Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 2021.1
  • 12/04/2020
  • Public Content
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

lapack_int
LAPACKE_spbsv
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_int
kd
,
lapack_int
nrhs
,
float
*
ab
,
lapack_int
ldab
,
float
*
b
,
lapack_int
ldb
);
lapack_int
LAPACKE_dpbsv
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_int
kd
,
lapack_int
nrhs
,
double
*
ab
,
lapack_int
ldab
,
double
*
b
,
lapack_int
ldb
);
lapack_int
LAPACKE_cpbsv
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_int
kd
,
lapack_int
nrhs
,
lapack_complex_float
*
ab
,
lapack_int
ldab
,
lapack_complex_float
*
b
,
lapack_int
ldb
);
lapack_int
LAPACKE_zpbsv
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_int
kd
,
lapack_int
nrhs
,
lapack_complex_double
*
ab
,
lapack_int
ldab
,
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
 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
The leading dimension of
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
 had an illegal value.
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.