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
This operator uses the routines lin_sol_gen or lin_sol_lsq (See Chapter 1, “Linear Systems” ).
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 |
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 located 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
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