Fortran求逆矩阵子程序.docx

! 求逆矩阵subroutine inverse(A,IA)implicit nonereal :: A(:,:), IA(:,:)real, allocatable :: B(:,:)integer :: i,j,N N = size(A,1) allocate(B(N,N)) ! 先把IA设定成单位矩阵forall(i=1:N,j=1:N,i==j) IA(i,j)=1.0forall(i=1:N,j=1:N,i/=j) IA(i,j)=0.0 ! 保存原先的矩阵A, 使用B来计算 B=A ! 把B化成对角线矩阵(除了对角线外,都为0)call Upper(B,IA,N) ! 先把B化成上三角矩阵call Lower(B,IA,N) ! 再把B化成下三角矩阵 ! 求解forall(i=1:N) IA(i,:)=IA(i,:)/B(i,i) returnend subroutine! 求上三角矩阵的子程序subroutine Upper(M,S,N)implicit noneinteger :: Nreal :: M(N,N)real :: S(N,N)integer :: I,Jreal :: Edo I=1,N-1do J=I+1,N E=M(J,I)/M(I,I) M(J,I:N)=M(J,I:N)-M(I,I:N)*ES(J,:)=S(J,:)-S(I,:)*Eend doend doreturnend subroutine Upper! 求下三角矩阵的子程序subroutine Lower(M,S,N)implicit noneinteger :: Nreal :: M(N,N)real :: S(N,N)integer :: I,Jreal :: Edo I=N,2,-1do J=I-1,1,-1 E=M(J,I)/M(I,I) M(J,1:N)=M(J,1:N)-M(I,1:N)*ES(J,:)=S(J,:)-S(I,:)*Eend doend doreturnend subroutine Lowerprogram qiuniimplicit noneinteger i,jreal::a(3,3),aa(3,3)print*,请输入a矩阵do i=1,3 do j=1,3 read*,a(i,j) enddoenddocall inverse(a,aa,3)print*,aaend! 求逆矩阵subroutine inverse(A,IA,N)implicit noneinteger :: i,j,N real A(N,N),IA(N,N),B(N,N) ! 先把IA设定成单位矩阵forall(i=1:N,j=1:N,i==j) IA(i,j)=1.0forall(i=1:N,j=1:N,i/=j) IA(i,j)=0.0 ! 保存原先的矩阵A, 使用B来计算 B=A ! 把B化成对角线矩阵(除了对角线外,都为0)call Upper(B,IA,N) ! 先把B化成上三角矩阵call Lower(B,IA,N) ! 再把B化成下三角矩阵 ! 求解forall(i=1:N) IA(i,:)=IA(i,:)/B(i,i) returnend subroutine! 求上三角矩阵的子程序subroutine Upper(M,S,N)implicit noneinteger :: Nreal :: M(N,N)real :: S(N,N)integer :: I,Jreal :: Edo I=1,N-1do J=I+1,N E=M(J,I)/M(I,I) M(J,I:N)=M(J,I:N)-M(I,I:N)*ES(J,:)=S(J,:)-S(I,:)*Eend doend doreturnend subroutine Upper! 求下三角矩阵的子程序subroutine Lower(M,S,N)implicit noneinteger :: Nreal :: M(N,N)real :: S(N,N)integer :: I,Jreal :: Edo I=N,2,-1do J=I-1,1,-1 E=M(J,I)/M(I,I) M(J,1:N)=M(J,1:N)-M(I,1:N)*ES(J,:)=S(J,:)-S(I,:)*Eend doend doreturnend subroutine Lower