Contents

# mkl_?spffrt2, mkl_?spffrtx

Computes the partial LDL
T
factorization of a symmetric matrix using packed storage.

## Syntax

Include Files
• mkl.h
Description
The routine computes the partial factorization
A
=
L
D
L
T
, where
L
is a lower triangular matrix and
D
is a diagonal matrix.
The routine assumes that the matrix
A
is factorizable. The routine does not perform pivoting and does not handle diagonal elements which are zero, which cause the routine to produce incorrect results without any indication.
Consider the matrix , where
a
is the element in the first row and first column of
A
,
b
is a column vector of size
n
- 1 containing the elements from the second through
n
-th column of
A
,
C
is the lower-right square submatrix of
A
, and
I
is the identity matrix.
The
mkl_?spffrt2
routine performs
ncolm
successive factorizations of the form .
The
mkl_?spffrtx
routine performs
ncolm
successive factorizations of the form .
The approximate number of floating point operations performed by real flavors of these routines is (1/6)*
ncolm
*(2*
ncolm
2
- 6*
ncolm
*
n
+ 3*
ncolm
+ 6*
n
2
- 6*
n
+ 7).
The approximate number of floating point operations performed by complex flavors of these routines is (1/3)*
ncolm
*(4*
ncolm
2
- 12*
ncolm
*
n
+ 9*
ncolm
+ 12*
n
2
- 18*
n
+ 8).
Input Parameters
ap
Array, size at least max(1,
n
(
n
+1)/2). The array
ap
contains the lower triangular part of the matrix
A
in packed storage (see Matrix Storage Schemes for
uplo
=
'L'
).
n
The order of matrix
A
;
n
0.
ncolm
The number of columns to factor,
ncolm
n
.
work
,
work2
Workspace arrays, size of each at least
n
.
Output Parameters
ap
Overwritten by the factor
L
. The first
ncolm
diagonal elements of the input matrix
A
are replaced with the diagonal elements of
D
. The subdiagonal elements of the first
ncolm
columns are replaced with the corresponding elements of
L
. The rest of the input array is updated as indicated in the Description section.
Specifying
ncolm
=
n
results in complete factorization
A
=
L
D
L
T
.

#### Product and Performance Information

1

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