linalg::mtx_inverse Interface Reference

Computes the inverse of a square matrix. More...

Public Member Functions
	mtx_inverse_dbl
	mtx_inverse_cmplx

Detailed Description

Computes the inverse of a square matrix.

Syntax

subroutine mtx_inverse(real(real64) a(:,:), optional integer(int32) iwork, optional real(real64) work(:), optional integer olwork, optional class(errors) err)
subroutine mtx_inverse(complex(real64) a(:,:), optional integer(int32) iwork, optional complex(real64) work(:), optional integer olwork, optional class(errors) err)

Parameters

[in,out]	a	On input, the N-by-N matrix to invert. On output, the inverted matrix.
[out]	iwork	An optional N-element integer workspace array.
[out]	work	An optional input, that if provided, prevents any local memory allocation. If not provided, the memory required is allocated within. If provided, the length of the array must be at least olwork.
[out]	olwork	An optional output used to determine workspace size. If supplied, the routine determines the optimal size for work, and returns without performing any actual calculations.
[in,out]	err	An optional errors-based object that if provided can be used to retrieve information relating to any errors encountered during execution. If not provided, a default implementation of the errors class is used internally to provide error handling. Possible errors and warning messages that may be encountered are as follows. LA_ARRAY_SIZE_ERROR: Occurs if a is not square. Will also occur if incorrectly sized workspace arrays are provided. LA_OUT_OF_MEMORY_ERROR: Occurs if local memory must be allocated, and there is insufficient memory available. LA_SINGULAR_MATRIX_ERROR: Occurs if the input matrix is singular.

Notes

This routine utilizes the LAPACK routines DGETRF to perform an LU factorization of the matrix, and DGETRI to invert the LU factored matrix (ZGETRF and ZGETRI in the complex case).

See Also

• Wikipedia
• Wolfram MathWorld

Usage

The following example illustrates the inversion of a 3-by-3 matrix.

program example
    use iso_fortran_env, only : real64, int32
    use linalg
    implicit none
 
    ! Variables
    real(real64) :: a(3,3), ai(3,3), c(3,3)
    integer(int32) :: i
 
    ! Construct the 3-by-3 matrix A to invert
    !     | 1   2   3 |
    ! A = | 4   5   6 |
    !     | 7   8   0 |
    a = reshape([1.0d0, 4.0d0, 7.0d0, 2.0d0, 5.0d0, 8.0d0, 3.0d0, 6.0d0, &
        0.0d0], [3, 3])
 
    ! Compute the inverse of A.  Notice, the original matrix is overwritten
    ! with it's inverse.
    ai = a
    call mtx_inverse(ai)
 
    ! Show that A * inv(A) = I
    c = matmul(a, ai)
 
    ! Display the inverse
    print '(A)', "Inverse:"
    do i = 1, size(ai, 1)
        print *, ai(i,:)
    end do
 
    ! Display the result of A * inv(A)
    print '(A)', "A * A**-1:"
    do i = 1, size(c, 1)
        print *, c(i,:)
    end do
end program

The above program produces the following output.

Inverse:
 -1.7777777777777777       0.88888888888888884      -0.11111111111111110
  1.5555555555555556      -0.77777777777777779       0.22222222222222221
 -0.11111111111111119      0.22222222222222227      -0.11111111111111112
A * A**-1:
  0.99999999999999989       5.5511151231257827E-017  -4.1633363423443370E-017
  5.5511151231257827E-017   1.0000000000000000       -8.3266726846886741E-017
  1.7763568394002505E-015  -8.8817841970012523E-016   1.0000000000000000

Definition at line 3051 of file linalg.f90.

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The documentation for this interface was generated from the following file:

• D:/Code/linalg/src/linalg.f90