Computes the inverse of a LU-factored distributed matrix.

## Syntax

void psgetri (MKL_INT *n , float *a , MKL_INT *ia , MKL_INT *ja , MKL_INT *desca , MKL_INT *ipiv , float *work , MKL_INT *lwork , MKL_INT *iwork , MKL_INT *liwork , MKL_INT *info );

void pdgetri (MKL_INT *n , double *a , MKL_INT *ia , MKL_INT *ja , MKL_INT *desca , MKL_INT *ipiv , double *work , MKL_INT *lwork , MKL_INT *iwork , MKL_INT *liwork , MKL_INT *info );

void pcgetri (MKL_INT *n , MKL_Complex8 *a , MKL_INT *ia , MKL_INT *ja , MKL_INT *desca , MKL_INT *ipiv , MKL_Complex8 *work , MKL_INT *lwork , MKL_INT *iwork , MKL_INT *liwork , MKL_INT *info );

void pzgetri (MKL_INT *n , MKL_Complex16 *a , MKL_INT *ia , MKL_INT *ja , MKL_INT *desca , MKL_INT *ipiv , MKL_Complex16 *work , MKL_INT *lwork , MKL_INT *iwork , MKL_INT *liwork , MKL_INT *info );

## Include Files

• mkl_scalapack.h

## Description

The p?getrifunction computes the inverse of a general distributed matrix sub(A) = A(ia:ia+n-1, ja:ja+n-1) using the LU factorization computed by p?getrf. This method inverts U and then computes the inverse of sub(A) by solving the system

inv(sub(A))*L = inv(U)

for inv(sub(A)).

## Input Parameters

n

(global) The number of rows and columns to be operated on, that is, the order of the distributed matrix sub(A) (n0).

a

(local)

Pointer into the local memory to an array of local size lld_a*LOCc(ja+n-1).

On entry, the array a contains the local pieces of the L and U obtained by the factorization sub(A) = P*L*U computed by p?getrf.

ia, ja

(global) The row and column indices in the global matrix A indicating the first row and the first column of the matrix sub(A), respectively.

desca

(global and local) array of size dlen_. The array descriptor for the distributed matrix A.

work

(local)

The array work of size lwork is a workspace array.

lwork

(local) The size of the array work. lwork must be at least

lworkLOCr(n+mod(ia-1,mb_a))*nb_a.

### Note

mod(x,y) is the integer remainder of x/y.

The array work is used to keep at most an entire column block of sub(A).

iwork

(local) Workspace array used for physically transposing the pivots, size liwork.

liwork

(local or global) The size of the array iwork.

The minimal value liwork of is determined by the following code:

`if NPROW == NPCOL then`
` liwork = LOCc(n_a + mod(ja-1,nb_a))+ nb_a `
`else `
` liwork = LOCc(n_a + mod(ja-1,nb_a)) + `
`max(ceil(ceil(LOCr(m_a)/mb_a)/(lcm/NPROW)),nb_a)`
`end if`

where lcm is the least common multiple of process rows and columns (NPROW and NPCOL).

## Output Parameters

ipiv

(local)

Array of size LOCr(m_a)+ mb_a.

This array contains the pivoting information.

If ipiv[i]=j, then the local row i+1 was swapped with the global row jwhere i=0, ... , LOCr(m_a) + mb_a- 1.

This array is tied to the distributed matrix A.

work[0]

On exit, work[0] contains the minimum value of lwork required for optimum performance.

iwork[0]

On exit, iwork[0] contains the minimum value of liwork required for optimum performance.

info

(global) If info=0, the execution is successful.

info < 0:

If the i-th argument is an array and the j-th entry, indexed j - 1, had an illegal value, then info = -(i*100+j); if the i-th argument is a scalar and had an illegal value, then info = -i.

info> 0:

If info = i, the matrix element U(i,i) is exactly zero. The factorization has been completed, but the factor U is exactly singular, and division by zero will occur if it is used to solve a system of equations.

## See Also

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