Developer Reference

  • 2020.2
  • 07/15/2020
  • Public Content
Contents

?gbsv

Computes the solution to the system of linear equations with a band coefficient matrix A and multiple right-hand sides.

Syntax

call sgbsv
(
n
,
kl
,
ku
,
nrhs
,
ab
,
ldab
,
ipiv
,
b
,
ldb
,
info
)
call dgbsv
(
n
,
kl
,
ku
,
nrhs
,
ab
,
ldab
,
ipiv
,
b
,
ldb
,
info
)
call cgbsv
(
n
,
kl
,
ku
,
nrhs
,
ab
,
ldab
,
ipiv
,
b
,
ldb
,
info
)
call zgbsv
(
n
,
kl
,
ku
,
nrhs
,
ab
,
ldab
,
ipiv
,
b
,
ldb
,
info
)
call gbsv
(
ab
,
b
[
,
kl
]
[
,
ipiv
]
[
,
info
]
)
Include Files
  • mkl.fi
    ,
    lapack.f90
Description
The routine solves for
X
the real or complex system of linear equations
A*X
=
B
, where
A
is an
n
-by-
n
band matrix with
kl
subdiagonals and
ku
superdiagonals, the columns of matrix
B
are individual right-hand sides, and the columns of
X
are the corresponding solutions.
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
.
Input Parameters
n
INTEGER
.
The order of
A
. The number of rows in
B
;
n
0.
kl
INTEGER
.
The number of subdiagonals within the band of
A
;
kl
0.
ku
INTEGER
.
The number of superdiagonals within the band of
A
;
ku
0.
nrhs
INTEGER
.
The number of right-hand sides. The number of columns in
B
;
nrhs
0.
ab
,
b
REAL
for
sgbsv
DOUBLE PRECISION
for
dgbsv
COMPLEX
for
cgbsv
DOUBLE COMPLEX
for
zgbsv
.
Arrays:
ab