Contents
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);
dgbsv computes the solution to a real system of linear equa-
tions 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 inter-
changes is used to factor A as A = L * U, where L is a pro-
duct of permutation and unit lower triangular matrices with
KL subdiagonals, and U is upper triangular with KL+KU super-
diagonals. The factored form of A is then used to solve the
system of equations A * X = B.
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 fac-
torization: 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 ille-
gal 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.
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; ele-
ments 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.