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447 lines
14 KiB
C
447 lines
14 KiB
C
#include "math.h"
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/*
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* DISUFQ Is an internal function to spec2nlsdat
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*
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* CALL: disufq(rvec,ivec,rA,iA, w,kw,h,g,nmin,nmax,m,n)
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*
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* rvec, ivec = real and imaginary parts of the resultant (size m X n).
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* rA, iA = real and imaginary parts of the amplitudes (size m X n).
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* w = vector with angular frequencies (w>=0)
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* kw = vector with wavenumbers (kw>=0)
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* h = water depth (h >=0)
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* g = constant acceleration of gravity
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* nmin = minimum index where rA(:,nmin) and iA(:,nmin) is
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* greater than zero.
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* nmax = maximum index where rA(:,nmax) and iA(:,nmax) is
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* greater than zero.
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* m = size(rA,1),size(iA,1)
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* n = size(rA,2),size(iA,2), or size(rvec,2),size(ivec,2)
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*
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* DISUFQ returns the summation of difference frequency and sum
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* frequency effects in the vector vec = rvec +sqrt(-1)*ivec.
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* The 2'nd order contribution to the Stokes wave is then calculated by
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* a simple 1D Fourier transform, real(FFT(vec)).
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*
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* Install gfortran and run the following to build the module:
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* f2py diffsumfunq.pyf disufq1.c -c --fcompiler=gnu95 --compiler=mingw32 -lmsvcr71
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*
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* by Per Andreas Brodtkorb 15.08.2001
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* revised pab 14.03.2002, 01.05.2002 22.07.2002, oct 2008
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*/
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void disufq(double *rvec, double *ivec,
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double *rA, double *iA,
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double *w, double *kw,
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double h, double g,
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int nmin, int nmax,
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int m, int n)
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{
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double Epij, Edij;
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double tmp1, tmp2, tmp3, tmp4, kfact;
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double w1, w2, kw1, kw2, Cg;
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double rrA, iiA, riA, irA;
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int i,jy,ix,iz1,iv1,ixi,jyi;
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//int iz2, iv2;
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//Initialize rvec and ivec to zero
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for (ix=0;ix<n*m;ix++) {
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rvec[ix] = 0.0;
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ivec[ix] = 0.0;
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}
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// kfact is set to 2 in order to exploit the symmetry.
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// If you set kfact to 1, you must uncomment all statements
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// including the expressions: rvec[iz2], rvec[iv2], ivec[iz2] and ivec[iv2].
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kfact = 2.0;
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if (h>10000){ /* deep water /Inifinite water depth */
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for (ix = nmin-1;ix<nmax;ix++) {
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ixi = ix*m;
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iz1 = 2*ixi;
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//iz2 = n*m-ixi;
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kw1 = kw[ix];
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Epij = kw1;
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for (i=0;i<m;i++,ixi++,iz1++) {
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rrA = rA[ixi]*rA[ixi]; ///
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iiA = iA[ixi]*iA[ixi]; ///
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riA = rA[ixi]*iA[ixi]; ///
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/// Sum frequency effects along the diagonal
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tmp1 = kfact*(rrA-iiA)*Epij;
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tmp2 = kfact*2.0*riA*Epij;
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rvec[iz1] += tmp1;
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ivec[iz1] += tmp2;
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//rvec[iz2] += tmp1;
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//ivec[iz2] -= tmp2;
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//iz2++;
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/// Difference frequency effects are zero along the diagonal
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/// and are thus not contributing to the mean.
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}
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for (jy = ix+1;jy<nmax;jy++){
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kw2 = kw[jy];
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Epij = 0.5*(kw2 + kw1);
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Edij = -0.5*(kw2 - kw1);
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//printf("Edij = %f Epij = %f \n", Edij,Epij);
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ixi = ix*m;
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jyi = jy*m;
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iz1 = ixi+jyi;
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iv1 = jyi-ixi;
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//iz2 = (n*m-iz1);
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//iv2 = (n*m-iv1);
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for (i = 0;i<m;i++,ixi++,jyi++,iz1++,iv1++) {
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rrA = rA[ixi]*rA[jyi]; ///rrA = rA[i][ix]*rA[i][jy];
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iiA = iA[ixi]*iA[jyi]; ///iiA = iA[i][ix]*iA[i][jy];
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riA = rA[ixi]*iA[jyi]; ///riA = rA[i][ix]*iA[i][jy];
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irA = iA[ixi]*rA[jyi]; ///irA = iA[i][ix]*rA[i][jy];
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/* Sum frequency effects */
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tmp1 = kfact*2.0*(rrA-iiA)*Epij;
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tmp2 = kfact*2.0*(riA+irA)*Epij;
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rvec[iz1] += tmp1;///rvec[i][ix+jy] += tmp1;
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ivec[iz1] += tmp2;///ivec[i][ix+jy] += tmp2;
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//rvec[iz2] += tmp1;///rvec[i][n*m-(ix+jy)] += tmp1;
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//ivec[iz2] -= tmp2;///ivec[i][n*m-(ix+jy)] -= tmp2;
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// iz2++;
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/* Difference frequency effects */
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tmp1 = kfact*2.0*(rrA+iiA)*Edij;
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tmp2 = kfact*2.0*(riA-irA)*Edij;
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rvec[iv1] += tmp1;///rvec[i][jy-ix] += tmp1;
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ivec[iv1] += tmp2;///ivec[i][jy-ix] += tmp2;
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//rvec[iv2] += tmp1;///rvec[i][n*m-(jy-ix)] += tmp1;
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//ivec[iv2] -= tmp2;///ivec[i][n*m-(jy-ix)] -= tmp2;
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//iv2++;
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}
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}
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}
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}
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else{ /* Finite water depth */
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for (ix = nmin-1;ix<nmax;ix++) {
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kw1 = kw[ix];
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w1 = w[ix];
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tmp1 = tanh(kw1*h);
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/// Cg, wave group velocity
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Cg = 0.5*g*(tmp1 + kw1*h*(1.0- tmp1*tmp1))/w1; /// OK
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tmp1 = 0.5*g*(kw1/w1)*(kw1/w1);
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tmp2 = 0.5*w1*w1/g;
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tmp3 = g*kw1/(w1*Cg);
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if (kw1*h<300.0){
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tmp4 = kw1/sinh(2.0*kw1*h);
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}
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else{ // To ensure sinh does not overflow.
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tmp4 = 0.0;
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}
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// Difference frequency effects finite water depth
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Edij = (tmp1-tmp2+tmp3)/(1.0-g*h/(Cg*Cg))-tmp4; /// OK
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// Sum frequency effects finite water depth
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Epij = (3.0*(tmp1-tmp2)/(1.0-tmp1/kw1*tanh(2.0*kw1*h))+3.0*tmp2-tmp1); /// OK
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//printf("Edij = %f Epij = %f \n", Edij,Epij);
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ixi = ix*m;
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iz1 = 2*ixi;
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//iz2 = n*m-ixi;
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for (i=0;i<m;i++,ixi++,iz1++) {
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rrA = rA[ixi]*rA[ixi]; ///
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iiA = iA[ixi]*iA[ixi]; ///
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riA = rA[ixi]*iA[ixi]; ///
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/// Sum frequency effects along the diagonal
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rvec[iz1] += kfact*(rrA-iiA)*Epij;
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ivec[iz1] += kfact*2.0*riA*Epij;
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//rvec[iz2] += kfact*(rrA-iiA)*Epij;
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//ivec[iz2] -= kfact*2.0*riA*Epij;
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//iz2++;
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/// Difference frequency effects along the diagonal
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/// are only contributing to the mean
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rvec[i] += 2.0*(rrA+iiA)*Edij;
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}
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for (jy = ix+1;jy<nmax;jy++) {
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// w1 = w[ix];
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// kw1 = kw[ix];
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w2 = w[jy];
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kw2 = kw[jy];
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tmp1 = g*(kw1/w1)*(kw2/w2);
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tmp2 = 0.5/g*(w1*w1+w2*w2+w1*w2);
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tmp3 = 0.5*g*(w1*kw2*kw2+w2*kw1*kw1)/(w1*w2*(w1+w2));
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tmp4 = (1-g*(kw1+kw2)/(w1+w2)/(w1+w2)*tanh((kw1+kw2)*h));
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Epij = (tmp1-tmp2+tmp3)/tmp4+tmp2-0.5*tmp1; /* OK */
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tmp2 = 0.5/g*(w1*w1+w2*w2-w1*w2); /*OK*/
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tmp3 = -0.5*g*(w1*kw2*kw2-w2*kw1*kw1)/(w1*w2*(w1-w2));
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tmp4 = (1.0-g*(kw1-kw2)/(w1-w2)/(w1-w2)*tanh((kw1-kw2)*h));
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Edij = (tmp1-tmp2+tmp3)/tmp4+tmp2-0.5*tmp1; /* OK */
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//printf("Edij = %f Epij = %f \n", Edij,Epij);
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ixi = ix*m;
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jyi = jy*m;
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iz1 = ixi+jyi;
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iv1 = jyi-ixi;
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// iz2 = (n*m-iz1);
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// iv2 = n*m-iv1;
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for (i=0;i<m;i++,ixi++,jyi++,iz1++,iv1++) {
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rrA = rA[ixi]*rA[jyi]; ///rrA = rA[i][ix]*rA[i][jy];
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iiA = iA[ixi]*iA[jyi]; ///iiA = iA[i][ix]*iA[i][jy];
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riA = rA[ixi]*iA[jyi]; ///riA = rA[i][ix]*iA[i][jy];
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irA = iA[ixi]*rA[jyi]; ///irA = iA[i][ix]*rA[i][jy];
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/* Sum frequency effects */
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tmp1 = kfact*2.0*(rrA-iiA)*Epij;
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tmp2 = kfact*2.0*(riA+irA)*Epij;
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rvec[iz1] += tmp1;///rvec[i][jy+ix] += tmp1;
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ivec[iz1] += tmp2;///ivec[i][jy+ix] += tmp2;
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//rvec[iz2] += tmp1;///rvec[i][n*m-(jy+ix)] += tmp1;
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//ivec[iz2] -= tmp2;///ivec[i][n*m-(jy+ix)] -= tmp2;
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//iz2++;
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/* Difference frequency effects */
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tmp1 = kfact*2.0*(rrA+iiA)*Edij;
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tmp2 = kfact*2.0*(riA-irA)*Edij;
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rvec[iv1] += tmp1;///rvec[i][jy-ix] += tmp1;
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ivec[iv1] += tmp2;///ivec[i][jy-ix] -= tmp2;
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//rvec[iv2] += tmp1;
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//ivec[iv2] -= tmp2;
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//iv2++;
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}
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}
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}
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}
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//return i;
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}
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/*
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* DISUFQ2 Is an internal function to spec2nlsdat
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*
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* CALL: disufq2(rsvec,isvec,rdvec,idvec,rA,iA, w,kw,h,g,nmin,nmax,m,n)
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*
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* rsvec, isvec = real and imaginary parts of the sum frequency
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* effects (size m X n).
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* rdvec, idvec = real and imaginary parts of the difference frequency
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* effects (size m X n).
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* rA, iA = real and imaginary parts of the amplitudes (size m X n).
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* w = vector with angular frequencies (w>=0)
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* kw = vector with wavenumbers (kw>=0)
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* h = water depth (h >=0)
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* g = constant acceleration of gravity
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* nmin = minimum index where rA(:,nmin) and iA(:,nmin) is
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* greater than zero.
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* nmax = maximum index where rA(:,nmax) and iA(:,nmax) is
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* greater than zero.
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* m = size(rA,1),size(iA,1)
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* n = size(rA,2),size(iA,2), or size(rvec,2),size(ivec,2)
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*
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* DISUFQ2 returns the summation of sum and difference frequency
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* frequency effects in the vectors svec = rsvec +sqrt(-1)*isvec and
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* dvec = rdvec +sqrt(-1)*idvec.
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* The 2'nd order contribution to the Stokes wave is then calculated by
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* a simple 1D Fourier transform, real(FFT(svec+dvec)).
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*
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*
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* This is a MEX-file for MATLAB.
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* by Per Andreas Brodtkorb 15.08.2001
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* revised pab 14.03.2002, 01.05.2002
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*/
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void disufq2(double *rsvec, double *isvec,
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double *rdvec, double *idvec,
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double *rA, double *iA,
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double *w, double *kw,
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double h, double g,
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int nmin, int nmax,
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int m, int n)
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{
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double Epij, Edij;
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double tmp1, tmp2, tmp3, tmp4, kfact;
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double w1, w2, kw1, kw2, Cg;
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double rrA, iiA, riA, irA;
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int i,jy,ix,iz1,iv1,ixi,jyi;
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//int iz2,iv2
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//Initialize rvec and ivec to zero
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for (ix=0;ix<n*m;ix++) {
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rsvec[ix] = 0.0;
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isvec[ix] = 0.0;
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rdvec[ix] = 0.0;
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idvec[ix] = 0.0;
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}
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// kfact is set to 2 in order to exploit the symmetry.
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// If you set kfact to 1, you must uncomment all statements
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// including the expressions: rvec[iz2], rvec[iv2], ivec[iz2] and ivec[iv2].
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kfact = 2.0;
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if (h>10000){ /* deep water /Inifinite water depth */
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for (ix = nmin-1;ix<nmax;ix++) {
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ixi = ix*m;
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iz1 = 2*ixi;
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//iz2 = n*m-ixi;
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kw1 = kw[ix];
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Epij = kw1;
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for (i=0;i<m;i++,ixi++,iz1++) {
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rrA = rA[ixi]*rA[ixi]; ///
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iiA = iA[ixi]*iA[ixi]; ///
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riA = rA[ixi]*iA[ixi]; ///
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/// Sum frequency effects along the diagonal
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tmp1 = kfact*(rrA-iiA)*Epij;
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tmp2 = kfact*2.0*riA*Epij;
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rsvec[iz1] += tmp1;
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isvec[iz1] += tmp2;
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//rsvec[iz2] += tmp1;
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//isvec[iz2] -= tmp2;
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//iz2++;
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/// Difference frequency effects are zero along the diagonal
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/// and are thus not contributing to the mean.
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}
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for (jy = ix+1;jy<nmax;jy++){
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kw2 = kw[jy];
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Epij = 0.5*(kw2 + kw1);
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Edij = -0.5*(kw2 - kw1);
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//printf("Edij = %f Epij = %f \n", Edij,Epij);
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ixi = ix*m;
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jyi = jy*m;
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iz1 = ixi+jyi;
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iv1 = jyi-ixi;
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//iz2 = (n*m-iz1);
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//iv2 = (n*m-iv1);
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for (i = 0;i<m;i++,ixi++,jyi++,iz1++,iv1++) {
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rrA = rA[ixi]*rA[jyi]; ///rrA = rA[i][ix]*rA[i][jy];
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iiA = iA[ixi]*iA[jyi]; ///iiA = iA[i][ix]*iA[i][jy];
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riA = rA[ixi]*iA[jyi]; ///riA = rA[i][ix]*iA[i][jy];
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irA = iA[ixi]*rA[jyi]; ///irA = iA[i][ix]*rA[i][jy];
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/* Sum frequency effects */
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tmp1 = kfact*2.0*(rrA-iiA)*Epij;
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tmp2 = kfact*2.0*(riA+irA)*Epij;
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rsvec[iz1] += tmp1; ///rvec[i][ix+jy] += tmp1;
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isvec[iz1] += tmp2; ///ivec[i][ix+jy] += tmp2;
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//rsvec[iz2] += tmp1;///rvec[i][n*m-(ix+jy)] += tmp1;
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//isvec[iz2] -= tmp2;///ivec[i][n*m-(ix+jy)] += tmp2;
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//iz2++;
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/* Difference frequency effects */
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tmp1 = kfact*2.0*(rrA+iiA)*Edij;
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tmp2 = kfact*2.0*(riA-irA)*Edij;
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rdvec[iv1] += tmp1;///rvec[i][jy-ix] += tmp1;
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idvec[iv1] += tmp2;///ivec[i][jy-ix] += tmp2;
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//rdvec[iv2] += tmp1;///rvec[i][n*m-(jy-ix)] += tmp1;
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//idvec[iv2] -= tmp2;///ivec[i][n*m-(jy-ix)] -= tmp2;
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// iv2++;
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}
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}
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}
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}
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else{ /* Finite water depth */
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for (ix = nmin-1;ix<nmax;ix++) {
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kw1 = kw[ix];
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w1 = w[ix];
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tmp1 = tanh(kw1*h);
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/// Cg, wave group velocity
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Cg = 0.5*g*(tmp1 + kw1*h*(1.0- tmp1*tmp1))/w1; /// OK
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tmp1 = 0.5*g*(kw1/w1)*(kw1/w1);
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tmp2 = 0.5*w1*w1/g;
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tmp3 = g*kw1/(w1*Cg);
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if (kw1*h<300.0){
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tmp4 = kw1/sinh(2.0*kw1*h);
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}
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else{ // To ensure sinh does not overflow.
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tmp4 = 0.0;
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}
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// Difference frequency effects finite water depth
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Edij = (tmp1-tmp2+tmp3)/(1.0-g*h/(Cg*Cg))-tmp4; /// OK
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// Sum frequency effects finite water depth
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Epij = (3.0*(tmp1-tmp2)/(1.0-tmp1/kw1*tanh(2.0*kw1*h))+3.0*tmp2-tmp1); /// OK
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//printf("Edij = %f Epij = %f \n", Edij,Epij);
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ixi = ix*m;
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iz1 = 2*ixi;
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//iz2 = n*m-ixi;
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for (i=0;i<m;i++,ixi++,iz1++) {
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rrA = rA[ixi]*rA[ixi]; ///
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iiA = iA[ixi]*iA[ixi]; ///
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riA = rA[ixi]*iA[ixi]; ///
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/// Sum frequency effects along the diagonal
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rsvec[iz1] += kfact*(rrA-iiA)*Epij;
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isvec[iz1] += kfact*2.0*riA*Epij;
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//rsvec[iz2] += kfact*(rrA-iiA)*Epij;
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//isvec[iz2] -= kfact*2.0*riA*Epij;
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/// Difference frequency effects along the diagonal
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/// are only contributing to the mean
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//printf(" %f \n",2.0*(rrA+iiA)*Edij);
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rdvec[i] += 2.0*(rrA+iiA)*Edij;
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}
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for (jy = ix+1;jy<nmax;jy++) {
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// w1 = w[ix];
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// kw1 = kw[ix];
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w2 = w[jy];
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kw2 = kw[jy];
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tmp1 = g*(kw1/w1)*(kw2/w2);
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tmp2 = 0.5/g*(w1*w1+w2*w2+w1*w2);
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tmp3 = 0.5*g*(w1*kw2*kw2+w2*kw1*kw1)/(w1*w2*(w1+w2));
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tmp4 = (1-g*(kw1+kw2)/(w1+w2)/(w1+w2)*tanh((kw1+kw2)*h));
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Epij = (tmp1-tmp2+tmp3)/tmp4+tmp2-0.5*tmp1; /* OK */
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tmp2 = 0.5/g*(w1*w1+w2*w2-w1*w2); /*OK*/
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tmp3 = -0.5*g*(w1*kw2*kw2-w2*kw1*kw1)/(w1*w2*(w1-w2));
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tmp4 = (1.0-g*(kw1-kw2)/(w1-w2)/(w1-w2)*tanh((kw1-kw2)*h));
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Edij = (tmp1-tmp2+tmp3)/tmp4+tmp2-0.5*tmp1; /* OK */
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//printf("Edij = %f Epij = %f \n", Edij,Epij);
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ixi = ix*m;
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jyi = jy*m;
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iz1 = ixi+jyi;
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iv1 = jyi-ixi;
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// iz2 = (n*m-iz1);
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// iv2 = (n*m-iv1);
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for (i=0;i<m;i++,ixi++,jyi++,iz1++,iv1++) {
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rrA = rA[ixi]*rA[jyi]; ///rrA = rA[i][ix]*rA[i][jy];
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iiA = iA[ixi]*iA[jyi]; ///iiA = iA[i][ix]*iA[i][jy];
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riA = rA[ixi]*iA[jyi]; ///riA = rA[i][ix]*iA[i][jy];
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irA = iA[ixi]*rA[jyi]; ///irA = iA[i][ix]*rA[i][jy];
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|
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/* Sum frequency effects */
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tmp1 = kfact*2.0*(rrA-iiA)*Epij;
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tmp2 = kfact*2.0*(riA+irA)*Epij;
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rsvec[iz1] += tmp1;///rsvec[i][jy+ix] += tmp1;
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isvec[iz1] += tmp2;///isvec[i][jy+ix] += tmp2;
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//rsvec[iz2] += tmp1;///rsvec[i][n*m-(jy+ix)] += tmp1;
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//isvec[iz2] -= tmp2;///isvec[i][n*m-(jy-ix)] += tmp2;
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//iz2++;
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|
|
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/* Difference frequency effects */
|
|
tmp1 = kfact*2.0*(rrA+iiA)*Edij;
|
|
tmp2 = kfact*2.0*(riA-irA)*Edij;
|
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rdvec[iv1] += tmp1;
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idvec[iv1] += tmp2;
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|
|
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//rdvec[iv2] += tmp1;
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//idvec[iv2] -= tmp2;
|
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// iv2++;
|
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}
|
|
}
|
|
}
|
|
}
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// return i;
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}
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