Contents

# ?hptri

Computes the inverse of a complex Hermitian matrix using
U
*
D
*
U
H
or
L
*
D
*
L
H
Bunch-Kaufman factorization of matrix in packed storage.

## Syntax

Include Files
• mkl.h
Description
The routine computes the inverse
inv(
A
)
of a complex Hermitian matrix
A
using packed storage. Before calling this routine, call
?hptrf
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 array
ap
stores the packed Bunch-Kaufman factorization
A
=
U*D*U
H
.
If
uplo
=
'L'
, the array
ap
stores the packed Bunch-Kaufman factorization
A
=
L*D*L
H
.
n
The order of the matrix
A
;
n
0
.
ap
Array
ap
(size max(1,
n
(
n
+1)/2)) contains the factorization of the matrix
A
, as returned by
?hptrf
.
ipiv
Array, size at least
max(1,
n
)
.
The
ipiv
array, as returned by
?hptrf
.
Output Parameters
ap
Overwritten by the matrix
inv(
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
D
is zero,
D
is singular, and the inversion could not be completed.
Application Notes
The computed inverse
X
satisfies the following error bounds:
`|D*UH*PT*X*P*U - I| ≤ c(n)ε(|D||UH|PT|X|P|U| + |D||D-1|)`
for
uplo
=
'U'
, and
`|D*LH*PT*X*PL - I| ≤ c(n)ε(|D||LH|PT|X|P|L| + |D||D-1|)`
for
uplo
=
'L'
. Here
c
(
n
)
is a modest linear function of
n
, and
ε
is the machine precision;
I
denotes the identity matrix.
The total number of floating-point operations is approximately
(8/3)
n
3
.
The real counterpart of this routine is
?sptri
.

#### Product and Performance Information

1

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