.i.
Computes the inverse matrix.
Operator Return Value
Matrix containing the inverse of A. (Output)
Required Operand
A — Matrix for which the inverse is to be computed. This is an array of rank 2 or 3. It may be real, double, complex, double complex. (Input)
Optional Variables, Reserved Names
The option and derived type names are given in the following tables:
Option Names for .i. | Option Value |
|---|---|
Use_lin_sol_gen_only | 1 |
Use_lin_sol_lsq_only | 2 |
I_options_for_lin_sol_gen | 3 |
I_options_for_lin_sol_lsq | 4 |
Skip_error_processing | 5 |
Name of Unallocated Option Array to Use for Setting Options | Use | Derived Type |
|---|---|---|
?_inv_options(:) | Use when setting options for calls hereafter. | ?_options |
?_inv_options_once(:) | Use when setting options for next call only. | ?_options |
For a description on how to use these options, see Matrix Optional Data Changes. See LIN_SOL_GEN and LIN_SOL_LSQ in Chapter 1, “Linear Systems” for the specific options for these routines.
FORTRAN 90 Interface
.i. A
Description
Computes the inverse matrix for square non-singular matrices using LIN_SOL_GEN, or the Moore-Penrose generalized inverse matrix for singular square matrices or rectangular matrices using LIN_SOL_LSQ. The operation may be read inverse or generalized inverse, and the results are in a precision and data type that matches the operand.
This operator requires a single operand. Since this is a unary operation, it has higher Fortran 90 precedence than any other intrinsic array operation.
Examples
Dense Matrix Example (operator_ex02.f90)
use linear_operators
implicit none
! This is the equivalent of Example 2 for LIN_SOL_GEN using operators
! and functions.
integer, parameter :: n=32
real(kind(1e0)) :: one=1e0, err, det_A, det_i
real(kind(1e0)), dimension(n,n) :: A, inv
! Generate a random matrix.
A = rand(A)
! Compute the matrix inverse and its determinant.
inv = .i.A; det_A = det(A)
! Compute the determinant for the inverse matrix.
det_i = det(inv)
! Check the quality of both left and right inverses.
err = (norm(EYE(n)-(A .x. inv))+norm(EYE(n)-(inv.x.A)))/cond(A)
if (err <= sqrt(epsilon(one)) .and. abs(det_A*det_i - one) <= &
sqrt(epsilon(one))) &
write (*,*) 'Example 2 for LIN_SOL_GEN (operators) is correct.'
end
Parallel Example (parallel_ex02.f90)
use linear_operators
use mpi_setup_int
implicit none
! This is the equivalent of Parallel Example 2 for .i. and det() with box
! data types, operators and functions.
integer, parameter :: n=32, nr=4
integer J
real(kind(1e0)) :: one=1e0
real(kind(1e0)), dimension(nr) :: err, det_A, det_i
real(kind(1e0)), dimension(n,n,nr) :: A, inv, R, S
! Setup for MPI.
MP_NPROCS=MP_SETUP()
! Generate a random matrix.
A = rand(A)
! Compute the matrix inverse and its determinant.
inv = .i.A; det_A = det(A)
! Compute the determinant for the inverse matrix.
det_i = det(inv)
! Check the quality of both left and right inverses.
DO J=1,nr; R(:,:,J)=EYE(N); END DO
S=R; R=R-(A .x. inv); S=S-(inv .x. A)
err = (norm(R)+norm(S))/cond(A)
if (ALL(err <= sqrt(epsilon(one)) .and. &
abs(det_A*det_i - one) <= sqrt(epsilon(one)))&
.and. MP_RANK == 0) &
write (*,*) 'Parallel Example 2 is correct.'
! See to any error messages and quit MPI.
MP_NPROCS=MP_SETUP('Final')
end
