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module lsqcurvefit!----------------------------------------module coment
!Version :V1.0
!Coded by :syz
!Date :2010.07.09
!-----------------------------------------------------
!Description : 任意阶多项式曲线拟合模块
!
!Post Script :
! 1.
! 2.
!
!-----------------------------------------------------
!Contains :
! 1. 拟合函数，基函数
! 2. 最小二乘法函数
!-----------------------------------------------------
!Parameters:
! 1.
! 2.
!-----------------------------------------------------
contains
subroutine solve(x,y,N,c,m)
!---------------------------------subroutinecomment
!Version :V1.0
!Coded by:syz
!Date :
!-----------------------------------------------------
!Purpose :任意阶多项式拟合函数
!
!Post Script :
! 1.
! 2.
! 3.
!-----------------------------------------------------
!Inputparameters:
! 1.x,y --- 输入数据
! 2.N --- x,y向量的维数
! 3.m----希望用m阶多项式拟合
!Output parameters:
! 1.
! 2.
!Common parameters:
! 1.
! 2.
!----------------------------------------------------
implicit real*8(a-z)
integer::N,m
real*8::x(n),y(n),c(M)
real*8::bv(M)
integer::i
!A系数矩阵
real*8::A(N,M)
!如果多项式阶数加1高于实测数据个数则报错
!-------------
if (m>n) then
write(11,101)
stop
end if
101 format(/,'warning:the order of polynomial+1 > the ',/,&
'number of date,that is forbidden')
!------------------------------
do i=1,n
call basefunc(bv,x(i),m)
A(i,:)=bv
end do
call leas_eq(A,y,c,N,m)
end subroutine solve
subroutine basefunc(bv,x,m)
!---------------------------------subroutinecomment
!Version :V1.0
!Coded by:syz
!Date :2010.07.09
!-----------------------------------------------------
!Purpose :任意阶多项式基函数
!
!Post Script :
! 1.
! 2.
! 3.
!-----------------------------------------------------
!Inputparameters:
! 1. x 标量
! 2. m 多项式阶数
!Output parameters:
! 1.
! 2.
!Common parameters:
! 1.
! 2.
!----------------------------------------------------
implicit real*8(a-z)
integer::M
real*8::bv(m)
integer::i
bv(1)=1d0
doi=2,m
bv(i)=bv(i-1)*x
end do
end subroutine basefunc
subroutineleas_eq(A,b,x,M,N)
!---------------------------------subroutinecomment
!Version :V1.0
!Coded by:syz
!Date :
!-----------------------------------------------------
!Purpose :通过修正的Gram-Schmidt正交化求最小二问题
! 方法函数
!-----------------------------------------------------
!Method :
! 对超定方程 A进行QR分解后方程变为
! QR x=b
! => Rx=Q'b R为上三角阵
! => 回带，可以求得最小二乘意义下的解
!-----------------------------------------------------
!Post Script :
! 1. 即求解超定方程组 Ax=b 其中A(M,N)M>N
! 2.
!----------------------------------------------------
implicit real*8(a-z)
integer::M,N
real*8::A(M,N),Q(M,N),R(N,N)
real*8::b(M)
real*8::QT(N,M)!Q的转置矩阵
real*8::QTb(N) !Q'b
real*8::x(N)
call gram_dec(A,Q,R,M,N)
QT=transpose(Q)
QTb=matmul(QT,b)!Rx=Q'b
call uptri(R,QTb,x,N) !回带
end subroutine leas_eq
subroutine gram_dec(A,Q,R,M,N)
!---------------------------------subroutinecomment
!Version :V1.0
!Coded by:syz
!Date :
!-----------------------------------------------------
!Purpose : 采用修正的Gram-Schmidt分解求矩阵的QR分解
!
!-----------------------------------------------------
!Inputparameters:
! 1. A原始矩阵
! 2. A(M,N)
!Output parameters:
! 1. 分解结果为Q(M,N):注意Q不是方阵，Q列向量为标准正交基
! 2. R(N,N)：R是方阵
! 3.
!----------------------------------------------------
!Post Script :
! 1.注意矩阵的维数，分解后Q列向量是正交的
! 2.关于编程方法可以参看《矩阵分析与应用》张贤达编著
! 3.详细的数学解释，可以参看麻省理工学院的
! 线性代数教材《Linear Algebra with Application》
!----------------------------------------------------
implicit real*8(a-z)
integer::M,N
integer::i,j,k
real*8::A(M,N),Q(M,N),R(N,N)
real*8::vec_temp(M)
R(1,1)=dsqrt(dot_product(a(:,1),a(:,1)))
Q(:,1)=a(:,1)/R(1,1)
do k=2,N
do j=1,k-1
R(j,k)=dot_product(Q(:,j),A(:,k))
end do
vec_temp=A(:,k)
do j=1,k-1
vec_temp=vec_temp-Q(:,j)*R(j,k)
end do
R(k,k)=dsqrt(dot_product(vec_temp,vec_temp))
Q(:,k)=vec_temp/R(k,k)
end do
end subroutine gram_dec
subroutine uptri(A,b,x,N)
!---------------------------------subroutinecomment
!Version :V1.0
!Coded by:syz
!Date :2010-4-8
!-----------------------------------------------------
!Purpose :上三角方程组的回带方法
! Ax=b
!-----------------------------------------------------
!Inputparameters:
! 1. A(N,N)系数矩阵
! 2. b(N)右向量
! 3. N方程维数
!Output parameters:
! 1.x方程的根
! 2.
!Common parameters:
!
!----------------------------------------------------
implicit real*8(a-z)
integer::i,j,k,N
real*8::A(N,N),b(N),x(N)
x(N)=b(N)/A(N,N)
!回带部分
do i=n-1,1,-1
x(i)=b(i)
do j=i+1,N
x(i)=x(i)-a(i,j)*x(j)
end do
x(i)=x(i)/A(i,i)
end do
end subroutine uptri
end module lsqcurvefit
program main
!--------------------------------------program comment
!Version :V1.0
!Coded by:syz
!Date :2010.07.09
!-----------------------------------------------------
!Purpose : 多项式拟合主函数
!
!Post Script :
! 1.
! 2.
!
!-----------------------------------------------------
!In put datafiles :
! 1.
! 2.
!Output data files:
! 1.
! 2.
!
!-----------------------------------------------------
uselsqcurvefit
implicit real*8(a-z)
real*8::x(7),y(7)
real*8::c1(3),c2(4),c3(9)
open(unit=11,file='result.txt')
x=(/-3d0,-2d0,-1d0,0d0,1d0,2d0,3d0/)
y=(/4d0,2d0,3d0,0d0,-1d0,-2d0,-5d0/)
call solve(x,y,7,c1,3)
call solve(x,y,7,c2,4)
write(11,101)c1,c2
101 format(/T4,'多项式拟合曲线拟合',//,&
T3,'采用二阶多项式拟合，系数为：',3(/,F16.11),//,&
T3,'采用三阶多项式拟合，系数为：',4(/,F16.11),/)
call solve(x,y,7,c3,9)
end program main
看起来效果还可以哦 8错8错 很不错 fcode 发表于 2014-1-23 22:08
看起来效果还可以哦
固定格式呢？ 珊瑚虫 发表于 2014-1-23 22:14
固定格式呢？
你可以试试，不敢说100%，大多数还是支持 我来顶顶，灌灌水:P:P:P:P:P REAL FUNCTION SDOT(N,SX,INCX,SY,INCY)
C
C FORMS THE DOT PRODUCT OF TWO VECTORS.
C USES UNROLLED LOOPS FOR INCREMENTS EQUAL TO ONE.
C JACK DONGARRA, LINPACK, 3/11/78.
C
REAL SX(1),SY(1),STEMP
INTEGER I,INCX,INCY,IX,IY,M,MP1,N
C
STEMP = 0.0E0
SDOT = 0.0E0
IF(N.LE.0)RETURN
IF(INCX.EQ.1.AND.INCY.EQ.1)GO TO 20
C
C CODE FOR UNEQUAL INCREMENTS OR EQUAL INCREMENTS
C NOT EQUAL TO 1
C
IX = 1
IY = 1
IF(INCX.LT.0)IX = (-N+1)*INCX + 1
IF(INCY.LT.0)IY = (-N+1)*INCY + 1
DO 10 I = 1,N
STEMP = STEMP + SX(IX)*SY(IY)
IX = IX + INCX
IY = IY + INCY
10 CONTINUE
SDOT = STEMP
RETURN
C
C CODE FOR BOTH INCREMENTS EQUAL TO 1
C
C
C CLEAN-UP LOOP
C
20 M = MOD(N,5)
IF( M .EQ. 0 ) GO TO 40
DO 30 I = 1,M
STEMP = STEMP + SX(I)*SY(I)
30 CONTINUE
IF( N .LT. 5 ) GO TO 60
40 MP1 = M + 1
DO 50 I = MP1,N,5
STEMP = STEMP + SX(I)*SY(I) + SX(I + 1)*SY(I + 1) +
* SX(I + 2)*SY(I + 2) + SX(I + 3)*SY(I + 3) + SX(I + 4)*SY(I + 4)
50 CONTINUE
60 SDOT = STEMP
RETURN
END
program main
implicit none
end program main
总算成功了，原来是在高级模式里面。 jeydragon 发表于 2014-5-12 22:41
总算成功了，原来是在高级模式里面。
<> 这个工具就可以，普通模式也有的哦
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