Contents

# ?pptrf

Computes the Cholesky factorization of a symmetric (Hermitian) positive-definite matrix using packed storage.

## Syntax

Include Files
• mkl.h
Description
The routine forms the Cholesky factorization of a symmetric positive-definite or, for complex data, Hermitian positive-definite packed matrix
A
:
 A = UT*U for real data, A = UH*U for complex data if uplo='U' A = L*LT for real data, A = L*LH for complex data if uplo='L'
where
L
is a lower triangular matrix and
U
is upper triangular.
This routine supports the Progress Routine feature. See Progress Function for details.
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 packed in the array
ap
, and how
A
is factored:
If
uplo
=
'U'
, the array
ap
stores the upper triangular part of the matrix
A
, and
A
is factored as
U
H
*U
.
If
uplo
=
'L'
, the array
ap
stores the lower triangular part of the matrix
A
;
A
is factored as
L*L
H
.
n
The order of matrix
A
;
n
0.
ap
Array, size at least max(1,
n
(
n
+1)/2). The array
ap
contains either the upper or the lower triangular part of the matrix
A
(as specified by
uplo
) in packed storage (see Matrix Storage Schemes).
Output Parameters
ap
Overwritten by the Cholesky factor
U
or
L
, as specified by
uplo
.
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, and the factorization could not be completed. This may indicate an error in forming the matrix
A
.
Application Notes
If
uplo
=
'U'
, the computed factor
U
is the exact factor of a perturbed matrix
A
+
E
, where
c
(
n
)
is a modest linear function of
n
, and
ε
is the machine precision.
A similar estimate holds for
uplo
=
'L'
.
The total number of floating-point operations is approximately
(1/3)
n
3
for real flavors and
(4/3)
n
3
for complex flavors.
After calling this routine, you can call the following routines:
to solve
A*X
=
B
to estimate the condition number of
A
to compute the inverse of
A
.

#### Product and Performance Information

1

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