Contents

# ?potri

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

## Syntax

Include Files
• mkl.h
Description
The routine computes the inverse
inv(
A
)
of a symmetric positive definite or, for complex flavors, Hermitian positive-definite matrix
A
. Before calling this routine, call
?potrf
to factorize
A
.
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 how the input matrix
A
has been factored:
If
uplo
=
'U'
, the upper triangle of
A
is stored.
If
uplo
=
'L'
, the lower triangle of
A
is stored.
n
The order of the matrix
A
;
n
0
.
a
Array
a
(size max(1,
lda
*
n
)).
Contains the factorization of the matrix
A
, as returned by
?potrf
.
lda
a
.
lda
max(1,
n
).
Output Parameters
a
Overwritten by the upper or lower triangle of the inverse of
A
.
Return Values
This function returns a value
info
.
If
info
= 0
, the execution is successful.
If
info
=
-i
, parameter
i
If
info
=
i
, the
i
-th diagonal element of the Cholesky factor (and therefore the factor itself) is zero, and the inversion could not be completed.
Application Notes
The computed inverse
X
satisfies the following error bounds:
```||XA - I||2
≤
c(n)ε
κ
2(A), ||AX -  I||2
≤
c(n)ε
κ
2(A),```
where
c
(
n
)
is a modest linear function of
n
, and
ε
is the machine precision;
I
denotes the identity matrix.
The 2-norm
||
A
||
2
of a matrix
A
is defined by
||
A
||
2
=
max
x
·
x
=1
(
A
x
·
A
x
)
1/2
, and the condition number
κ
2
(
A
)
is defined by
κ
2
(
A
) = ||
A
||
2
||
A
-1
||
2
.
The total number of floating-point operations is approximately
(2/3)
n
3
for real flavors and
(8/3)
n
3
for complex flavors.

#### Product and Performance Information

1

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