, int lda, int *ipivot, double *b, int ldb, int *info); void dgbsv_64(long n, long kl, long ku, long nrhs, double *a, long lda, long *ipivot, double *b, long ldb, long *info); PURPOSE dgbsv 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 super- diagonals, 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 triangu- lar with KL+KU superdiagonals. The factored form of A is then used to solve the system of equations A*X=B. ARGUMENTS N (input) The number of linear equations, i.e., the order of the matrix A. N >= 0. KL (input) The number of subdiagonals within the band of A. KL >= 0. KU (input) The number of superdiagonals within the band of A. KU >= 0. NRHS (input) The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. A (input/output) 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 A as follows: A(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 fac- torization are stored in rows KL+KU+2 to 2*KL+KU+1. See below for further details. LDA (input) The leading dimension of the array A. LDA >= 2*KL+KU+1. IPIVOT (output) The pivot indices that define the permutation matrix P; row i of the matrix was interchanged with row IPIVOT(i). B (input/output) 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) The leading dimension of the array B. LDB >= max(1,N). INFO (output) = 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 ele- ments of U because of fill-in resulting from the row interchanges. 7 Nov 2015 dgbsv(3P)