zgbsv - compute the solution to a complex 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 ZGBSV(N, KL, KU, NRHS, A, LDA, IPIVOT, B, LDB, INFO) DOUBLE COMPLEX A(LDA,*), B(LDB,*) INTEGER N, KL, KU, NRHS, LDA, LDB, INFO INTEGER IPIVOT(*) SUBROUTINE ZGBSV_64(N, KL, KU, NRHS, A, LDA, IPIVOT, B, LDB, INFO) DOUBLE COMPLEX A(LDA,*), B(LDB,*) INTEGER*8 N, KL, KU, NRHS, LDA, LDB, INFO INTEGER*8 IPIVOT(*) F95 INTERFACE SUBROUTINE GBSV(N, KL, KU, NRHS, A, LDA, IPIVOT, B, LDB, INFO) COMPLEX(8), DIMENSION(:,:) :: A, B INTEGER :: N, KL, KU, NRHS, LDA, LDB, INFO INTEGER, DIMENSION(:) :: IPIVOT SUBROUTINE GBSV_64(N, KL, KU, NRHS, A, LDA, IPIVOT, B, LDB, INFO) COMPLEX(8), DIMENSION(:,:) :: A, B INTEGER(8) :: N, KL, KU, NRHS, LDA, LDB, INFO INTEGER(8), DIMENSION(:) :: IPIVOT C INTERFACE #include <sunperf.h> void zgbsv(int n, int kl, int ku, int nrhs, doublecomplex *a, int lda, int *ipivot, doublecomplex *b, int ldb, int *info); void zgbsv_64(long n, long kl, long ku, long nrhs, doublecomplex *a, long lda, long *ipivot, doublecomplex *b, long ldb, long *info);
Oracle Solaris Studio Performance Library zgbsv(3P)
NAME
zgbsv - compute the solution to a complex 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 ZGBSV(N, KL, KU, NRHS, A, LDA, IPIVOT, B, LDB, INFO)
DOUBLE COMPLEX A(LDA,*), B(LDB,*)
INTEGER N, KL, KU, NRHS, LDA, LDB, INFO
INTEGER IPIVOT(*)
SUBROUTINE ZGBSV_64(N, KL, KU, NRHS, A, LDA, IPIVOT, B, LDB,
INFO)
DOUBLE COMPLEX A(LDA,*), B(LDB,*)
INTEGER*8 N, KL, KU, NRHS, LDA, LDB, INFO
INTEGER*8 IPIVOT(*)
F95 INTERFACE
SUBROUTINE GBSV(N, KL, KU, NRHS, A, LDA, IPIVOT, B, LDB,
INFO)
COMPLEX(8), DIMENSION(:,:) :: A, B
INTEGER :: N, KL, KU, NRHS, LDA, LDB, INFO
INTEGER, DIMENSION(:) :: IPIVOT
SUBROUTINE GBSV_64(N, KL, KU, NRHS, A, LDA, IPIVOT, B,
LDB, INFO)
COMPLEX(8), DIMENSION(:,:) :: A, B
INTEGER(8) :: N, KL, KU, NRHS, LDA, LDB, INFO
INTEGER(8), DIMENSION(:) :: IPIVOT
C INTERFACE
#include <sunperf.h>
void zgbsv(int n, int kl, int ku, int nrhs, doublecomplex *a, int lda,
int *ipivot, doublecomplex *b, int ldb, int *info);
void zgbsv_64(long n, long kl, long ku, long nrhs, doublecomplex *a,
long lda, long *ipivot, doublecomplex *b, long ldb, long
*info);
PURPOSE
zgbsv computes the solution to a complex 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 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. i.br 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 zgbsv(3P)