?hetri
?hetri
Computes the inverse of a complex Hermitian matrix using
U
*D
*U
H
or L
*D
*L
H
Bunch-Kaufman factorization.Syntax
lapack_int
LAPACKE_chetri
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_complex_float
*
a
,
lapack_int
lda
,
const
lapack_int
*
ipiv
);
lapack_int
LAPACKE_zhetri
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_complex_double
*
a
,
lapack_int
lda
,
const
lapack_int
*
ipiv
);
Include Files
- mkl.h
Description
The routine computes the inverse
inv(
of a complex Hermitian matrix A
)A
. Before calling this routine, call ?hetrf
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 matrixAhas been factored:If, the arrayuplo='U'astores the Bunch-Kaufman factorization.A=U*D*UHIf, the arrayuplo='L'astores the Bunch-Kaufman factorization.A=L*D*LH
- n
- The order of the matrixA;.n≥0
- a,
- Arraya(size max(1,contains the factorization of the matrixlda*n))A, as returned by?hetrf. The second dimension ofamust be at leastmax(1,.n)
- lda
- The leading dimension ofa;.lda≥max(1,n)
- ipiv
Output Parameters
- a
- Overwritten by then-by-nmatrix inv(A).
Return Values
This function returns a value
info
.If , the execution is successful.
info
= 0If
info
= -i
, parameter i
had an illegal value.If , the
info
= i
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*P*L - I| ≤ c(n)ε(|D||LH|PT|X|P|L| + |D||D-1|)
for . Here is a modest linear function of
uplo
= 'L'
c
(n
)n
, and ε
is the machine precision; I
denotes the identity matrix.The total number of floating-point operations is approximately
(8/3)
for complex flavors.n
3
The real counterpart of this routine is
?sytri
.