| 1 |
|
|---|
| 2 | /* ------------------------ Projet BAORadio --------------------
|
|---|
| 3 | Classes to compute 3D power spectrum and noise power spectrum
|
|---|
| 4 | R. Ansari - Nov 2008 ... Dec 2010
|
|---|
| 5 | --------------------------------------------------------------- */
|
|---|
| 6 |
|
|---|
| 7 | #include "specpk.h"
|
|---|
| 8 | #include "randr48.h"
|
|---|
| 9 | #include "ctimer.h"
|
|---|
| 10 |
|
|---|
| 11 | //------------------------------------
|
|---|
| 12 | // Class SpectralShape
|
|---|
| 13 | // -----------------------------------
|
|---|
| 14 |
|
|---|
| 15 | double Pnu1(double nu)
|
|---|
| 16 | {
|
|---|
| 17 | return ( sqrt(sqrt(nu)) / ((nu+1.0)/0.2) *
|
|---|
| 18 | (1+0.2*cos(2*M_PI*(nu-2.)*0.15)*exp(-nu/50.)) );
|
|---|
| 19 | }
|
|---|
| 20 |
|
|---|
| 21 | double Pnu2(double nu)
|
|---|
| 22 | {
|
|---|
| 23 | if (nu < 1.e-9) return 0.;
|
|---|
| 24 | return ((1.-exp(-nu/0.5))/nu*(1+0.25*cos(2*M_PI*nu*0.1)*exp(-nu/20.)) );
|
|---|
| 25 | }
|
|---|
| 26 |
|
|---|
| 27 |
|
|---|
| 28 | double Pnu3(double nu)
|
|---|
| 29 | {
|
|---|
| 30 | return ( log(nu/100.+1)*(1+sin(2*M_PI*nu/300))*exp(-nu/4000) );
|
|---|
| 31 | }
|
|---|
| 32 |
|
|---|
| 33 |
|
|---|
| 34 | double Pnu4(double nu)
|
|---|
| 35 | {
|
|---|
| 36 | double x = (nu-0.5)/0.05;
|
|---|
| 37 | double rc = 2*exp(-x*x);
|
|---|
| 38 | x = (nu-3.1)/0.27;
|
|---|
| 39 | rc += exp(-x*x);
|
|---|
| 40 | x = (nu-7.6)/1.4;
|
|---|
| 41 | rc += 0.5*exp(-x*x);
|
|---|
| 42 | return ( rc+2.*exp(-x*x) );
|
|---|
| 43 | }
|
|---|
| 44 |
|
|---|
| 45 | //--------------------------------------------------
|
|---|
| 46 | // -- SpectralShape class : test P(k) class
|
|---|
| 47 | //--------------------------------------------------
|
|---|
| 48 | // Constructor
|
|---|
| 49 | SpectralShape::SpectralShape(int typ)
|
|---|
| 50 | {
|
|---|
| 51 | typ_=typ;
|
|---|
| 52 | SetRenormFac();
|
|---|
| 53 | }
|
|---|
| 54 |
|
|---|
| 55 | // Return the spectral power for a given wave number wk
|
|---|
| 56 | double SpectralShape::operator() (double wk)
|
|---|
| 57 | {
|
|---|
| 58 | wk/=DeuxPI;
|
|---|
| 59 | double retv=1.;
|
|---|
| 60 | switch (typ_)
|
|---|
| 61 | {
|
|---|
| 62 | case 1:
|
|---|
| 63 | retv=Pnu1(wk);
|
|---|
| 64 | break;
|
|---|
| 65 | case 2:
|
|---|
| 66 | retv=Pnu2(wk);
|
|---|
| 67 | break;
|
|---|
| 68 | case 3:
|
|---|
| 69 | retv=Pnu3(wk);
|
|---|
| 70 | break;
|
|---|
| 71 | case 4:
|
|---|
| 72 | retv=Pnu4(wk);
|
|---|
| 73 | break;
|
|---|
| 74 | default :
|
|---|
| 75 | {
|
|---|
| 76 | // global shape
|
|---|
| 77 | double csp = pow( (2*sin(sqrt(sqrt(wk/7.)))),2.);
|
|---|
| 78 | if (csp < 0.) return 0.;
|
|---|
| 79 |
|
|---|
| 80 | // Adding some pics
|
|---|
| 81 | double picpos[5] = {75.,150.,225.,300.,375.,};
|
|---|
| 82 |
|
|---|
| 83 | for(int k=0; k<5; k++) {
|
|---|
| 84 | double x0 = picpos[k];
|
|---|
| 85 | if ( (wk > x0-25.) && (wk < x0+25.) ) {
|
|---|
| 86 | double x = (wk-x0);
|
|---|
| 87 | csp *= (1.+0.5*exp(-(x*x)/(2.*5*5)));
|
|---|
| 88 | break;
|
|---|
| 89 | }
|
|---|
| 90 | }
|
|---|
| 91 | retv=csp;
|
|---|
| 92 | }
|
|---|
| 93 | break;
|
|---|
| 94 | }
|
|---|
| 95 | return retv*renorm_fac;
|
|---|
| 96 | }
|
|---|
| 97 | // Return a vector representing the power spectrum (for checking)
|
|---|
| 98 | Histo SpectralShape::GetPk(int n)
|
|---|
| 99 | {
|
|---|
| 100 | if (n<16) n = 256;
|
|---|
| 101 | Histo h(0.,1024.*DeuxPI,n);
|
|---|
| 102 | for(int k=0; k<h.NBins(); k++) h(k) = Value((k+0.5)*h.BinWidth());
|
|---|
| 103 | return h;
|
|---|
| 104 | }
|
|---|
| 105 |
|
|---|
| 106 | double SpectralShape::Sommek2Pk(double kmax, int n)
|
|---|
| 107 | {
|
|---|
| 108 | double dk=kmax/(double)n;
|
|---|
| 109 | double s=0.;
|
|---|
| 110 | for(int i=1; i<=n; i++) {
|
|---|
| 111 | double ck=(double)i*dk;
|
|---|
| 112 | s += Value(ck)*ck*ck;
|
|---|
| 113 | }
|
|---|
| 114 | return s*dk*4.*M_PI;
|
|---|
| 115 | }
|
|---|
| 116 | //--------------------------------------------------
|
|---|
| 117 | // -- Four2DResponse class : test P(k) class
|
|---|
| 118 |
|
|---|
| 119 | //---------------------------------------------------------------
|
|---|
| 120 | // -- Four3DPk class : 3D fourier amplitudes and power spectrum
|
|---|
| 121 | //---------------------------------------------------------------
|
|---|
| 122 | // Constructeur avec Tableau des coeff. de Fourier en argument
|
|---|
| 123 | Four3DPk::Four3DPk(TArray< complex<TF> > & fourcoedd, RandomGeneratorInterface& rg)
|
|---|
| 124 | : rg_(rg), fourAmp(fourcoedd)
|
|---|
| 125 | {
|
|---|
| 126 | SetPrtLevel();
|
|---|
| 127 | SetCellSize();
|
|---|
| 128 | }
|
|---|
| 129 | // Constructor
|
|---|
| 130 | Four3DPk::Four3DPk(RandomGeneratorInterface& rg, sa_size_t szx, sa_size_t szy, sa_size_t szz)
|
|---|
| 131 | : rg_(rg), fourAmp(szx, szy, szz)
|
|---|
| 132 | {
|
|---|
| 133 | SetPrtLevel();
|
|---|
| 134 | SetCellSize();
|
|---|
| 135 | }
|
|---|
| 136 |
|
|---|
| 137 |
|
|---|
| 138 | // Generate mass field Fourier Coefficient
|
|---|
| 139 | void Four3DPk::ComputeFourierAmp(SpectralShape& pk)
|
|---|
| 140 | {
|
|---|
| 141 | // We generate a random gaussian real field
|
|---|
| 142 | // fourAmp represent 3-D fourier transform of a real input array.
|
|---|
| 143 | // The second half of the array along Y and Z contain negative frequencies
|
|---|
| 144 | // double fnorm = 1./sqrt(2.*fourAmp.Size());
|
|---|
| 145 | double fnorm = 1.;
|
|---|
| 146 | double kxx, kyy, kzz;
|
|---|
| 147 | // sa_size_t is large integer type
|
|---|
| 148 | for(sa_size_t kz=0; kz<fourAmp.SizeZ(); kz++) {
|
|---|
| 149 | kzz = (kz>fourAmp.SizeZ()/2) ? (double)(fourAmp.SizeZ()-kz)*dkz_ : (double)kz*dkz_;
|
|---|
| 150 | for(sa_size_t ky=0; ky<fourAmp.SizeY(); ky++) {
|
|---|
| 151 | kyy = (ky>fourAmp.SizeY()/2) ? (double)(fourAmp.SizeY()-ky)*dky_ : (double)ky*dky_;
|
|---|
| 152 | for(sa_size_t kx=0; kx<fourAmp.SizeX(); kx++) {
|
|---|
| 153 | double kxx=(double)kx*dkx_;
|
|---|
| 154 | double wk = sqrt(kxx*kxx+kyy*kyy+kzz*kzz);
|
|---|
| 155 | double amp = sqrt(pk(wk)*fnorm/2.);
|
|---|
| 156 | fourAmp(kx, ky, kz) = complex<TF>(rg_.Gaussian(amp), rg_.Gaussian(amp)); // renormalize fourier coeff usin
|
|---|
| 157 | }
|
|---|
| 158 | }
|
|---|
| 159 | }
|
|---|
| 160 | if (prtlev_>2)
|
|---|
| 161 | cout << " Four3DPk::ComputeFourierAmp() done ..." << endl;
|
|---|
| 162 | }
|
|---|
| 163 |
|
|---|
| 164 | // Generate mass field Fourier Coefficient
|
|---|
| 165 | void Four3DPk::ComputeNoiseFourierAmp(Four2DResponse& resp, bool crmask)
|
|---|
| 166 | {
|
|---|
| 167 | TMatrix<r_4> mask(fourAmp.SizeY(), fourAmp.SizeX());
|
|---|
| 168 | // fourAmp represent 3-D fourier transform of a real input array.
|
|---|
| 169 | // The second half of the array along Y and Z contain negative frequencies
|
|---|
| 170 | double kxx, kyy, kzz, rep, amp;
|
|---|
| 171 | // sa_size_t is large integer type
|
|---|
| 172 | for(sa_size_t kz=0; kz<fourAmp.SizeZ(); kz++) {
|
|---|
| 173 | kzz = (kz>fourAmp.SizeZ()/2) ? -(double)(fourAmp.SizeZ()-kz)*dkz_ : (double)kz*dkz_;
|
|---|
| 174 | for(sa_size_t ky=0; ky<fourAmp.SizeY(); ky++) {
|
|---|
| 175 | kyy = (ky>fourAmp.SizeY()/2) ? -(double)(fourAmp.SizeY()-ky)*dky_ : (double)ky*dky_;
|
|---|
| 176 | for(sa_size_t kx=0; kx<fourAmp.SizeX(); kx++) {
|
|---|
| 177 | kxx=(double)kx*dkx_;
|
|---|
| 178 | rep = resp(kxx, kyy);
|
|---|
| 179 | if (crmask&&(kz==0)) mask(ky,kx)=((rep<1.e-8)?9.e9:(1./rep));
|
|---|
| 180 | if (rep<1.e-8) fourAmp(kx, ky, kz) = complex<TF>(9.e9,0.);
|
|---|
| 181 | else {
|
|---|
| 182 | amp = 1./sqrt(rep)/sqrt(2.);
|
|---|
| 183 | fourAmp(kx, ky, kz) = complex<TF>(rg_.Gaussian(amp), rg_.Gaussian(amp));
|
|---|
| 184 | }
|
|---|
| 185 | }
|
|---|
| 186 | }
|
|---|
| 187 | }
|
|---|
| 188 | if (prtlev_>2) fourAmp.Show();
|
|---|
| 189 | if (crmask) {
|
|---|
| 190 | POutPersist po("mask.ppf");
|
|---|
| 191 | po << mask;
|
|---|
| 192 | }
|
|---|
| 193 | if (prtlev_>0)
|
|---|
| 194 | cout << " Four3DPk::ComputeNoiseFourierAmp() done ..." << endl;
|
|---|
| 195 | }
|
|---|
| 196 |
|
|---|
| 197 | // Compute mass field from its Fourier Coefficient
|
|---|
| 198 | TArray<TF> Four3DPk::ComputeMassDens()
|
|---|
| 199 | {
|
|---|
| 200 | TArray<TF> massdens;
|
|---|
| 201 | // Backward fourier transform of the fourierAmp array
|
|---|
| 202 | FFTWServer ffts(true);
|
|---|
| 203 | ffts.setNormalize(true);
|
|---|
| 204 | ffts.FFTBackward(fourAmp, massdens, true);
|
|---|
| 205 | // cout << " Four3DPk::ComputeMassDens() done NbNeg=" << npbz << " / NPix=" << massDens.Size() << endl;
|
|---|
| 206 | cout << " Four3DPk::ComputeMassDens() done NPix=" << massdens.Size() << endl;
|
|---|
| 207 | return massdens;
|
|---|
| 208 | }
|
|---|
| 209 |
|
|---|
| 210 | // Compute power spectrum as a function of wave number k
|
|---|
| 211 | // cells with amp^2=re^2+im^2>s2cut are ignored
|
|---|
| 212 | // Output : power spectrum (profile histogram)
|
|---|
| 213 | HProf Four3DPk::ComputePk(double s2cut, int nbin, double kmin, double kmax)
|
|---|
| 214 | {
|
|---|
| 215 | // The second half of the array along Y (matrix rows) contain
|
|---|
| 216 | // negative frequencies
|
|---|
| 217 | // int nbh = sqrt(fourAmp.SizeX()*fourAmp.SizeX()+fourAmp.SizeY()*fourAmp.SizeY()/4.+fourAmp.SizeZ()*fourAmp.SizeY()/4.);
|
|---|
| 218 | // The profile histogram will contain the mean value of FFT amplitude
|
|---|
| 219 | // as a function of wave-number k = sqrt((double)(kx*kx+ky*ky))
|
|---|
| 220 | // if (nbin < 1) nbin = nbh/2;
|
|---|
| 221 | if ((kmax<0.)||(kmax<kmin)) {
|
|---|
| 222 | kmin=0.;
|
|---|
| 223 | double maxx=fourAmp.SizeX()*dkx_;
|
|---|
| 224 | double maxy=fourAmp.SizeY()*dky_/2;
|
|---|
| 225 | double maxz=fourAmp.SizeZ()*dkz_/2;
|
|---|
| 226 | kmax=sqrt(maxx*maxx+maxy*maxy+maxz*maxz);
|
|---|
| 227 | }
|
|---|
| 228 | if (nbin<2) nbin=128;
|
|---|
| 229 | HProf hp(kmin, kmax, nbin);
|
|---|
| 230 | hp.SetErrOpt(false);
|
|---|
| 231 | ComputePkCumul(hp, s2cut);
|
|---|
| 232 | return hp;
|
|---|
| 233 | }
|
|---|
| 234 |
|
|---|
| 235 | // Compute power spectrum as a function of wave number k
|
|---|
| 236 | // Cumul dans hp - cells with amp^2=re^2+im^2>s2cut are ignored
|
|---|
| 237 | void Four3DPk::ComputePkCumul(HProf& hp, double s2cut)
|
|---|
| 238 | {
|
|---|
| 239 | uint_8 nmodeok=0;
|
|---|
| 240 | // fourAmp represent 3-D fourier transform of a real input array.
|
|---|
| 241 | // The second half of the array along Y and Z contain negative frequencies
|
|---|
| 242 | double kxx, kyy, kzz;
|
|---|
| 243 | // sa_size_t is large integer type
|
|---|
| 244 | // We ignore 0th term in all frequency directions ...
|
|---|
| 245 | for(sa_size_t kz=1; kz<fourAmp.SizeZ(); kz++) {
|
|---|
| 246 | kzz = (kz > fourAmp.SizeZ()/2) ? (double)(fourAmp.SizeZ()-kz)*dkz_ : (double)kz*dkz_;
|
|---|
| 247 | for(sa_size_t ky=1; ky<fourAmp.SizeY(); ky++) {
|
|---|
| 248 | kyy = (ky > fourAmp.SizeY()/2) ? (double)(fourAmp.SizeY()-ky)*dky_ : (double)ky*dky_;
|
|---|
| 249 | for(sa_size_t kx=1; kx<fourAmp.SizeX(); kx++) { // ignore the 0th coefficient (constant term)
|
|---|
| 250 | double kxx=(double)kx*dkx_;
|
|---|
| 251 | complex<TF> za = fourAmp(kx, ky, kz);
|
|---|
| 252 | if (za.real()>8.e9) continue;
|
|---|
| 253 | double wk = sqrt(kxx*kxx+kyy*kyy+kzz*kzz);
|
|---|
| 254 | double amp2 = za.real()*za.real()+za.imag()*za.imag();
|
|---|
| 255 | if ((s2cut>1.e-9)&&(amp2>s2cut)) continue;
|
|---|
| 256 | hp.Add(wk, amp2);
|
|---|
| 257 | nmodeok++;
|
|---|
| 258 | }
|
|---|
| 259 | }
|
|---|
| 260 | }
|
|---|
| 261 | if ((prtlev_>1)||((prtlev_>0)&&(s2cut>1.e-9))) {
|
|---|
| 262 | cout << " Four3DPk::ComputePkCumul/Info : NModeOK=" << nmodeok << " / NMode=" << fourAmp.Size()
|
|---|
| 263 | << " -> " << 100.*(double)nmodeok/(double)fourAmp.Size() << "%" << endl;
|
|---|
| 264 | }
|
|---|
| 265 | return;
|
|---|
| 266 | }
|
|---|
| 267 |
|
|---|
| 268 | // Compute noise power spectrum as a function of wave number k
|
|---|
| 269 | // No random generation, computes profile of noise sigma^2
|
|---|
| 270 | // cells with amp^2=re^2+im^2>s2cut are ignored
|
|---|
| 271 | // Output : noise power spectrum (profile histogram)
|
|---|
| 272 | HProf Four3DPk::ComputeNoisePk(Four2DResponse& resp, Histo& fracmodok, DataTable& dt,
|
|---|
| 273 | double s2cut, int nbin, double kmin, double kmax)
|
|---|
| 274 | {
|
|---|
| 275 | // The second half of the array along Y (matrix rows) contain
|
|---|
| 276 | // negative frequencies
|
|---|
| 277 | // int nbh = sqrt(fourAmp.SizeX()*fourAmp.SizeX()+fourAmp.SizeY()*fourAmp.SizeY()/4.+fourAmp.SizeZ()*fourAmp.SizeY()/4.);
|
|---|
| 278 | // The profile histogram will contain the mean value of noise sigma^2
|
|---|
| 279 | // as a function of wave-number k = sqrt((double)(kx*kx+ky*ky))
|
|---|
| 280 | // if (nbin < 1) nbin = nbh/2;
|
|---|
| 281 | if ((kmax<0.)||(kmax<kmin)) {
|
|---|
| 282 | kmin=0.;
|
|---|
| 283 | double maxx=fourAmp.SizeX()*dkx_;
|
|---|
| 284 | double maxy=fourAmp.SizeY()*dky_/2;
|
|---|
| 285 | double maxz=fourAmp.SizeZ()*dkz_/2;
|
|---|
| 286 | kmax=sqrt(maxx*maxx+maxy*maxy+maxz*maxz);
|
|---|
| 287 | }
|
|---|
| 288 | if (nbin<2) nbin=128;
|
|---|
| 289 | HProf hp(kmin, kmax, nbin);
|
|---|
| 290 | hp.SetErrOpt(false);
|
|---|
| 291 | Histo hmcnt(kmin, kmax, nbin);
|
|---|
| 292 | Histo hmcntok(kmin, kmax, nbin);
|
|---|
| 293 |
|
|---|
| 294 | uint_8 nmodeok=0;
|
|---|
| 295 | // fourAmp represent 3-D fourier transform of a real input array.
|
|---|
| 296 | // The second half of the array along Y and Z contain negative frequencies
|
|---|
| 297 | double kxx, kyy, kzz;
|
|---|
| 298 | // sa_size_t is large integer type
|
|---|
| 299 | // We ignore 0th term in all frequency directions ...
|
|---|
| 300 | for(sa_size_t kz=1; kz<fourAmp.SizeZ(); kz++) {
|
|---|
| 301 | kzz = (kz > fourAmp.SizeZ()/2) ? (double)(fourAmp.SizeZ()-kz)*dkz_ : (double)kz*dkz_;
|
|---|
| 302 | for(sa_size_t ky=1; ky<fourAmp.SizeY(); ky++) {
|
|---|
| 303 | kyy = (ky > fourAmp.SizeY()/2) ? (double)(fourAmp.SizeY()-ky)*dky_ : (double)ky*dky_;
|
|---|
| 304 | for(sa_size_t kx=1; kx<fourAmp.SizeX(); kx++) { // ignore the 0th coefficient (constant term)
|
|---|
| 305 | double kxx=(double)kx*dkx_;
|
|---|
| 306 | double wk = sqrt(kxx*kxx+kyy*kyy+kzz*kzz);
|
|---|
| 307 | double amp2 = 1./resp(kxx, kyy);
|
|---|
| 308 | hmcnt.Add(wk);
|
|---|
| 309 | if ((s2cut>1.e-9)&&(amp2>s2cut)) continue;
|
|---|
| 310 | hmcntok.Add(wk);
|
|---|
| 311 | hp.Add(wk, amp2);
|
|---|
| 312 | nmodeok++;
|
|---|
| 313 | }
|
|---|
| 314 | }
|
|---|
| 315 | }
|
|---|
| 316 | if ((prtlev_>1)||((prtlev_>0)&&(s2cut>1.e-9))) {
|
|---|
| 317 | cout << " Four3DPk::ComputeNoisePk/Info : NModeOK=" << nmodeok << " / NMode=" << fourAmp.Size()
|
|---|
| 318 | << " -> " << 100.*(double)nmodeok/(double)fourAmp.Size() << "%" << endl;
|
|---|
| 319 | }
|
|---|
| 320 |
|
|---|
| 321 | fracmodok=hmcntok/hmcnt;
|
|---|
| 322 |
|
|---|
| 323 | char* nomcol[5] = {"k","pnoise","nmode","nmodok","fracmodok"};
|
|---|
| 324 | dt.Clear();
|
|---|
| 325 | dt.AddDoubleColumn(nomcol[0]);
|
|---|
| 326 | dt.AddDoubleColumn(nomcol[1]);
|
|---|
| 327 | dt.AddIntegerColumn(nomcol[2]);
|
|---|
| 328 | dt.AddIntegerColumn(nomcol[3]);
|
|---|
| 329 | dt.AddFloatColumn(nomcol[4]);
|
|---|
| 330 | DataTableRow dtr = dt.EmptyRow();
|
|---|
| 331 | for(int_4 ib=0; ib<hp.NBins(); ib++) {
|
|---|
| 332 | dtr[0]=hp.BinCenter(ib);
|
|---|
| 333 | dtr[1]=hp(ib);
|
|---|
| 334 | dtr[2]=hmcnt(ib);
|
|---|
| 335 | dtr[3]=hmcntok(ib);
|
|---|
| 336 | dtr[4]=fracmodok(ib);
|
|---|
| 337 | dt.AddRow(dtr);
|
|---|
| 338 | }
|
|---|
| 339 | return hp;
|
|---|
| 340 | }
|
|---|
| 341 |
|
|---|
| 342 | //-----------------------------------------------------
|
|---|
| 343 | // -- MassDist2D class : 2D mass distribution
|
|---|
| 344 | // --- PkNoiseCalculator : Classe de calcul du spectre de bruit PNoise(k)
|
|---|
| 345 | // determine par une reponse 2D de l'instrument
|
|---|
| 346 | //-----------------------------------------------------
|
|---|
| 347 | PkNoiseCalculator::PkNoiseCalculator(Four3DPk& pk3, Four2DResponse& rep, double s2cut, int ngen,
|
|---|
| 348 | const char* tit)
|
|---|
| 349 | : pkn3d(pk3), frep(rep), S2CUT(s2cut), NGEN(ngen), title(tit)
|
|---|
| 350 | {
|
|---|
| 351 | SetPrtLevel();
|
|---|
| 352 | }
|
|---|
| 353 |
|
|---|
| 354 | HProf PkNoiseCalculator::Compute()
|
|---|
| 355 | {
|
|---|
| 356 | Timer tm(title.c_str());
|
|---|
| 357 | tm.Nop();
|
|---|
| 358 | HProf hnd;
|
|---|
| 359 | cout << "PkNoiseCalculator::Compute() " << title << " NGEN=" << NGEN << " S2CUT=" << S2CUT << endl;
|
|---|
| 360 | for(int igen=0; igen<NGEN; igen++) {
|
|---|
| 361 | pkn3d.ComputeNoiseFourierAmp(frep);
|
|---|
| 362 | if (igen==0) hnd = pkn3d.ComputePk(S2CUT);
|
|---|
| 363 | else pkn3d.ComputePkCumul(hnd,S2CUT);
|
|---|
| 364 | if ((prtlev_>0)&&(igen>0)&&(((igen-1)%prtmodulo_)==0))
|
|---|
| 365 | cout << " PkNoiseCalculator::Compute() - done igen=" << igen << " / MaxNGen=" << NGEN << endl;
|
|---|
| 366 | }
|
|---|
| 367 | return hnd;
|
|---|
| 368 | }
|
|---|
| 369 |
|
|---|
| 370 |
|
|---|
| 371 | //-----------------------------------------------------
|
|---|
| 372 | // -- MassDist2D class : 2D mass distribution
|
|---|
| 373 | //-----------------------------------------------------
|
|---|
| 374 | // Constructor
|
|---|
| 375 | MassDist2D::MassDist2D(GenericFunc& pk, int size, double meandens)
|
|---|
| 376 | : pkSpec(pk) , sizeA((size>16)?size:16) , massDens(sizeA, sizeA),
|
|---|
| 377 | meanRho(meandens) , fg_fourAmp(false) , fg_massDens(false)
|
|---|
| 378 | {
|
|---|
| 379 | }
|
|---|
| 380 |
|
|---|
| 381 | // To the computation job
|
|---|
| 382 | void MassDist2D::Compute()
|
|---|
| 383 | {
|
|---|
| 384 | ComputeFourierAmp();
|
|---|
| 385 | ComputeMassDens();
|
|---|
| 386 | }
|
|---|
| 387 |
|
|---|
| 388 | // Generate mass field Fourier Coefficient
|
|---|
| 389 | void MassDist2D::ComputeFourierAmp()
|
|---|
| 390 | {
|
|---|
| 391 | if (fg_fourAmp) return; // job already done
|
|---|
| 392 | // We generate a random gaussian real field
|
|---|
| 393 | double sigma = 1.;
|
|---|
| 394 | // The following line fills the array by gaussian random numbers
|
|---|
| 395 | //--Replaced-- massDens = RandomSequence(RandomSequence::Gaussian, 0., sigma);
|
|---|
| 396 | // Can be replaced by
|
|---|
| 397 | DR48RandGen rg;
|
|---|
| 398 | for(sa_size_t ir=0; ir<massDens.NRows(); ir++) {
|
|---|
| 399 | for(sa_size_t jc=0; jc<massDens.NCols(); jc++) {
|
|---|
| 400 | massDens(ir, jc) = rg.Gaussian(sigma);
|
|---|
| 401 | }
|
|---|
| 402 | }
|
|---|
| 403 | // --- End of random filling
|
|---|
| 404 |
|
|---|
| 405 | // Compute fourier transform of the random gaussian field -> white noise
|
|---|
| 406 | FFTWServer ffts(true);
|
|---|
| 407 | ffts.setNormalize(true);
|
|---|
| 408 | ffts.FFTForward(massDens, fourAmp);
|
|---|
| 409 |
|
|---|
| 410 | // fourAmp represent 2-D fourier transform of a real input array.
|
|---|
| 411 | // The second half of the array along Y (matrix rows) contain
|
|---|
| 412 | // negative frequencies
|
|---|
| 413 | // double fnorm = 1./sqrt(2.*fourAmp.Size());
|
|---|
| 414 | // PUT smaller value for fnorm and check number of zeros
|
|---|
| 415 | double fnorm = 1.;
|
|---|
| 416 | // sa_size_t is large integer type
|
|---|
| 417 | for(sa_size_t ky=0; ky<fourAmp.NRows(); ky++) {
|
|---|
| 418 | double kyy = ky;
|
|---|
| 419 | if (ky > fourAmp.NRows()/2) kyy = fourAmp.NRows()-ky; // negative frequencies
|
|---|
| 420 | for(sa_size_t kx=0; kx<fourAmp.NCols(); kx++) {
|
|---|
| 421 | double wk = sqrt((double)(kx*kx+kyy*kyy));
|
|---|
| 422 | double amp = pkSpec(wk)*fnorm;
|
|---|
| 423 | fourAmp(ky, kx) *= amp; // renormalize fourier coeff using
|
|---|
| 424 | }
|
|---|
| 425 | }
|
|---|
| 426 | fg_fourAmp = true;
|
|---|
| 427 | cout << " MassDist2D::ComputeFourierAmp() done ..." << endl;
|
|---|
| 428 | }
|
|---|
| 429 |
|
|---|
| 430 | // Compute mass field from its Fourier Coefficient
|
|---|
| 431 | void MassDist2D::ComputeMassDens()
|
|---|
| 432 | {
|
|---|
| 433 | if (fg_massDens) return; // job already done
|
|---|
| 434 | if (!fg_fourAmp) ComputeFourierAmp(); // Check fourier amp generation
|
|---|
| 435 |
|
|---|
| 436 | // Backward fourier transform of the fourierAmp array
|
|---|
| 437 | FFTWServer ffts(true);
|
|---|
| 438 | ffts.setNormalize(true);
|
|---|
| 439 | ffts.FFTBackward(fourAmp, massDens, true);
|
|---|
| 440 | // We consider that massDens represents delta rho/rho
|
|---|
| 441 | // rho = (delta rho/rho + 1) * MeanDensity
|
|---|
| 442 | massDens += 1.;
|
|---|
| 443 | // We remove negative values
|
|---|
| 444 | sa_size_t npbz = 0;
|
|---|
| 445 | for (sa_size_t i=0; i<massDens.NRows(); i++)
|
|---|
| 446 | for (sa_size_t j=0; j<massDens.NCols(); j++)
|
|---|
| 447 | if (massDens(i,j) < 0.) { npbz++; massDens(i,j) = 0.; }
|
|---|
| 448 | massDens *= meanRho;
|
|---|
| 449 | cout << " MassDist2D::ComputeMassDens() done NbNeg=" << npbz << " / NPix=" << massDens.Size() << endl;
|
|---|
| 450 | }
|
|---|
| 451 |
|
|---|
| 452 | // Compute power spectrum as a function of wave number k
|
|---|
| 453 | // Output : power spectrum (profile histogram)
|
|---|
| 454 | HProf MassDist2D::ReconstructPk(int nbin)
|
|---|
| 455 | {
|
|---|
| 456 | // The second half of the array along Y (matrix rows) contain
|
|---|
| 457 | // negative frequencies
|
|---|
| 458 | int nbh = sqrt(2.0)*fourAmp.NCols();
|
|---|
| 459 | // The profile histogram will contain the mean value of FFT amplitude
|
|---|
| 460 | // as a function of wave-number k = sqrt((double)(kx*kx+ky*ky))
|
|---|
| 461 | if (nbin < 1) nbin = nbh/2;
|
|---|
| 462 | HProf hp(-0.5, nbh-0.5, nbin);
|
|---|
| 463 | hp.SetErrOpt(false);
|
|---|
| 464 |
|
|---|
| 465 | for(int ky=0; ky<fourAmp.NRows(); ky++) {
|
|---|
| 466 | double kyy = ky;
|
|---|
| 467 | if (ky > fourAmp.NRows()/2) kyy = fourAmp.NRows()-ky; // negative frequencies
|
|---|
| 468 | for(int kx=0; kx<fourAmp.NCols(); kx++) {
|
|---|
| 469 | double wk = sqrt((double)(kx*kx+kyy*kyy));
|
|---|
| 470 | complex<r_8> za = fourAmp(ky, kx);
|
|---|
| 471 | double amp = sqrt(za.real()*za.real()+za.imag()*za.imag());
|
|---|
| 472 | hp.Add(wk, amp);
|
|---|
| 473 | }
|
|---|
| 474 | }
|
|---|
| 475 | return hp;
|
|---|
| 476 | }
|
|---|
| 477 |
|
|---|
![(please configure the [header_logo] section in trac.ini)](/PI/chrome/site/your_project_logo.png){kind=logo}
