?getri
?getri
Computes the inverse of an LU-factored general matrix.
Syntax
lapack_int
LAPACKE_sgetri
(
int
matrix_layout
,
lapack_int
n
,
float
*
a
,
lapack_int
lda
,
const
lapack_int
*
ipiv
);
lapack_int
LAPACKE_dgetri
(
int
matrix_layout
,
lapack_int
n
,
double
*
a
,
lapack_int
lda
,
const
lapack_int
*
ipiv
);
lapack_int
LAPACKE_cgetri
(
int
matrix_layout
,
lapack_int
n
,
lapack_complex_float
*
a
,
lapack_int
lda
,
const
lapack_int
*
ipiv
);
lapack_int
LAPACKE_zgetri
(
int
matrix_layout
,
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 general matrix A
)A
. Before calling this routine, call ?getrf
to factorize A
.Input Parameters
- matrix_layout
- Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR).
- n
- The order of the matrixA;.n≥0
- a
- Arraya(size max(1,contains the factorization of the matrixlda*n))A, as returned by?getrf:. The second dimension ofA=P*L*Uamust be at leastmax(1,.n)
- lda
- The leading dimension ofa;.lda≥max(1,n)
- ipiv
- Array, size at leastmax(1,.n)Theipivarray, as returned by?getrf.
Output Parameters
- a
- Overwritten by then-by-nmatrixinv(.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 the factor U
is zero, U
is singular, and the inversion could not be completed.Application Notes
The computed inverse
X
satisfies the following error bound: |XA - I| ≤ c(n)ε|X|P|L||U|,
where is a modest linear function of .
c
(n
)n
; ε
is the machine precision; I
denotes the identity matrix; P
, L
, and U
are the factors of the matrix factorization A
= P*L*U
The total number of floating-point operations is approximately
(4/3)
for real flavors and n
3
(16/3)
for complex flavors.n
3