Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

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

lapack_int
LAPACKE_chptri
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_complex_float
*
ap
,
const
lapack_int
*
ipiv
);
lapack_int
LAPACKE_zhptri
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_complex_double
*
ap
,
const
lapack_int
*
ipiv
);
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
 had an illegal value.
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*U
H
*P
T
*X*P*U - I| ≤ c(n)ε(|D||U
H
|P
T
|X|P|U| + |D||D
-1
|)
for
uplo
 =
'U'
, and 
|D*L
H
*P
T
*X*PL - I| ≤ c(n)ε(|D||L
H
|P
T
|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.