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

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