Contents

# ?potrf

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

## Syntax

Include Files
• mkl.h
Description
The routine forms the Cholesky factorization of a symmetric positive-definite or, for complex data, Hermitian positive-definite 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 stored and how
A
is factored:
If
uplo
=
'U'
, the array
a
stores the upper triangular part of the matrix
A
, and the strictly lower triangular part of the matrix is not referenced.
If
uplo
=
'L'
, the array
a
stores the lower triangular part of the matrix
A
, and the strictly upper triangular part of the matrix is not referenced.
n
Specifies the order of the matrix
A
. The value of
n
must be at least zero.
a
Array, size max(1,
lda
*
n
. The array
a
contains either the upper or the lower triangular part of the matrix
A
(see
uplo
).
lda
The leading dimension of
a
. Must be at least max(1,
n
).
Output Parameters
a
The upper or lower triangular part of
a
is 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
had an illegal value.
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 or
(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.