Contents

# ?gbsv

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

## Syntax

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
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
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

Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.

Notice revision #20110804