Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

Contents

?gbsv

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

Syntax

lapack_int
LAPACKE_sgbsv
(
int
matrix_layout
,
lapack_int
n
,
lapack_int
kl
,
lapack_int
ku
,
lapack_int
nrhs
,
float
*
ab
,
lapack_int
ldab
,
lapack_int
*
ipiv
,
float
*
b
,
lapack_int
ldb
);
lapack_int
LAPACKE_dgbsv
(
int
matrix_layout
,
lapack_int
n
,
lapack_int
kl
,
lapack_int
ku
,
lapack_int
nrhs
,
double
*
ab
,
lapack_int
ldab
,
lapack_int
*
ipiv
,
double
*
b
,
lapack_int
ldb
);
lapack_int
LAPACKE_cgbsv
(
int
matrix_layout
,
lapack_int
n
,
lapack_int
kl
,
lapack_int
ku
,
lapack_int
nrhs
,
lapack_complex_float
*
ab
,
lapack_int
ldab
,
lapack_int
*
ipiv
,
lapack_complex_float
*
b
,
lapack_int
ldb
);
lapack_int
LAPACKE_zgbsv
(
int
matrix_layout
,
lapack_int
n
,
lapack_int
kl
,
lapack_int
ku
,
lapack_int
nrhs
,
lapack_complex_double
*
ab
,
lapack_int
ldab
,
lapack_int
*
ipiv
,
lapack_complex_double
*
b
,
lapack_int
ldb
);
Include Files
  • mkl.h
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
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
n
The order of
A
. The number of rows in
B
;
n
≥
 0.
kl
The number of subdiagonals within the band of
A
;
kl
≥
 0.
ku
The number of superdiagonals within the band of
A
;
ku
≥
 0.
nrhs
The number of right-hand sides. The number of columns in
B
;
nrhs
≥
 0.
ab
,
b
Arrays:
ab
(size max(1,
ldab
*
n
))
,
b
of size max(1,
ldb
*
nrhs
) for column major layout and max(1,
ldb
*
n
) for row major layout
.
The array
ab
 contains the matrix
A
 in band storage (see Matrix Storage Schemes).
The array
b
 contains the matrix
B
 whose columns are the right-hand sides for the systems of equations.
ldab
The leading dimension of the array
ab
. (
ldab
≥
 2
kl
 +
ku
 +1)
ldb
The leading dimension of
b
;
ldb
≥
 max(1,
n
) for column major layout and
ldb
≥
nrhs
 for row major layout
.
Output Parameters
ab
Overwritten by
L
 and
U
.
U
 is stored as an upper triangular band matrix with
kl
 +
ku
 superdiagonals and
L
 is stored as a lower triangular band matrix with
kl
 subdiagonals. See Matrix Storage Schemes.
b
Overwritten by the solution matrix
X
.
ipiv
Array, size at least
max(1,
n
)
. The pivot indices: row
i
 was interchanged with row
ipiv
[
i
-1]
.
Return Values
This function returns a value
info
.
If
info
 = 0
, the execution is successful.
If
info
 =
-i
, parameter
i
 had an illegal value.
If
info
 =
i
,
U
i
,
i
 is exactly zero. The factorization has been completed, but the factor
U
 is exactly singular, so the solution could not be computed.

Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.