3*1向量叉乘：

      subroutine vecprod(dvin1,dvin2,dvout)

      implicit none

      real(8), intent(in) :: dvin1(3), dvin2(3)

      real(8), intent(out) :: dvout(3)

      dvout(1)=dvin1(2)*dvin2(3)-dvin1(3)*dvin2(2)

      dvout(2)=dvin1(3)*dvin2(1)-dvin1(1)*dvin2(3)

      dvout(3)=dvin1(1)*dvin2(2)-dvin1(2)*dvin2(1) 

      return

      end subroutine vecprod

3*1向量點乘：

      subroutine dotprod(dvin1,dvin2,dvout)

      implicit none

      real(8), intent(in) :: dvin1(3), dvin2(3)

      real(8), intent(out) :: dvout(3)

      dvout = dvin1(1)*dvin2(1)+dvin1(2)*dvin2(2)+dvin1(3)*dvin2(3)

      dvout = abs(dvout)

      return

      end subroutine dotprod

3*3矩陣的行列式的值：

      subroutine deter3x3(dmin,d)

      implicit none

      real(8), intent(in) :: dmin(3,3)

      real(8), intent(out) :: d

      d = 0.

      d = dmin(1,1)*dmin(2,2)*dmin(3,3) + 

     + dmin(1,2)*dmin(2,3)*dmin(3,1) + 

     + dmin(2,1)*dmin(3,2)*dmin(1,3) -

     + dmin(1,3)*dmin(2,2)*dmin(3,1) -

     + dmin(1,1)*dmin(2,3)*dmin(3,2) -

     + dmin(1,2)*dmin(2,1)*dmin(3,3)

      return

      end subroutine deter3x3

2*2矩陣的行列式的值：

      subroutine deter2x2(dmin,d)

      implicit none

      real(8), intent(in) :: dmin(2,2)

      real(8), intent(out) :: d

      d=0.

      d=dmin(1,1)*dmin(2,2)-dmin(1,2)*dmin(2,1)

      return

      end subroutine deter2x2

3*3的矩陣相乘：

      subroutine mmult(dm1,dm2,dm)

      implicit none

      real(8), intent(in) :: dm1(3,3), dm2(3,3)

      real(8), intent(out) :: dm(3,3)

      integer :: i, j, k

      real(8) :: x

      do i=1,3

          do j=1,3

              x=0.0

              do k=1,3

                  x=x+dm1(i,k)*dm2(k,j)

              end do

              dm(i,j)=x

          end do

      end do

      return

      end subroutine mmult