Developer Reference for Intel® oneAPI Math Kernel Library for C
?getri
Computes the inverse of an LU-factored general matrix.
Syntax
lapack_intLAPACKE_sgetri ( intmatrix_layout , lapack_intn , float*a , lapack_intlda , constlapack_int*ipiv );
lapack_intLAPACKE_dgetri ( intmatrix_layout , lapack_intn , double*a , lapack_intlda , constlapack_int*ipiv );
lapack_intLAPACKE_cgetri ( intmatrix_layout , lapack_intn , lapack_complex_float*a , lapack_intlda , constlapack_int*ipiv );
lapack_intLAPACKE_zgetri ( intmatrix_layout , lapack_intn , lapack_complex_double*a , lapack_intlda , constlapack_int*ipiv );
Include Files
mkl.h
Description
sgetri dgetri cgetri zgetri getri
The routine computes the inverse inv(A) of a general matrix A . Before calling this routine, call ?getrf (Computes the LU factorization of a general m-by-n matrix.) 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 matrix A ; n≥ 0 .
a , work
Arrays: a(lda,*) , work(*) .
a(lda,*) contains the factorization of the matrix A , as returned by ?getrf (Computes the LU factorization of a general m-by-n matrix.) : A = P*L*U .
work(*) is a workspace array of dimension at least max(1,lwork) .
a
Array a (size max(1, lda * n )) contains the factorization of the matrix A , as returned by GUID-A02DB70F-9704-42A4-9071-D409D783D911.xml#GUID-A02DB70F-9704-42A4-9071-D409D783D911 : A = P*L*U . The second dimension of a must be at least max(1,n) .
lda
The leading dimension of a ; lda≥ max(1, n) .
ipiv
Array, size at least max(1, n) .
The ipiv array, as returned by ?getrf (Computes the LU factorization of a general m-by-n matrix.) .
lwork
The size of the work array; lwork ≥ n .
If lwork = -1 , then a workspace query is assumed; the routine only calculates the optimal size of the work array, returns this value as the first entry of the work array, and no error message related to lwork is issued by xerbla .
Output Parameters
a
Overwritten by the n -by- n matrix inv(A) .
work(1)
If info = 0 , on exit work(1) contains the minimum value of lwork required for optimum performance. Use this lwork for subsequent runs.
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 the factor U is zero, U is singular, and the inversion could not be completed.
LAPACK 95 Interface Notes
There exist FORTRAN 77 and FORTRAN 95 interfaces for this routine. See the Intel® oneMKL Fortran Developer Reference for details.
Application Notes
The computed inverse \(X\) satisfies the following error bound:
\[|XA - I| \leq c(n)\varepsilon|X|P|L||U|,\]
where c(n) is a modest linear function of n ; \(\varepsilon\) 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 \((4/3)n^{3}\) for real flavors and \((16/3)n^{3}\) for complex flavors.