| 1 | /* ======================================================================== *\
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| 2 | !
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| 3 | ! *
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| 4 | ! * This file is part of MARS, the MAGIC Analysis and Reconstruction
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| 5 | ! * Software. It is distributed to you in the hope that it can be a useful
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| 6 | ! * and timesaving tool in analysing Data of imaging Cerenkov telescopes.
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| 7 | ! * It is distributed WITHOUT ANY WARRANTY.
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| 8 | ! *
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| 9 | ! * Permission to use, copy, modify and distribute this software and its
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| 10 | ! * documentation for any purpose is hereby granted without fee,
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| 11 | ! * provided that the above copyright notice appear in all copies and
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| 12 | ! * that both that copyright notice and this permission notice appear
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| 13 | ! * in supporting documentation. It is provided "as is" without express
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| 14 | ! * or implied warranty.
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| 15 | ! *
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| 16 | !
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| 17 | !
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| 18 | ! Author(s): Christoph Kolodziejski, 11/2004 <mailto:>
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| 19 | ! Author(s): Thomas Bretz, 11/2004 <mailto:tbretz@astro.uni-wuerzburg.de>
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| 20 | !
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| 21 | ! Copyright: MAGIC Software Development, 2004-2005
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| 22 | !
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| 23 | !
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| 24 | \* ======================================================================== */
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| 25 |
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| 26 | //////////////////////////////////////////////////////////////////////////////
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| 27 | //
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| 28 | // MHexagonalFT
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| 29 | //
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| 30 | // This is a class representating a (fast) fourier transformation explicitly
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| 31 | // for hexagonal geometries as described in astro-ph/0409388.
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| 32 | //
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| 33 | //
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| 34 | // WARNING:
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| 35 | // ========
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| 36 | // Be carefull using the fast transformation (Prepare())! The precalculation
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| 37 | // consumes a lot of memory. fPsi has the size of 2*n^4 (while n is the
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| 38 | // number of rows in fourier space). For the enhanced MAGIC camery fPsi has
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| 39 | // the size 27691682*sizeof(float) = 105.6MB (Std MAGIC: ~12MB)
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| 40 | //
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| 41 | // The runtime is more or less determined by the speed of accessing a
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| 42 | // huge amount of memory (see above) sequentially.
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| 43 | //
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| 44 | //
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| 45 | // Coordinate systems:
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| 46 | // ===================
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| 47 | //
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| 48 | // original hexagonal structure enhanced hexagonal structure
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| 49 | // ---------------------------- ----------------------------
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| 50 | //
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| 51 | // structure
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| 52 | // ---------
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| 53 | //
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| 54 | // h h h f f h h h f f
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| 55 | // h h h h f h h h h f
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| 56 | // h h h h h -----> h h h h h
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| 57 | // h h h h h h h h
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| 58 | // h h h h h h
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| 59 | // f f
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| 60 | // f
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| 61 | //
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| 62 | // numbering
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| 63 | // ---------
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| 64 | // d c b m n o p q r s
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| 65 | // e 4 3 a g h i j k l
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| 66 | // f 5 1 2 9 -----> b c d e f
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| 67 | // g 6 7 8 7 8 9 a
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| 68 | // h i j 4 5 6
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| 69 | // 2 3
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| 70 | // 1
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| 71 | //
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| 72 | // In reality the fourier space looks like because of symmetries:
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| 73 | //
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| 74 | // real part imaginary part
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| 75 | // --------- --------------
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| 76 | // m n o p o n m m n o 0 -o -n -m
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| 77 | // g h i i h g g h i -i -h -g
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| 78 | // b c d c b b c 0 -c -b
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| 79 | // 7 8 8 7 7 8 -8 -7
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| 80 | // 4 5 4 4 0 -4
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| 81 | // 2 2 2 -2
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| 82 | // 1 0
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| 83 | //
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| 84 | // column: GetK() row: GetM()
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| 85 | // -------------- -----------
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| 86 | // 6 5 4 3 2 1 0 0 1 2 3 4 5 6
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| 87 | // 5 4 3 2 1 0 0 1 2 3 4 5
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| 88 | // 4 3 2 1 0 0 1 2 3 4
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| 89 | // 3 2 1 0 0 1 2 3
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| 90 | // 2 1 0 0 1 2
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| 91 | // 1 0 0 1
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| 92 | // 0 0
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| 93 | //
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| 94 | // row: GetRow() (m+k) column: GetCol() (m-k)
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| 95 | // ------------------- ----------------------
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| 96 | // 6 6 6 6 6 6 6 -6 -4 -2 0 2 4 6
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| 97 | // 5 5 5 5 5 5 -5 -3 -1 1 3 5
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| 98 | // 4 4 4 4 4 -4 -2 0 2 4
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| 99 | // 3 3 3 3 -3 -1 1 3
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| 100 | // 2 2 2 -2 0 2
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| 101 | // 1 1 -1 1
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| 102 | // 0 0
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| 103 | //
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| 104 | //
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| 105 | // The coordinates of the pixels in the triangle are:
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| 106 | //
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| 107 | // Double_t dx; // Distance of too pixels in x
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| 108 | // Double_t dy; // Distance of to pixel rows in y
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| 109 | // Int_t idx; // Index of pixel in triangle (see above)
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| 110 | //
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| 111 | // const Float_t x = dx*GetCol(idx);
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| 112 | // const Float_t y = dy*Int_t(GetRow(idx)-2*GetNumRows()/3);
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| 113 | //
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| 114 | // You can use MGeomCam::GetPixelIdxXY(x, y) to get the corresponding index
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| 115 | // in space space.
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| 116 | //
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| 117 | //////////////////////////////////////////////////////////////////////////////
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| 118 | #include "MHexagonalFT.h"
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| 119 |
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| 120 | #include <TMath.h>
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| 121 |
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| 122 | #include "MLog.h"
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| 123 | #include "MLogManip.h"
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| 124 |
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| 125 | #include "MArrayD.h"
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| 126 |
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| 127 | ClassImp(MHexagonalFT);
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| 128 |
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| 129 | using namespace std;
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| 130 |
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| 131 | // ---------------------------------------------------------------------------
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| 132 | //
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| 133 | // Default Constructor - empty
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| 134 | //
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| 135 | MHexagonalFT::MHexagonalFT()
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| 136 | {
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| 137 | }
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| 138 |
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| 139 | // ---------------------------------------------------------------------------
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| 140 | //
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| 141 | // Default Constructor - num is the number of lines the fourier space has.
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| 142 | // It calls Prepare to fill the arrays with the necessary coefficients.
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| 143 | //
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| 144 | // Here are some simple rules to calculate parameters in a hexagonal space:
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| 145 | //
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| 146 | // Number of Rings (r) ---> Number of Pixels (p)
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| 147 | // p = 3*r*(r-1)+1
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| 148 | //
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| 149 | // Number of Pixels (p) ---> Number of Rings (r)
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| 150 | // p = (sqrt(9+12*(p-1))+3)/6
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| 151 | //
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| 152 | // Number of pixels at one border == number of rings (r)
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| 153 | // Row of border == number of rings (r)
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| 154 | //
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| 155 | // Number of rows to get a triangle: 3r-2
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| 156 | //
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| 157 | MHexagonalFT::MHexagonalFT(Int_t num)
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| 158 | {
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| 159 | Prepare(num);
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| 160 | }
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| 161 |
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| 162 | // ---------------------------------------------------------------------------
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| 163 | //
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| 164 | // Calculate the contents of: fM, fK, fP, fIdx and fPsi.
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| 165 | //
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| 166 | // While fPsi are the fourier coefficients, fM and fK are the hexagonal x and
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| 167 | // y coordinates of the pixel corresponding to the index i which is the
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| 168 | // common index of all arrays. fP is P(i,j) for all pixels.
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| 169 | //
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| 170 | // fIdx is also filled and used for reverse mapping. Due to the geometry
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| 171 | // the right and left side of the fourier space triangle has identical
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| 172 | // values. fIdx 'maps' the indices from the right to the left side.
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| 173 | //
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| 174 | void MHexagonalFT::Prepare(Int_t num)
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| 175 | {
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| 176 | fNumRows = num;
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| 177 |
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| 178 | fPsi.Set(num*num*num*num*2);
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| 179 |
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| 180 | Int_t lim = num*(num+1)/2;
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| 181 |
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| 182 | fM.Set(lim);
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| 183 | fK.Set(lim);
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| 184 | fP.Set(lim);
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| 185 | fIdx.Set(lim);
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| 186 |
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| 187 | for(int j=0; j<num; j++)
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| 188 | {
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| 189 | for(int n=0; n+j<num; n++)
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| 190 | {
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| 191 | int idx1 = (j+n)*(j+n+1)/2 + j;
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| 192 |
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| 193 | fM[idx1]=n;
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| 194 | fK[idx1]=j;
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| 195 |
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| 196 | fP[idx1]=P(j,n);
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| 197 |
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| 198 | for(int k=0; k<num; k++)
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| 199 | {
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| 200 | for(int m=0; m+k<num; m++)
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| 201 | {
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| 202 | const Double_t dx = TMath::Pi()*(m-k)/(num-1)/3;
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| 203 | const Double_t dy = TMath::Pi()*(m+k)/(num-1);
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| 204 |
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| 205 | const Double_t cos1 = TMath::Cos(dy*(j+n));
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| 206 | const Double_t cos2 = TMath::Cos(dy*j);
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| 207 | const Double_t cos3 = TMath::Cos(dy*n);
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| 208 |
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| 209 | const Double_t psire = 2*(
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| 210 | +cos1*TMath::Cos(dx*(j-n))
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| 211 | +cos2*TMath::Cos(dx*(j+2*n))
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| 212 | +cos3*TMath::Cos(dx*(2*j+n)));
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| 213 |
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| 214 | const Double_t psiim = 2*(
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| 215 | +cos1*TMath::Sin(dx*(j-n))
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| 216 | +cos2*TMath::Sin(dx*(j+2*n))
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| 217 | -cos3*TMath::Sin(dx*(2*j+n)));
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| 218 |
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| 219 | const Int_t idx3 = (k+m)*(k+m+1)/2 + k;
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| 220 | const Int_t id1 = idx1*lim + idx3;
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| 221 |
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| 222 | fPsi[id1*2] = psire;
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| 223 | fPsi[id1*2+1] = psiim;
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| 224 | }
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| 225 | }
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| 226 | }
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| 227 | }
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| 228 |
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| 229 | for (int idx1=0; idx1<lim; idx1++)
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| 230 | {
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| 231 | int n = fM[idx1];
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| 232 | int j = fK[idx1];
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| 233 |
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| 234 | int idx0;
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| 235 | for (idx0=0; idx0<lim; idx0++)
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| 236 | if (fM[idx0]==j && fK[idx0]==n)
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| 237 | break;
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| 238 |
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| 239 | fIdx[idx1]=idx0;
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| 240 | }
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| 241 |
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| 242 | }
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| 243 |
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| 244 | // ---------------------------------------------------------------------------
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| 245 | //
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| 246 | // Do a fast forward tranformation. Because all coefficients are
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| 247 | // precalculated, the tranformation is reduced to a simple pointer based
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| 248 | // loop over the coeffiecients multiplied with the corresponding input
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| 249 | // values.
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| 250 | //
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| 251 | // Parameters:
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| 252 | // inre: array storing the real part of the input (eg. pixel contents)
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| 253 | // outre: array storing the real part of the output
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| 254 | // outim: array storing the imaginary part of the output
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| 255 | //
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| 256 | // inre must be of the size of the fourier space triangle. The pixel
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| 257 | // contents must have been mapped into this new space with the proper
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| 258 | // pixel indices. The size of outre and outim is set accordingly.
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| 259 | //
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| 260 | // After initialization (Prepare()) you can get the size of the arrays with
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| 261 | // GetNumKnots()
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| 262 | //
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| 263 | // For the definition of the coordinate system see class description
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| 264 | //
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| 265 | void MHexagonalFT::TransformFastFWD(const MArrayD &inre, MArrayD &outre,
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| 266 | MArrayD &outim) const
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| 267 | {
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| 268 | const UInt_t num = fP.GetSize();
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| 269 |
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| 270 | if (inre.GetSize()!=num)
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| 271 | {
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| 272 | cout << "ERROR - MHexagonalFT prepared for different size." << endl;
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| 273 | return;
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| 274 | }
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| 275 |
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| 276 | outre.Set(num);
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| 277 | outim.Set(num);
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| 278 |
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| 279 | const Int_t cnt = 108*(fNumRows-1)*(fNumRows-1);
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| 280 |
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| 281 | const Float_t *endp = fP.GetArray()+num;
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| 282 |
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| 283 | for (UInt_t idx1=0; idx1<num; idx1++)
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| 284 | {
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| 285 | if (fK[idx1]>fM[idx1])
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| 286 | continue;
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| 287 |
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| 288 | Double_t sumre=0;
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| 289 | Double_t sumim=0;
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| 290 |
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| 291 | Float_t *psi = fPsi.GetArray() + idx1*num*2;
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| 292 | Float_t *p = fP.GetArray();
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| 293 | Double_t *re = inre.GetArray();
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| 294 |
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| 295 | // 1st access to psi: const Float_t psire = *psi++;
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| 296 | // 2nd access to psi: const Float_t psiim = *psi++;
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| 297 | // sumre += f * *psire;
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| 298 | // sumim += f * *psiim;
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| 299 | while (p<endp)
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| 300 | {
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| 301 | const Double_t f = *p++ * *re++;
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| 302 |
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| 303 | sumre += f * *psi++;
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| 304 | sumim += f * *psi++;
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| 305 | }
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| 306 |
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| 307 | const Double_t factor2 = fP[idx1]/cnt;
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| 308 |
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| 309 | outre[fIdx[idx1]] = (outre[idx1] = factor2 * sumre);
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| 310 | outim[fIdx[idx1]] = -(outim[idx1] = -factor2 * sumim);
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| 311 | }
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| 312 | }
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| 313 |
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| 314 | // ---------------------------------------------------------------------------
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| 315 | //
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| 316 | // Do a fast backward tranformation. Because all coefficients are
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| 317 | // precalculated, the tranformation is reduced to a simple pointer based
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| 318 | // loop over the coeffiecients multiplied with the corresponding input
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| 319 | // values.
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| 320 | //
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| 321 | // Parameters:
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| 322 | // inre: outre of TransformFastBwd
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| 323 | // inim: outim of TransformFastBwd
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| 324 | // outre: backward tranformed real part of the resulting
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| 325 | //
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| 326 | // inre and inim must be of the size of the fourier space triangle. The
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| 327 | // pixel contents must have been mapped into this new space with the proper
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| 328 | // pixel indices. The size of outre is set accordingly.
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| 329 | //
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| 330 | // After initialization (Prepare()) you can get the size of the arrays with
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| 331 | // GetNumKnots()
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| 332 | //
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| 333 | // For the definition of the coordinate system see class description
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| 334 | //
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| 335 | void MHexagonalFT::TransformFastBWD(const MArrayD &inre, const MArrayD &inim,
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| 336 | MArrayD &outre) const
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| 337 | {
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| 338 | const UInt_t num = fP.GetSize();
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| 339 |
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| 340 | // Sanity check: check size of arrays
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| 341 | if (inre.GetSize()!=num)
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| 342 | {
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| 343 | cout << "ERROR - MHexagonalFT prepared for different size." << endl;
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| 344 | return;
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| 345 | }
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| 346 | if (inim.GetSize()!=num)
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| 347 | {
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| 348 | cout << "ERROR - MHexagonalFT prepared for different size." << endl;
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| 349 | return;
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| 350 | }
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| 351 | outre.Set(num);
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| 352 |
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| 353 | const Double_t *endre = inre.GetArray()+num;
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| 354 |
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| 355 | for (UInt_t idx1=0; idx1<num; idx1++)
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| 356 | {
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| 357 | Float_t *psi = fPsi.GetArray() + idx1*num*2;
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| 358 | Double_t *im = inim.GetArray();
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| 359 | Double_t *re = inre.GetArray();
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| 360 |
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| 361 | Double_t sumre=0;
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| 362 | while (re<endre)
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| 363 | {
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| 364 | const Float_t psire = *psi++;
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| 365 | const Float_t psiim = *psi++;
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| 366 |
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| 367 | sumre += *re++ * psire - *im++ * psiim;
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| 368 | }
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| 369 |
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| 370 | outre[idx1] = sumre;
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| 371 | }
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| 372 | }
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| 373 |
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| 374 | // ---------------------------------------------------------------------------
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| 375 | //
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| 376 | // This is a slow (direct) version of the tranformation. It is identical
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| 377 | // for forward and backward tranformation.
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| 378 | //
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| 379 | // The whole calculation is done straight forward without any precalculation.
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| 380 | //
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| 381 | // Parameters:
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| 382 | // inre: real part of input
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| 383 | // inim: imaginary part of input
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| 384 | // outre: real part of output
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| 385 | // outim: imaginary part of output
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| 386 | // fwd: kTRUE for forward, kFALSE for backward transformations
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| 387 | //
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| 388 | // After initialization (Prepare()) you can get the size of the arrays with
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| 389 | // GetNumKnots()
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| 390 | //
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| 391 | // For the definition of the coordinate system see class description
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| 392 | //
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| 393 | // It is currently not tested!
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| 394 | //
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| 395 | void MHexagonalFT::TransformSlow(const MArrayD &inre, const MArrayD &inim,
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| 396 | MArrayD &outre, MArrayD &outim,
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| 397 | Bool_t fwd)
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| 398 | {
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| 399 | static const Double_t fgSqrt3 = TMath::Sqrt(3.);
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| 400 | static const Double_t fgTan30 = TMath::Tan(30*TMath::DegToRad())*3;
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| 401 |
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| 402 | Int_t num = (Int_t)TMath::Sqrt((Float_t)inim.GetSize());
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| 403 | Int_t cnt = 108*(num-1)*(num-1);
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| 404 | Int_t inv = fwd?-1:1;
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| 405 |
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| 406 | // FIXME: For p(j,n)
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| 407 | fNumRows = num;
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| 408 |
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| 409 | for(int j=0; j<num; j++)
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| 410 | {
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| 411 | for(int n=0; n+j<num; n++)
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| 412 | {
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| 413 | if (j-n>0 && fwd)
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| 414 | continue;
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| 415 |
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| 416 | Double_t sumre=0;
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| 417 | Double_t sumim=0;
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| 418 |
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| 419 | for(int k=0; k<num; k++)
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| 420 | {
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| 421 | for(int m=0; m+k<num; m++)
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| 422 | {
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| 423 | Double_t dx = 0.5*(m-k)/num;
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| 424 | Double_t dy = 0.5*(m+k)/num*fgTan30;
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| 425 |
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| 426 | dx *= TMath::TwoPi()/3;
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| 427 | dy *= TMath::TwoPi()/fgSqrt3;
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| 428 |
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| 429 | const Double_t cos1 = TMath::Cos(dy*(j+n));
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| 430 | const Double_t cos2 = TMath::Cos(dy*j);
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| 431 | const Double_t cos3 = TMath::Cos(dy*n);
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| 432 |
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| 433 | //Alternatie nach Paper:
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| 434 | const Double_t psire = 2*(
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| 435 | +cos1*TMath::Cos(dx*(j-n))
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| 436 | +cos2*TMath::Cos(dx*(j+2*n))
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| 437 | +cos3*TMath::Cos(dx*(2*j+n)));
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| 438 |
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| 439 | const Double_t psiim = 2*inv*(
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| 440 | +cos1*TMath::Sin(dx*(j-n))
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| 441 | +cos2*TMath::Sin(dx*(j+2*n))
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| 442 | -cos3*TMath::Sin(dx*(2*j+n)));
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| 443 |
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| 444 | const Double_t factor = (fwd==1?P(k,m):1.);
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| 445 |
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| 446 | sumre += factor * (inre[k*num+m]*psire - inim[k*num+m]*psiim);
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| 447 | sumim += factor * (inre[k*num+m]*psiim + inim[k*num+m]*psire);
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| 448 | }
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| 449 | }
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| 450 |
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| 451 | const Double_t factor = (fwd==1?P(j,n)/cnt:1.);
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| 452 |
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| 453 | outre[j*num+n] = factor * sumre;
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| 454 | outim[j*num+n] = factor * sumim;
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| 455 |
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| 456 | if (fwd)
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| 457 | {
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| 458 | outre[n*num+j] = factor * sumre;
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| 459 | outim[n*num+j] = -factor * sumim;
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| 460 | }
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| 461 | }
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| 462 | }
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| 463 | }
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| 464 |
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| 465 |
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