## Developer Reference

• 2020.2
• 07/15/2020
• Public Content
Contents

# ?pptri

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

## Syntax

Include Files
• mkl.fi
,
lapack.f90
Description
The routine computes the inverse
inv(
A
)
of a symmetric positive definite or, for complex flavors, Hermitian positive-definite matrix
A
in packed form. Before calling this routine, call
?pptrf
to factorize
A
.
Input Parameters
uplo
CHARACTER*1
.
Must be
'U'
or
'L'
.
Indicates whether
the upper or lower triangular factor is stored in
ap
:
If
uplo
=
'U'
, then the upper triangular factor is stored.
If
uplo
=
'L'
, then the lower triangular factor is stored.
n
INTEGER
.
The order of the matrix
A
;
n
0
.
ap
REAL
for
spptri
DOUBLE PRECISION
for
dpptri
COMPLEX
for
cpptri
DOUBLE COMPLEX
for
zpptri
.
Array, size at least max(1,
n
(
n
+1)/2).
Contains the factorization of the packed matrix
A
, as returned by
?pptrf
.
The dimension
ap
must be at least max(1,
n
(
n
+1)/2).
Output Parameters
ap
Overwritten by the packed
n
-by-
n
matrix
inv(
A
)
.
info
INTEGER
.
If
info
= 0
, the execution is successful.
If
info
=
-i
, the
i
-th parameter had an illegal value.
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.
LAPACK 95 Interface Notes
Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or reconstructible arguments, see LAPACK 95 Interface Conventions.
Specific details for the routine
pptri
interface are as follows:
ap
Holds the array
A
of size
(
n
*(
n
+1)/2)
.
uplo
Must be
'U'
or
'L'
. The default value is
'U'
.
Application Notes
The computed inverse
X
satisfies the following error bounds:
`||XA - I||2≤c(n)εκ2(A), ||AX - I||2≤c(n)εκ2(A),`
where
c