Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 2021.1
  • 12/04/2020
  • Public Content
Contents

mkl_?spffrt2
,
mkl_?spffrtx

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

Syntax

void
mkl_sspffrt2
(
float
*ap
,
const
MKL_INT
*n
,
const
MKL_INT
*ncolm
,
float
*work
,
float
*work2
);
void
mkl_dspffrt2
(
double
*ap
,
const
MKL_INT
*n
,
const
MKL_INT
*ncolm
,
double
*work
,
double
*work2
);
void
mkl_cspffrt2
(
MKL_Complex8
*ap
,
const
MKL_INT
*n
,
const
MKL_INT
*ncolm
,
MKL_Complex8
*work
,
MKL_Complex8
*work2
);
void
mkl_zspffrt2
(
MKL_Complex16
*ap
,
const
MKL_INT
*n
,
const
MKL_INT
*ncolm
,
MKL_Complex16
*work
,
MKL_Complex16
*work2
);
void
mkl_sspffrtx
(
float
*ap
,
const
MKL_INT
*n
,
const
MKL_INT
*ncolm
,
float
*work
,
float
*work2
);
void
mkl_dspffrtx
(
double
*ap
,
const
MKL_INT
*n
,
const
MKL_INT
*ncolm
,
double
*work
,
double
*work2
);
void
mkl_cspffrtx
(
MKL_Complex8
*ap
,
const
MKL_INT
*n
,
const
MKL_INT
*ncolm
,
MKL_Complex8
*work
,
MKL_Complex8
*work2
);
void
mkl_zspffrtx
(
MKL_Complex16
*ap
,
const
MKL_INT
*n
,
const
MKL_INT
*ncolm
,
MKL_Complex16
*work
,
MKL_Complex16
*work2
);
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.