通用版1.L - Delta-wave

三角坐标系中点距离计算
本文介绍了一种在特殊三角形坐标系中计算两点间距离的方法,通过数学公式确定了坐标系中任意点的位置,并提供了计算两点间曼哈顿距离的C语言代码。
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
int main()
{
    int a,b,x1,y1,z1,x2,y2,z2,res,n,m;
    while(~scanf("%d%d",&n,&m)){
        //a=sqrt(n);
        a=(int)(sqrt((double)n-1))+1;
       // b=sqrt(m);
        b=(int)(sqrt((double)m-1))+1;
        x1=(a*a-n)/2+1;
        y1=a;
        z1=(n-(a-1)*(a-1)-1)/2+1;


        x2=(b*b-m)/2+1;
        y2=b;
        z2=(m-(b-1)*(b-1)-1)/2+1;
        res=abs(x1-x2)+abs(y1-y2)+abs(z1-z2);
        if(res<0)res=-1*res;
        // printf("%d,%d,%d,%d,%d,%d\n",x1,y1,z1,x2,y2,z2);
        printf("%d\n",res);
    }
    return 0;
}

在三角形中建立一个坐标系,x,y,z轴沿如图所示建立,可以求出每个点的坐标

这样每个点就有了唯一的坐标,比如n==2时,n的坐标是(2,2,1),要确定某一个点的坐标,要计算坐标,先算出n在第几行,也就是y轴坐标,然后可以知道该行第一个数a和最后一个数b,(n-a)/2+1是n的x轴坐标,(b-n)/2+1是z轴坐标

计算出两点坐标后,对应坐标相减后取绝对值,然后加起来,就是两点距离。

! P-1D-UCDR-HOC-2021+Pro1.f90 !------------------------------------------------------------------------------------ ! The progrom for 1-D Unsteady Nonlinear Advection Diffusion Reaction Equation using Thomas method !-------------------------------------------------------------- ! Four-order accurcy in both time and space with full implicit scheme !-------------------------------------------------------------- ! Lin Zhang and Yongbin Ge, Numerical solution of nonlinear advection ! diffusion reaction equation using high-order compact difference method, ! Applied Numerical Mathematics,2021, 166: 127–145. !-------------------------------------------------------------- ! Model equation: ! ut+u*ux=eps*uxx !------------------------------------------------------------------------------------------------------------------------------------- !$debug ! use PORTLIB implicit double precision (a-h,o-z) parameter(it=100000) common/vari/u(it),u1(it),ub(it),u2(it),u3(it),u4(it),fu(it),ue(it),ux3(it),uxx3(it),uxx(it),ux(it),Rx(it),Rxx(it),Rx1(it),Rxx1(it),Rx3(it),Rxx3(it),Rx2(it),Rxx2(it),uxx1(it),ux1(it),uxx2(it),ux2(it) common/const1/N,itfa,eps,Rmin,Rmax common/const2/ni1 character(len=1) endchar !ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc !-----default parameters !ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc ! !------------------default parameters------------------------------------------------ write(*,*)'***************************************************' write(*,*)'Definition:' write(*,*)' N: Number of grid subdomain in space direction' write(*,*)' Nnode: Number of grid points' write(*,*)' h: =1/N, space step-length' write(*,*)' T: Total time for computation to be reached' write(*,*)' dt: Time step-length' write(*,*)' Tstep: =T/dt,total time steps to reach T' write(*,*)' v: Diffusion coefficient' write(*,*)' u: Numerical solution' write(*,*)' errmax: Maximum error on the final time step' write(*,*)' errL2: L2-norm error on the final time step' write(*,*)' errRMS: RMS error on the final time step' write(*,*)' erraver: Average error on the final time step' ! write(*,*)' CPUtime: CPUtime exclude input and output time' write(*,*)'***************************************************' open(5,file='output.dat',status='unknown') write(*,*) ' ' write(*,*)'Please input parameters as follows:' !------------------------------------------------------------------------------------------------------------------------------------- 1000 continue write(*,*) 'N= T= ' read(*,*) N,T !------------------------------------------------------------------------------------------------------------------------------------- write(*,*)'Display the computing process? input "y" to be,or "n" not to:' read(*,*) endchar IF (endchar.GE.'a'.AND.endchar.LE.'z') then endchar = CHAR(ICHAR(endchar) -ICHAR('a') +ICHAR('A')); end if; if(endchar.eq.'Y') then write(*,30) end if !------------------------------------------------------------------------------------------------------------------------------------- CPUtime1=TIMEF() pi=4.d0*datan(1.d0) pii=pi*pi Rmin=0.d0 Rmax=1.d0 h=(Rmax-Rmin)/float(N) tol=1.0e-13 eps=0.001d0 !v dt=0.01 itfas=idnint(T/dt) !------------------------------------------------------------------------------------------------------------------------------------- !----- grid numbers for all levles--------- ! ni1=N+1 !-----initial ---------------- t=0.d0 do 26 i=1,ni1 x=Rmin+(i-1)*h ub(i)=2.d0*eps*pi*dsin(pi*x)/(100.d0+dcos(pi*x)) !!! 26 continue do 70 m=1,itfas !-----assembly coefficients------------------ !*************************To Calculated value of u(i)(u(dt/2,h)) when dt=dt/2************************************ t=m*dt u(1)=0.d0 u(ni1)=0.d0 num0=0 300 num0=num0+1 errux=0.0 erruxx=0.0 do 200 i=1,ni1 Rx(i)=ux(i) Rxx(i)=uxx(i) 200 continue call adi2(ux,ub,uxx,ni1,it) call adi3(uxx,ub,ux,ni1,it) do 201 i=1,ni1 errx=dabs(Rx(i)-ux(i)) errxx=dabs(Rxx(i)-uxx(i)) errux=dmax1(errux,errx) erruxx=dmax1(erruxx,errxx) 201 continue if(errux.gt.tol.and.erruxx.gt.tol) then goto 300 end if do 289 i=1,ni1 u1(i)=ub(i)+(1.d0/2.d0)*dt*(eps*uxx(i)-ub(i)*ux(i)) 289 continue num1=0 400 num1=num1+1 err1ux=0.0 err1uxx=0.0 do 202 i=1,ni1 Rx1(i)=ux1(i) Rxx1(i)=uxx1(i) 202 continue call adi2(ux1,u1,uxx1,ni1,it) call adi3(uxx1,u1,ux1,ni1,it) do 203 i=1,ni1 err1x=dabs(Rx1(i)-ux1(i)) err1xx=dabs(Rxx1(i)-uxx1(i)) err1ux=dmax1(err1ux,err1x) err1uxx=dmax1(err1uxx,err1xx) 203 continue if(err1ux.gt.tol.and.err1uxx.gt.tol) then goto 400 end if do 291 i=1,ni1 u2(i)=u1(i)+1.d0/2.d0*dt*(eps*uxx1(i)-u1(i)*ux1(i)) 291 continue num2=0 500 num2=num2+1 err2ux=0.0 err2uxx=0.0 do 204 i=1,ni1 Rx2(i)=ux2(i) Rxx2(i)=uxx2(i) 204 continue call adi2(ux2,u2,uxx2,ni1,it) call adi3(uxx2,u2,ux2,ni1,it) do 205 i=1,ni1 err2x=dabs(Rx2(i)-ux2(i)) err2xx=dabs(Rxx2(i)-uxx2(i)) err2ux=dmax1(err2ux,err2x) err2uxx=dmax1(err2uxx,err2xx) 205 continue if(err2ux.gt.tol.and.err2uxx.gt.tol) then goto 500 end if do 293 i=1,ni1 u3(i)=2.d0/3.d0*ub(i)+1.d0/3.d0*u2(i)+1.d0/6.d0*dt*(eps*uxx2(i)-u2(i)*ux2(i)) 293 continue num3=0 502 num3=num3+1 err3ux=0.0 err3uxx=0.0 do 402 i=1,ni1 Rx3(i)=ux3(i) Rxx3(i)=uxx3(i) 402 continue call adi2(ux3,u3,uxx3,ni1,it) call adi3(uxx3,u3,ux3,ni1,it) do 206 i=1,ni1 err3x=dabs(Rx3(i)-ux3(i)) err3xx=dabs(Rxx3(i)-uxx3(i)) err3ux=dmax1(err3ux,err3x) err3uxx=dmax1(err3uxx,err3xx) 206 continue if(err3ux.gt.tol.and.err3uxx.gt.tol) then goto 502 end if do 292 i=1,ni1 u4(i)=u3(i)+1.d0/2.d0*dt*(eps*uxx3(i)-u3(i)*ux3(i)) 292 continue do 294 i=2,ni1-1 u(i)=u4(i) 294 continue do 295 i=1,ni1 ub(i)=u(i) 295 continue if(endchar.eq.'Y') then do 61 i=1,ni1 t=m*dt x=Rmin+h*(i-1) ue(i)=2.d0*eps*pi*dexp(-pii*eps*t)*dsin(pi*x)/(100.d0+dexp(-pii*eps*t)*dcos(pi*x)) write(*,122) t,x,u(i),ue(i),dabs(u(i)-ue(i)) 61 continue end if 70 continue CPUtime2=TIMEF() CPUtime=CPUtime2-CPUtime1 if(endchar.eq.'Y') then write(*,30) end if ! !-----Calculate the value of various errors in the final time step------------------- ! errmax=0.d0 errL2=0.d0 RMS=0.d0 erraver=0.d0 do 2000 i=1,ni1 x=Rmin+h*(i-1) t=dt*itfas ue(i)=2.d0*eps*pi*dexp(-pii*eps*t)*dsin(pi*x)/(100.d0+dexp(-pii*eps*t)*dcos(pi*x)) errf=dabs(u(i)-ue(i)) erraver=erraver+errf errmax=dmax1(errmax,errf) errL2=errL2+errf*errf RMS=RMS+errf*errf 2000 continue write(*,*) ue(2),u(2),u(2)-ue(2) errL2=dsqrt(h*errL2) RMS=dsqrt(RMS/(N+1)) erraver=erraver/(N+1) ! !-----keep stata for Tecplot to draw pictures------------ ! open(1,file='fig_u_ue_err.dat',status='unknown') do 2004 i=1,ni1 x=Rmin+(i-1)*h write(1,222) x,u(i),ue(i),dabs(u(i)-ue(i)) 2004 continue close(1) 222 format(3x,f14.8,3(3x,e14.8)) open(2,file='fig_u.dat',status='unknown') write(2,*) 'variable=x u' write(2,*) 'Zone T=grids F=point I=',ni1 do 2005 i=1,ni1 x=Rmin+(i-1)*h write(2,*) x,u(i) 2005 continue close(2) open(3,file='fig_ue.dat',status='unknown') write(3,*) 'variable=x ue' write(3,*) 'Zone T=grids F=point I=',ni1 do 3006 i=1,ni1 x=Rmin+(i-1)*h write(3,*) x,ue(i) 3006 continue close(3) open(4,file='fig_error.dat',status='unknown') write(4,*) 'variable=x error' write(4,*) 'Zone T=grids F=point I=',ni1 do 2007 i=1,ni1 x=Rmin+(i-1)*h write(4,*) x,dabs(u(i)-ue(i)) 2007 continue close(4) !*****************************Print input and default parameters and Print ouput and computed results****************** open(5,file='output.dat',status='old') write(5,*)'****************************************************' write(*,*)'*************Print input and default parameters*****' write(*,*)'N= ',N write(5,*)'N= ',N write(5,*)'Nnode= ',N+1 write(*,*)'Nnode= ',N+1 write(*,*)'h= ',h write(5,*)'h= ',h write(*,*)'eps= ',eps write(5,*)'eps= ',eps write(*,*)'tol= ',tol write(5,*)'tol= ',tol write(*,*)'T= ',T write(5,*)'T= ',T write(*,*)'itfas= ',itfas write(5,*)'itfas= ',itfas write(*,*)'**************Print ouput and computed results*****' write(*,*)'errmax= ',errmax write(5,*)'errmax= ',errmax write(*,*)'errL2= ',errL2 write(5,*)'errL2= ',errL2 write(*,*)'errRMS= ',RMS write(5,*)'errRMS= ',RMS write(*,*)'erraver= ',erraver write(5,*)'erraver= ',erraver write(*,*)'CPUtime= ',CPUtime write(5,*)'CPUtime= ',CPUtime write(*,*)'continued? input y to be,or n to stop:' read(*,*) endchar if (endchar.GE.'a'.AND.endchar.LE.'z') then endchar = CHAR(ICHAR(endchar) -ICHAR('a') +ICHAR('A')); end if; if(endchar.eq.'Y') then goto 1000 else goto 2001 end if 2001 write(*,*)'Please input <0-9> to return!' read(*,*) endchar 30 format (7x,'t',11x,'x',10x,'Numerical',12x,'Exact',14x,'Error') 122 format(3x,f8.5,3x,f8.5,3x,e16.8,3x,e16.8,3x,e16.8) stop end !************************************************************** ! subroutine adi1(uxx,ub,ni,it) ! implicit double precision(a-h,o-z) ! dimension ub(it),uxx(it) ! dimension a(100000),b(100000),c(100000),d(100000) ! pi=4.d0*datan(1.d0) ! h=1.d0/float(ni) ! h2=h*h ! a(1)=1.d0 ! b(1)=51.d0/52.d0 ! c(1)=0.d0 ! d(1)=12293.d0*ub(1)/(2340.d0*h2)-18903.d0*ub(2)/(1040.d0*h2)+2891.d0*ub(3)/(104.d0*h2)-23941.d0*ub(4)/(936.d0*h2)+387.d0*ub(5)/(26.d0*h2)-5063.d0*ub(6)/(1040.d0*h2)+494.d0*ub(7)/(720.d0*h2) ! do 2023 i=2,ni-1 ! a(i)=5.d0/6.d0 ! b(i)=1.d0/12.d0 ! c(i)=1.d0/12.d0 ! d(i)=(-2.d0*ub(i)+ub(i+1)+ub(i-1))/h2 !2023 continue ! a(ni)=1.d0 ! b(ni)=0.d0 ! c(ni)=-51.d0/52.d0 ! d(ni)=17599.d0*ub(ni)/(4680.d0*h2)-17237.d0*ub(ni-1)/(1040.d0*h2)+795.d0*ub(ni-2)/(26.d0*h2)-28735.d0*ub(ni-3)/(936.d0*h2)+1871.d0*ub(ni-4)/(104.d0*h2)-6117.d0*ub(ni-5)/(1040.d0*h2)+596.d0*ub(ni-6)/(720.d0*h2) ! call trid(1,ni,a,b,c,d) ! do 2024 i=1,ni ! uxx(i)=d(i) !2024 continue ! return ! end subroutine adi2(ux,ub,uxx,ni,it) implicit double precision(a-h,o-z) dimension ux(it),ub(it),uxx(it) dimension a(100000),b(100000),c(100000),d(100000),f(100000),e(100000) common/const1/N,itfas,eps,Rmin,Rmax h=(Rmax-Rmin)/float(ni-1) d(1)=(1.d0/h)*(-2218.d0*ub(1)/735.d0+72001.d0*ub(2)/12600.d0-95.d0*ub(3)/28.d0+1193.d0*ub(4)/126.d0-919.d0*ub(5)/126.d0+2981.d0*ub(6)/840.d0-6263.d0*ub(7)/6300.d0+6.d0*ub(8)/49.d0) d(ni+1)=(1.d0/h)*(134.d0*ub(ni+1)/245.d0-25153.d0*ub(ni)/4200.d0+877.d0*ub(ni-1)/140.d0-50.d0*ub(ni-2)/20.d0-161.d0*ub(ni-3)/126.d0+571.d0*ub(ni-4)/280.d0-2011.d0*ub(ni-5)/2100.d0-727.d0*ub(ni-6)/4410.d0) d(ni)=(1.d0/h)*(-5803.d0*ub(ni+1)/2520.d0-226.d0*ub(ni)/45.d0+3521.d0*ub(ni-1)/720.d0-31.d0*ub(ni-2)/18.d0-121.d0*ub(ni-3)/72.d0+84.d0*ub(ni-4)/45.d0-607.d0*ub(ni-5)/720.d0-91.d0*ub(ni-6)/630.d0) d(2)=(1.d0/h)*(-6541.d0*0.d0+211.d0*ub(2)/30.d0-1505.d0*ub(3)/144.d0+104.d0*ub(4)/9.d0-209.d0*ub(5)/24.d0-377.d0*ub(6)/90.d0-839.d0*ub(7)/720.d0+1.d0*ub(8)/7.d0) a(1)=1.d0 b(1)=187.d0/210.d0 c(1)=0.d0 f(1)=0.d0 e(1)=0.d0 a(2)=0.d0 b(2)=-1.d0/12.d0 c(2)=1.d0 f(2)=0.d0 e(2)=0.d0 do 20001 i=3,ni-1 a(i)=1.d0 b(i)=1.d0/3.d0 c(i)=1.d0/3.d0 f(i)=0.d0 e(i)=0.d0 d(i)=1.d0*ub(i+2)/(36.d0*h)-1.d0*ub(i-2)/(36.d0*h)+14.d0*ub(i+1)/(18.d0*h)-14.d0*ub(i-1)/(18.d0*h) 20001 continue a(ni+1)=1.d0 c(ni+1)=-187.d0/210.d0 b(ni+1)=0.d0 f(ni+1)=0.d0 e(ni+1)=0.d0 a(ni)=0.d0 c(ni)=1.d0/12.d0 b(ni)=1.d0 f(ni)=0.d0 e(ni)=0.d0 call pentad(1,ni,e,f,a,b,c,d) do 20004 i=1,ni ux(i)=d(i) 20004 continue return end !--------------------------------------------------------------------------------------------------------------------- subroutine adi3(uxx,ub,ux,ni,it) implicit double precision(a-h,o-z) dimension ux(it),ub(it),uxx(it) dimension a(100000),b(100000),c(100000),d(100000),f(100000),e(100000) common/const1/N,itfas,eps,Rmin,Rmax h=(Rmax-Rmin)/float(ni-1) h2=h*h d(1)=(1.d0/h2)*(64447.d0*ub(1)/11088.d0-13401973.d0*ub(2)/498960.d0+479153.d0*ub(3)/7920.d0-1359929.d0*ub(4)/15840.d0+1176541.d0*ub(5)/14256.d0-211403.d0*ub(6)/3960.d0+176807.d0*ub(7)/7920.d0-495793.d0*ub(8)/90720.d0+751.d0*ub(9)/1260.d0) d(ni+1)=(1.d0/h2)*(2583661.d0*ub(ni+1)/443520.d0-18855749.d0*ub(ni)/686070.d0+328961.d0*ub(ni-1)/5280.d0-1416017.d0*ub(ni-2)/15840.d0+4945481.d0*ub(ni-3)/57024.d0-149477.d0*ub(ni-4)/2640.d0+378583.d0*ub(ni-5)/15840.d0-5894719.d0*ub(ni-6)/997920.d0+96167.d0*ub(ni-7)/147840.d0) d(2)=(1.d0/h2)*(140531.d0*ub(1)/23688.d0-18529.d0*ub(2)/658.d0+532891.d0*ub(3)/8460.d0-125317.d0*ub(4)/1410.d0+144553.d0*ub(5)/1692.d0-235567.d0*ub(6)/4230.d0+349969.d0*ub(7)/8460.d0-171791.d0*ub(8)/29610.d0+1609.d0*ub(9)/2520.d0) d(ni)=(1.d0/h2)*(645671.d0*ub(ni+1)/108570.d0-8750519.d0*ub(ni)/325710.d0+5683279.d0*ub(ni-1)/93060.d0-827195.d0*ub(ni-2)/9306.d0+153419.d0*ub(ni-3)/282.d0-273665.d0*ub(ni-4)/9306.d0+2232799.d0*ub(ni-5)/93060.d0-1931399.d0*ub(ni-6)/325710.d0+905.d0*ub(ni-7)/1386.d0) a(1)=1.d0 b(1)=41.d0/792.d0 c(1)=0.d0 f(1)=0.d0 e(1)=0.d0 a(2)=0.d0 b(2)=-26.d0/47.d0 c(2)=1.d0 f(2)=0.d0 e(2)=0.d0 do 20001 i=3,ni-1 a(i)=1.d0 b(i)=2.d0/11.d0 c(i)=2.d0/11.d0 f(i)=0.d0 e(i)=0.d0 d(i)=3.d0*(ub(i+2)-2.d0*ub(i)+ub(i-2))/(44.d0*h2)+12.d0*(ub(i+1)-2*ub(i)+ub(i-1))/(11.d0*h2) 20001 continue a(ni+1)=1.d0 c(ni+1)=-41.d0/729.d0 b(ni+1)=0.d0 f(ni+1)=0.d0 e(ni+1)=0.d0 a(ni)=0.d0 c(ni)=26.d0/47.d0 b(ni)=1.d0 f(ni)=0.d0 e(ni)=0.d0 call pentad(1,ni,e,f,a,b,c,d) do 20004 i=1,ni uxx(i)=d(i) 20004 continue return end !----------------------------------------------------------------- subroutine pentad(n0,n,a,b,c,d) parameter(iu=100000) implicit real*8(a-h,o-z) dimension a(iu),b(iu),c(iu),d(iu),f(iu),e(iu) dimension alpha(iu), beta(iu), gamma(iu), rho(iu), y(iu) !ccccccccccccccccccccccccccccccccccccccccccccccc ! e = 下二对角 (i-2) ! f = 下主对角 (i-1) ! a = 主对角 (i) ! b = 上主对角 (i+1) ! c = 上二对角 (i+2) ! d = 右端向量 !cccccccccccccccccccccccccccccccccccccccccccccccccc if(n0 .ge. n) return ! 前向消去 do k = n0, n if(k .eq. n0) then ! 首行 alpha(k) = a(k) beta(k) = b(k) gamma(k) = c(k) rho(k) = d(k) else if(k .eq. n0+1) then ! 第二行 r = f(k) / alpha(k-1) alpha(k) = a(k) - r * beta(k-1) beta(k) = b(k) gamma(k) = c(k) rho(k) = d(k) - r * rho(k-1) else ! 一般行处理 r1 = f(k) / alpha(k-1) r2 = e(k) / alpha(k-2) alpha(k) = a(k) - r1 * beta(k-1) - r2 * gamma(k-2) beta(k) = b(k) - r1 * gamma(k-1) gamma(k) = c(k) rho(k) = d(k) - r1 * rho(k-1) - r2 * rho(k-2) end if end do ! 回代 y(n) = rho(n) / alpha(n) y(n-1) = (rho(n-1) - beta(n-1)*y(n)) / alpha(n-1) do k = n-2, n0, -1 y(k) = (rho(k) - beta(k)*y(k+1) - gamma(k)*y(k+2)) / alpha(k) end do ! 将解复制回d数组 do k = n0, n d(k) = y(k) end do return end 将上面这个程序转换为MATLAB程序
08-26
%% 船舶航线优化主程序 clear; clc; close all; %% 参数设置 % 船舶参数(Suezmax型) ship.L_pp = 228.9; % 垂线间长(m) ship.B = 32.26; % 船宽(m) ship.T = 14.471; % 吃水(m) ship.Cb = 0.803; % 方形系数 ship.D = 8.5; % 螺旋桨直径(m) ship.sfoc = 104; % 燃油消耗率(g/kWh) ship.V = 12; % 设计航速(kn) ship.V_max = 16; % 最大航速(kn) ship.V_min = 10; % 最小航速(kn) ship.P_max = 32000; % 最大主机功率(kW) ship.rho_sea = 1026; % 海水密度(kg/m^3) ship.rho_air = 1.225; % 空气密度(kg/m^3) ship.A_T = 1918; % 水面上的最大横向面积(m^2) % 算法参数 population_size = 50; % 种群大小 max_generations = 100; % 最大迭代次数 pc = 0.8; % 交叉概率 pm = 0.1; % 变异概率 T0 = 100; % 初始温度 alpha = 0.95; % 退火系数 start_time = datetime(2025,2,12,18,0,0); % 航线参数 start_port = [35.2391, 119.7921]; % 日照港 end_port = [-28.5202, 114.3272]; % 杰拉尔顿港 max_segments = 30; % 最大航段数 lat_range = [-30, 55]; lon_range = [110, 160]; %% 气象数据加载与预处理 % 读取NetCDF文件 op_ncfile = 'C:\Users\dell\Downloads\41c65edbd5a653750e1d93b2a34fe6a8.nc'; wv_ncfile = 'C:\Users\dell\Downloads\abbf6737917f8802584d2b89ac9cf3ca.nc'; % 获取维度信息 op_lon = ncread(op_ncfile, 'longitude'); % 风场文件经度向量 op_lat = ncread(op_ncfile, 'latitude'); % 风场文件纬度向量 time = ncread(op_ncfile, 'valid_time'); % 时间(小时数,从1900-01-01起) wv_lon = ncread(wv_ncfile, 'longitude'); % 浪场文件经度向量 wv_lat = ncread(wv_ncfile, 'latitude'); % 浪场文件纬度向量 % 正确时间转换(基于NC文件元数据) time_ref = datetime(1970,1,1, 'TimeZone', 'UTC'); % 明确指定UTC时区 date_vec = time_ref + seconds(time); % 保持UTC时区 % 提取2025年1-2月数据 start_date = datetime(2025,2,12, 'TimeZone', 'UTC'); end_date = datetime(2025,2,27,23,59,59, 'TimeZone', 'UTC'); time_mask = (date_vec >= start_date) & (date_vec <= end_date); time_idx = find(time_mask); % 读取气象变量(优化维度处理) % 注意:NetCDF维度顺序通常为(longitude, latitude, time) u10 = permute(ncread(op_ncfile, 'u10', [1,1,1], [Inf, Inf, Inf]), [2,1,3]); % 调整为(lat,lon,time) v10 = permute(ncread(op_ncfile, 'v10', [1,1,1], [Inf, Inf, Inf]), [2,1,3]); swh = permute(ncread(wv_ncfile, 'swh', [1,1,1], [Inf, Inf, Inf]), [2,1,3]); cdww = permute(ncread(wv_ncfile, 'cdww', [1,1,1], [Inf, Inf, Inf]), [2,1,3]); % 创建纬度-经度网格 [LonGrid, LatGrid] = meshgrid(op_lon, op_lat); % 构建气象数据结构体 weather_data = struct(... 'op_lon', op_lon, ... % 经度向量 [nLon×1] 'op_lat', op_lat, ... % 纬度向量 [nLat×1] 'wv_lon', wv_lon, ... % 经度向量 [nLon×1] 'wv_lat', wv_lat, ... % 纬度向量 [nLat×1] 'LonGrid', LonGrid, ... % 经度网格 [nLat×nLon] 'LatGrid', LatGrid, ... % 纬度网格 [nLat×nLon] 'time', date_vec(time_idx), ... % 时间向量 [nTime×1] 'u10', u10(:,:,time_idx), ... % 风速U分量 [nLat×nLon×nTime] 'v10', v10(:,:,time_idx), ... % 风速V分量 [nLat×nLon×nTime] 'swh', swh(:,:,time_idx), ... % 有效波高 [nLat×nLon×nTime] 'cdww', cdww(:,:,time_idx)); % 波浪阻力系数 [nLat×nLon×nTime] %% 初始化种群 population = initialize_population(population_size, start_port, end_port, max_segments, lat_range, lon_range); %% 混合遗传算法主循环 best_fitness = inf; best_route = []; best_fuel = Inf; best_time = Inf; fitness_history = zeros(max_generations, 1); temperature = T0; for gen = 1:max_generations % 计算适应度 fitness = zeros(population_size, 1); fuel_consumptions = zeros(population_size, 1); total_times = zeros(population_size, 1); for i = 1:population_size [fitness(i), fuel_consumptions(i), total_times(i)] = calculate_fitness(population{i}, ship, weather_data, start_time); end % 记录最佳个体 [min_fitness, idx] = min(fitness); current_fuel = fuel_consumptions(idx); current_time = total_times(idx); if min_fitness < best_fitness best_fitness = min_fitness; best_route = population{idx}; best_fuel = current_fuel; best_time = current_time; end fitness_history(gen) = best_fitness; % 选择操作 selected = tournament_selection(population, fitness, population_size/2); % 交叉操作 offspring = hybrid_crossover(selected, pc, start_port, end_port); % 变异操作 offspring = mutation(offspring, pm, lat_range, lon_range); % 合并种群 combined_population = [population; offspring]; offspring_fitness = zeros(length(offspring), 1); for i = 1:length(offspring) offspring_fitness(i) = calculate_fitness(offspring{i}, ship, weather_data, start_time); end combined_fitness = [fitness; offspring_fitness]; % 模拟退火选择 population = simulated_annealing_selection(combined_population, combined_fitness, population_size, temperature); % 更新温度 temperature = alpha * temperature; % 显示进度 fprintf('Generation %d: Fitness=%.2f, Fuel=%.2fkg, Time=%.2fh (Current) | Best: Fitness=%.2f, Fuel=%.2fkg, Time=%.2fh\n',... gen, min_fitness, current_fuel, current_time, best_fitness, best_fuel, best_time); % 更新温度 temperature = alpha * temperature; end %% 结果可视化 plot_route(best_route, start_port, end_port, weather_data); figure; plot(1:max_generations, fitness_history); xlabel('Generation'); ylabel('Best Fitness'); title('Convergence Curve'); %% 初始化种群函数 function population = initialize_population(pop_size, start_port, end_port, max_segments, lat_range, lon_range) population = cell(pop_size, 1); % 初始化为列向量 for i = 1:pop_size num_segments = randi([2, max_segments]); route = zeros(num_segments+1, 2); route(1,:) = start_port; route(end,:) = end_port; % 生成中间点 for j = 2:num_segments while true new_lat = lat_range(1) + (lat_range(2)-lat_range(1))*rand(); new_lon = lon_range(1) + (lon_range(2)-lon_range(1))*rand(); if ~isequal([new_lat, new_lon], start_port) && ~isequal([new_lat, new_lon], end_port) route(j,:) = [new_lat, new_lon]; break; end end end population{i} = route; % 按经度排序中间点,确保东向航行 route(2:end-1,:) = sortrows(route(2:end-1,:), 2); end end %% 适应度计算函数 function [fitness, total_fuel, total_time] = calculate_fitness(route, ship, weather_data, start_time) % 检查路径有效性 if isempty(route) || size(route,1) < 2 || any(isnan(route(:))) fitness = Inf; return; end total_distance = 0; total_time = 0; total_fuel = 0; % 计算每个航段的参数 for i = 1:size(route,1)-1 % 计算航段距离 (大圆距离) [dist, ~] = lldistkm(route(i,:), route(i+1,:)); if isnan(dist) % 如果距离计算失败 fitness = Inf; return; end total_distance = total_distance + dist; % 获取航段中点位置和时间的气象数据 mid_point = [(route(i,1)+route(i+1,1))/2, (route(i,2)+route(i+1,2))/2]; segment_time = start_time + seconds(total_time*3600); segment_time.TimeZone = 'UTC'; % 强制设置时区 % 双线性插值获取气象数据 [u10, v10, swh, cdww] = get_weather_data(mid_point, segment_time, weather_data); % 计算航向角 (0-360度,正北为0) heading = calculate_heading(route(i,:), route(i+1,:)); % 计算相对风向和波向 wind_dir = atan2d(v10, u10); % 风向(度) wind_speed = sqrt(u10^2 + v10^2); rel_wind_angle = wrapTo360(wind_dir - heading); % 计算船舶实际速度 (考虑风浪影响) [V_actual, fuel_consumption] = calculate_ship_performance(ship, wind_speed, rel_wind_angle, swh, cdww); % 计算航段时间和燃油消耗 segment_time_hours = dist / (V_actual * 1.852); % 海里转公里 total_time = total_time + segment_time_hours; total_fuel = total_fuel + fuel_consumption * segment_time_hours; % 添加航速有效性检查 if V_actual <= 0 || isnan(V_actual) fitness = Inf; return; end % 添加时间计算保护 segment_time_hours = max(0, dist / (V_actual * 1.852)); end % 适应度函数 (加权和) fuel_weight = 0.6; % 燃油消耗权重 fitness = fuel_weight * total_fuel + (1-fuel_weight) * total_time; fprintf('Segment %d: V=%.2fkn, Fuel=%.2fkg/h, Time=%.2fh\n',... i, V_actual, fuel_consumption, segment_time); end %% 气象数据获取函数 function [u10, v10, swh, cdww] = get_weather_data(point, time, weather_data) % 双线性插值获取气象数据 % 风场数据 (0.25°分辨率) [u10, v10] = bilinear_interp(point(1), point(2), time, ... weather_data.op_lat, weather_data.op_lon, weather_data.time, ... weather_data.u10, weather_data.v10); % 浪场数据 (0.5°分辨率) [swh, cdww] = bilinear_interp(point(1), point(2), time, ... weather_data.wv_lat, weather_data.wv_lon, weather_data.time, ... weather_data.swh, weather_data.cdww); end %% 双线性插值法函数 function [varargout] = bilinear_interp(lat, lon, time, lat_grid, lon_grid, time_grid, varargin) % 通用双线性插值函数 varargout = cell(1, nargin-6); % 找到最近的4个空间点和2个时间点 [lat_idx, lon_idx, time_idx, weights] = find_nearest_points(lat, lon, time, lat_grid, lon_grid, time_grid); for i = 1:length(varargin) var = varargin{i}; % 空间插值 spatial_interp = (1-weights(1))*(1-weights(2)) * var(lat_idx(1), lon_idx(1), time_idx(1)) + ... (1-weights(1))*weights(2) * var(lat_idx(1), lon_idx(2), time_idx(1)) + ... weights(1)*(1-weights(2)) * var(lat_idx(2), lon_idx(1), time_idx(1)) + ... weights(1)*weights(2) * var(lat_idx(2), lon_idx(2), time_idx(1)); % 时间插值 if length(time_idx) > 1 spatial_interp2 = (1-weights(1))*(1-weights(2)) * var(lat_idx(1), lon_idx(1), time_idx(2)) + ... (1-weights(1))*weights(2) * var(lat_idx(1), lon_idx(2), time_idx(2)) + ... weights(1)*(1-weights(2)) * var(lat_idx(2), lon_idx(1), time_idx(2)) + ... weights(1)*weights(2) * var(lat_idx(2), lon_idx(2), time_idx(2)); varargout{i} = (1-weights(3)) * spatial_interp + weights(3) * spatial_interp2; else varargout{i} = spatial_interp; end end end %% 最近的网格点寻找函数 function [lat_idx, lon_idx, time_idx, weights] = find_nearest_points(lat, lon, time, lat_grid, lon_grid, time_grid) % 找到最近的网格点和插值权重 % 纬度 [~, lat_idx(1)] = min(abs(lat_grid - lat)); if lat_grid(lat_idx(1)) < lat lat_idx(2) = min(lat_idx(1)+1, length(lat_grid)); else lat_idx(2) = max(lat_idx(1)-1, 1); end weights(1) = (lat - lat_grid(lat_idx(1))) / (lat_grid(lat_idx(2)) - lat_grid(lat_idx(1))); % 经度 [~, lon_idx(1)] = min(abs(lon_grid - lon)); if lon_grid(lon_idx(1)) < lon lon_idx(2) = min(lon_idx(1)+1, length(lon_grid)); else lon_idx(2) = max(lon_idx(1)-1, 1); end weights(2) = (lon - lon_grid(lon_idx(1))) / (lon_grid(lon_idx(2)) - lon_grid(lon_idx(1))); % 时间 time_diff = abs(time_grid - time); [~, time_idx(1)] = min(time_diff); if time_grid(time_idx(1)) < time time_idx(2) = min(time_idx(1)+1, length(time_grid)); else time_idx(2) = max(time_idx(1)-1, 1); end if length(time_idx) > 1 weights(3) = seconds(time - time_grid(time_idx(1))) / seconds(time_grid(time_idx(2)) - time_grid(time_idx(1))); end end %% 角度计算函数 function heading = calculate_heading(point1, point2) % 计算两点之间的航向角 (0-360度,正北为0) lat1 = deg2rad(point1(1)); lon1 = deg2rad(point1(2)); lat2 = deg2rad(point2(1)); lon2 = deg2rad(point2(2)); dLon = lon2 - lon1; y = sin(dLon) * cos(lat2); x = cos(lat1) * sin(lat2) - sin(lat1) * cos(lat2) * cos(dLon); heading = wrapTo360(rad2deg(atan2(y, x))); end %% 船舶油耗及速度计算函数 function [V_actual, fuel_consumption] = calculate_ship_performance(ship, wind_speed, rel_wind_angle, swh, cdww) % 计算考虑风浪影响的船舶实际速度和燃油消耗 % 计算风阻力 R_wind = 0.5 * ship.rho_air * wind_speed^2 * ship.A_T * abs(cosd(rel_wind_angle)); % 计算波浪阻力 (简化模型) R_wave = 0.5 * ship.rho_sea * (swh/2)^2 * ship.B * ship.T * (1 + 4 * (ship.T/ship.L_pp)^2); % 计算静水阻力 R_water = 0.5 * ship.rho_sea * ship.L_pp * ship.B * cdww; V_knots = ship.V; % 初始使用设计航速 V_ms = V_knots * 0.5144; % 节转m/s % 总静水阻力 R_total = R_wind + R_wave + R_water; % 考虑风浪影响的速度损失 (经验公式) speed_loss = 0.05 * (swh/4) + 0.02 * wind_speed/10; V_actual = max(ship.V_min, ship.V * (1 - speed_loss)); % 计算燃油消耗 (简化模型) V_actual_ms = V_actual * 0.5144; % 节转m/s power_required = R_total * V_actual_ms / 0.6; % 推进效率0.6 fuel_consumption = power_required * ship.sfoc / 1e6; % kg/h end %% 选择算子 function selected = tournament_selection(population, fitness, num_selected) % 锦标赛选择 selected = cell(num_selected, 1); for i = 1:num_selected % 随机选择2个个体进行竞争 candidates = randperm(length(population), 2); if fitness(candidates(1)) < fitness(candidates(2)) selected{i} = population{candidates(1)}; else selected{i} = population{candidates(2)}; end end end %% 交叉算子 function offspring = hybrid_crossover(parents, pc, start_port, end_port) offspring = cell(length(parents), 1); % 确保子代数量与父代相同 i = 1; while i <= length(parents) if i+1 > length(parents) % 处理奇数情况:最后一个父代直接复制 offspring{i} = parents{i}; break; end if rand() < pc parent1 = parents{i}; parent2 = parents{i+1}; % 检查父代路径有效性 if size(parent1,1) < 3 || size(parent2,1) < 3 offspring{i} = parent1; offspring{i+1} = parent2; i = i + 2; continue; end min_len = min(size(parent1,1), size(parent2,1)); if min_len <= 2 offspring{i} = parent1; offspring{i+1} = parent2; i = i + 2; continue; end % 随机交叉点 crossover_point = randi([2, min_len-1]); % 生成子代 child1 = [parent1(1:crossover_point,:); parent2(crossover_point+1:end,:)]; child2 = [parent2(1:crossover_point,:); parent1(crossover_point+1:end,:)]; % 确保子代有效性 child1(1,:) = start_port; child1(end,:) = end_port; child2(1,:) = start_port; child2(end,:) = end_port; offspring{i} = child1; offspring{i+1} = child2; else % 不交叉时直接复制父代 offspring{i} = parents{i}; offspring{i+1} = parents{i+1}; end i = i + 2; % 移动到下一对父代 end end %% 变异算子 function mutated_pop = mutation(population, pm, lat_range, lon_range) mutated_pop = cell(size(population)); for i = 1:length(population) if rand() < pm route = population{i}; if size(route,1) <= 2 mutated_pop{i} = route; continue; end idx = randi([2, size(route,1)-1]); % 随机选择中间点 new_lat = lat_range(1) + (lat_range(2)-lat_range(1))*rand(); new_lon = lon_range(1) + (lon_range(2)-lon_range(1))*rand(); route(idx,:) = [new_lat, new_lon]; mutated_pop{i} = route; else mutated_pop{i} = population{i}; end end end %% 模拟退火 function new_population = simulated_annealing_selection(population, fitness, pop_size, temperature) % 模拟退火选择 [~, sorted_idx] = sort(fitness); new_population = cell(pop_size, 1); % 保留最优个体 new_population{1} = population{sorted_idx(1)}; % 对其他个体进行退火选择 for i = 2:pop_size % 随机选择两个个体 candidates = randperm(length(population), 2); delta = fitness(candidates(2)) - fitness(candidates(1)); % 接受概率 if delta < 0 new_population{i} = population{candidates(2)}; else p = exp(-delta / temperature); if rand() < p new_population{i} = population{candidates(2)}; else new_population{i} = population{candidates(1)}; end end end end %% 绘图函数 function plot_route(route, start_port, end_port, weather_data) % 绘制优化后的航线 figure; % 绘制地图背景 worldmap([-40 60], [100 170]); load coastlines; plotm(coastlat, coastlon); % 绘制航线 plotm(route(:,1), route(:,2), 'r-o', 'LineWidth', 2); plotm(start_port(1), start_port(2), 'go', 'MarkerSize', 10, 'MarkerFaceColor', 'g'); plotm(end_port(1), end_port(2), 'bo', 'MarkerSize', 10, 'MarkerFaceColor', 'b'); % 添加标题和图例 title('Optimized Ship Route from Dalian to Gladstone'); legend('Route', 'Dalian', 'Gladstone', 'Location', 'best'); % 添加气象数据示例 (可选) hold on; [LON, LAT] = meshgrid(weather_data.op_lon, weather_data.op_lat); quiverm(LAT(1:5:end,1:5:end), LON(1:5:end,1:5:end), ... weather_data.u10(1:5:end,1:5:end,1), weather_data.v10(1:5:end,1:5:end,1), 'k'); hold off; end %% 距离及角度计算函数 function [km, arc] = lldistkm(latlon1, latlon2) % 计算两点之间的大圆距离 lat1 = latlon1(1); lon1 = latlon1(2); lat2 = latlon2(1); lon2 = latlon2(2); R = 6371; % 地球半径(km) lat1 = deg2rad(lat1); lon1 = deg2rad(lon1); lat2 = deg2rad(lat2); lon2 = deg2rad(lon2); delta_lat = lat2 - lat1; delta_lon = lon2 - lon1; a = sin(delta_lat/2)^2 + cos(lat1) * cos(lat2) * sin(delta_lon/2)^2; c = 2 * atan2(sqrt(a), sqrt(1-a)); km = R * c; arc = rad2deg(c); end 那你把这个代码修改一下发给我
05-28
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