Contents

# ?pbsv

Computes the solution to the system of linear equations with a symmetric or Hermitian positive-definite 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
symmetric/Hermitian positive definite band matrix, the columns of matrix
B
are individual right-hand sides, and the columns of
X
are the corresponding solutions.
The Cholesky decomposition is used to factor
A
as
A
=
U
T
*U
(real flavors) and
A
=
U
H
*U
(complex flavors), if
uplo
=
'U'
or
A
=
L*L
T
(real flavors) and
A
=
L*L
H
(complex flavors), if
uplo
=
'L'
,
where
U
is an upper triangular band matrix and
L
is a lower triangular band matrix, with the same number of superdiagonals or subdiagonals as
A
. 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
).
uplo
Must be
'U'
or
'L'
.
Indicates whether the upper or lower triangular part of
A
is stored:
If
uplo
=
'U'
, the upper triangle of
A
is stored.
If
uplo
=
'L'
, the lower triangle of
A
is stored.
n
The order of matrix
A
;
n
0.
kd
The number of superdiagonals of the matrix
A
if
uplo
=
'U'
, or the number of subdiagonals if
uplo
=
'L'
;
kd
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 upper or the lower triangular part of the matrix
A
(as specified by
uplo
) 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
kd
+1.
ldb
b
;
ldb
max(1,
n
) for column major layout and
ldb
nrhs
for row major layout
.
Output Parameters
ab
The upper or lower triangular part of
A
(in band storage) is overwritten by the Cholesky factor
U
or
L
, as specified by
uplo
, in the same storage format as
A
.
b
Overwritten by the solution matrix
X
.
Return Values
This function returns a value
info
.
If
info
= 0
, the execution is successful.
If
info
=
-i
, parameter
i
If
info
=
i
, the leading minor of order
i
(and therefore the matrix
A
itself) is not positive-definite, so the factorization could not be completed, and the solution has not been 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 reserverd 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