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