Contents

# ?pbstf

Computes a split Cholesky factorization of a real symmetric or complex Hermitian positive-definite banded matrix used in
?sbgst
/
?hbgst
.

## Syntax

Include Files
• mkl.h
Description
The routine computes a split Cholesky factorization of a real symmetric or complex Hermitian positive-definite band matrix
B
. It is to be used in conjunction with sbgst/hbgst.
The factorization has the form
B
=
S
T
*S
(or
B
=
S
H
*S
for complex flavors), where
S
is a band matrix of the same bandwidth as
B
and the following structure: S is upper triangular in the first (
n
+
kb
)/2 rows and lower triangular in the remaining rows.
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'
.
If
uplo
=
'U'
,
bb
stores the upper triangular part of
B
.
If
uplo
=
'L'
,
bb
stores the lower triangular part of
B
.
n
The order of the matrix
B
(
n
0
).
kb
The number of super- or sub-diagonals in
B
(
kb
0
).
bb
bb
(size at least max(1,
ldbb
*
n
) for column major layout and at least max(1,
ldbb
*(
kb
+ 1)) for row major layout)
is an array containing either upper or lower triangular part of the matrix
B
(as specified by
uplo
) in band storage format.
ldbb
bb
; must be at least
kb
+1
for column major and at least max(1,
n
) for row major
.
Output Parameters
bb
On exit, this array is overwritten by the elements of the split Cholesky factor
S
.
Return Values
This function returns a value
info
.
If
info
=0
, the execution is successful.
If
info
=
i
, then the factorization could not be completed, because the updated element
b
i
i
would be the square root of a negative number; hence the matrix
B
is not positive-definite.
If
info
=
-i
, the
i
-th parameter had an illegal value.
Application Notes
The computed factor
S
is the exact factor of a perturbed matrix
B
+
E
, where c
(
n
) is a modest linear function of
n
, and
ε
is the machine precision.
The total number of floating-point operations for real flavors is approximately
n
(
kb
+1)
2
. The number of operations for complex flavors is 4 times greater. All these estimates assume that
kb
is much less than
n
.
After calling this routine, you can call sbgst/hbgst to solve the generalized eigenproblem
Az
=
λ
Bz
, where
A
and
B
are banded and
B
is positive-definite.

#### Product and Performance Information

1

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