// 转载自: http://fortranwiki.org/fortran/show/Matrix+inversion
// 这里仅适用于 小型矩阵 2*2,3*3,4*4 的矩阵求逆。事实上,对于这种规模的矩阵,直接写出求逆的结果速度更快。
// 这里3*3 的矩阵我已经验证过了,其余的未验证。一般矩阵的求逆方法原链接中也有。
pure function matinv2(A) result(B)
!! Performs a direct calculation of the inverse of a 2×2 matrix.
complex(wp), intent(in) :: A(2,2) !! Matrix
complex(wp) :: B(2,2) !! Inverse matrix
complex(wp) :: detinv
! Calculate the inverse determinant of the matrix
detinv = 1/(A(1,1)*A(2,2) - A(1,2)*A(2,1))
! Calculate the inverse of the matrix
B(1,1) = +detinv * A(2,2)
B(2,1) = -detinv * A(2,1)
B(1,2) = -detinv * A(1,2)
B(2,2) = +detinv * A(1,1)
end function
pure function matinv3(A) result(B)
!! Performs a direct calculation of the inverse of a 3×3 matrix.
complex(wp), intent(in) :: A(3,3) !! Matrix
complex(wp) :: B(3,3) !! Inverse matrix
complex(wp) :: detinv
! Calculate the inverse determinant of the matrix
detinv = 1/(A(1,1)*A(2,2)*A(3,3) - A(1,1)*A(2,3)*A(3,2)&
- A(1,2)*A(2,1)*A(3,3) + A(1,2)*A(2,3)*A(3,1)&
+ A(1,3)*A(2,1)*A(3,2) - A(1,3)*A(2,2)*A(3,1))
! Calculate the inverse of the matrix
B(1,1) = +detinv * (A(2,2)*A(3,3) - A(2,3)*A(3,2))
B(2,1) = -detinv * (A(2,1)*A(3,3) - A(2,3)*A(3,1))
B(3,1) = +detinv * (A(2,1)*A(3,2) - A(2,2)*A(3,1))
B(1,2) = -detinv * (A(1,2)*A(3,3) - A(1,3)*A(3,2))
B(2,2) = +detinv * (A(1,1)*A(3,3) - A(1,3)*A(3,1))
B(3,2) = -detinv * (A(1,1)*A(3,2) - A(1,2)*A(3,1))
B(1,3) = +detinv * (A(1,2)*A(2,3) - A(1,3)*A(2,2))
B(2,3) = -detinv * (A(1,1)*A(2,3) - A(1,3)*A(2,1))
B(3,3) = +detinv * (A(1,1)*A(2,2) - A(1,2)*A(2,1))
end function
pure function matinv4(A) result(B)
!! Performs a direct calculation of the inverse of a 4×4 matrix.
complex(wp), intent(in) :: A(4,4) !! Matrix
complex(wp) :: B(4,4) !! Inverse matrix
complex(wp) :: detinv
! Calculate the inverse determinant of the matrix
detinv = &
1/(A(1,1)*(A(2,2)*(A(3,3)*A(4,4)-A(3,4)*A(4,3))+A(2,3)*(A(3,4)*A(4,2)-A(3,2)*A(4,4))+A(2,4)*(A(3,2)*A(4,3)-A(3,3)*A(4,2)))&
- A(1,2)*(A(2,1)*(A(3,3)*A(4,4)-A(3,4)*A(4,3))+A(2,3)*(A(3,4)*A(4,1)-A(3,1)*A(4,4))+A(2,4)*(A(3,1)*A(4,3)-A(3,3)*A(4,1)))&
+ A(1,3)*(A(2,1)*(A(3,2)*A(4,4)-A(3,4)*A(4,2))+A(2,2)*(A(3,4)*A(4,1)-A(3,1)*A(4,4))+A(2,4)*(A(3,1)*A(4,2)-A(3,2)*A(4,1)))&
- A(1,4)*(A(2,1)*(A(3,2)*A(4,3)-A(3,3)*A(4,2))+A(2,2)*(A(3,3)*A(4,1)-A(3,1)*A(4,3))+A(2,3)*(A(3,1)*A(4,2)-A(3,2)*A(4,1))))
! Calculate the inverse of the matrix
B(1,1) = detinv*(A(2,2)*(A(3,3)*A(4,4)-A(3,4)*A(4,3))+A(2,3)*(A(3,4)*A(4,2)-A(3,2)*A(4,4))+A(2,4)*(A(3,2)*A(4,3)-A(3,3)*A(4,2)))
B(2,1) = detinv*(A(2,1)*(A(3,4)*A(4,3)-A(3,3)*A(4,4))+A(2,3)*(A(3,1)*A(4,4)-A(3,4)*A(4,1))+A(2,4)*(A(3,3)*A(4,1)-A(3,1)*A(4,3)))
B(3,1) = detinv*(A(2,1)*(A(3,2)*A(4,4)-A(3,4)*A(4,2))+A(2,2)*(A(3,4)*A(4,1)-A(3,1)*A(4,4))+A(2,4)*(A(3,1)*A(4,2)-A(3,2)*A(4,1)))
B(4,1) = detinv*(A(2,1)*(A(3,3)*A(4,2)-A(3,2)*A(4,3))+A(2,2)*(A(3,1)*A(4,3)-A(3,3)*A(4,1))+A(2,3)*(A(3,2)*A(4,1)-A(3,1)*A(4,2)))
B(1,2) = detinv*(A(1,2)*(A(3,4)*A(4,3)-A(3,3)*A(4,4))+A(1,3)*(A(3,2)*A(4,4)-A(3,4)*A(4,2))+A(1,4)*(A(3,3)*A(4,2)-A(3,2)*A(4,3)))
B(2,2) = detinv*(A(1,1)*(A(3,3)*A(4,4)-A(3,4)*A(4,3))+A(1,3)*(A(3,4)*A(4,1)-A(3,1)*A(4,4))+A(1,4)*(A(3,1)*A(4,3)-A(3,3)*A(4,1)))
B(3,2) = detinv*(A(1,1)*(A(3,4)*A(4,2)-A(3,2)*A(4,4))+A(1,2)*(A(3,1)*A(4,4)-A(3,4)*A(4,1))+A(1,4)*(A(3,2)*A(4,1)-A(3,1)*A(4,2)))
B(4,2) = detinv*(A(1,1)*(A(3,2)*A(4,3)-A(3,3)*A(4,2))+A(1,2)*(A(3,3)*A(4,1)-A(3,1)*A(4,3))+A(1,3)*(A(3,1)*A(4,2)-A(3,2)*A(4,1)))
B(1,3) = detinv*(A(1,2)*(A(2,3)*A(4,4)-A(2,4)*A(4,3))+A(1,3)*(A(2,4)*A(4,2)-A(2,2)*A(4,4))+A(1,4)*(A(2,2)*A(4,3)-A(2,3)*A(4,2)))
B(2,3) = detinv*(A(1,1)*(A(2,4)*A(4,3)-A(2,3)*A(4,4))+A(1,3)*(A(2,1)*A(4,4)-A(2,4)*A(4,1))+A(1,4)*(A(2,3)*A(4,1)-A(2,1)*A(4,3)))
B(3,3) = detinv*(A(1,1)*(A(2,2)*A(4,4)-A(2,4)*A(4,2))+A(1,2)*(A(2,4)*A(4,1)-A(2,1)*A(4,4))+A(1,4)*(A(2,1)*A(4,2)-A(2,2)*A(4,1)))
B(4,3) = detinv*(A(1,1)*(A(2,3)*A(4,2)-A(2,2)*A(4,3))+A(1,2)*(A(2,1)*A(4,3)-A(2,3)*A(4,1))+A(1,3)*(A(2,2)*A(4,1)-A(2,1)*A(4,2)))
B(1,4) = detinv*(A(1,2)*(A(2,4)*A(3,3)-A(2,3)*A(3,4))+A(1,3)*(A(2,2)*A(3,4)-A(2,4)*A(3,2))+A(1,4)*(A(2,3)*A(3,2)-A(2,2)*A(3,3)))
B(2,4) = detinv*(A(1,1)*(A(2,3)*A(3,4)-A(2,4)*A(3,3))+A(1,3)*(A(2,4)*A(3,1)-A(2,1)*A(3,4))+A(1,4)*(A(2,1)*A(3,3)-A(2,3)*A(3,1)))
B(3,4) = detinv*(A(1,1)*(A(2,4)*A(3,2)-A(2,2)*A(3,4))+A(1,2)*(A(2,1)*A(3,4)-A(2,4)*A(3,1))+A(1,4)*(A(2,2)*A(3,1)-A(2,1)*A(3,2)))
B(4,4) = detinv*(A(1,1)*(A(2,2)*A(3,3)-A(2,3)*A(3,2))+A(1,2)*(A(2,3)*A(3,1)-A(2,1)*A(3,3))+A(1,3)*(A(2,1)*A(3,2)-A(2,2)*A(3,1)))
end function