DWT working and tested

examples/Makefile.am

@@ -9,6 +9,7 @@ endif
 noinst_PROGRAMS =           \
     exCompiledDoubleFunction\
     exDerivative            \
+    exDWT                   \
     exFit                   \
     exFitSample             \
     exIntegrator            \
@@ -30,6 +31,10 @@ exDerivative_SOURCES              = exDerivative.cpp
 exDerivative_CXXFLAGS             = $(COM_CXXFLAGS)
 exDerivative_LDFLAGS              = -L../lib/.libs -lLatAnalyze
 
+exDWT_SOURCES                     = exDWT.cpp
+exDWT_CXXFLAGS                    = $(COM_CXXFLAGS)
+exDWT_LDFLAGS                     = -L../lib/.libs -lLatAnalyze
+
 exFit_SOURCES                     = exFit.cpp
 exFit_CXXFLAGS                    = $(COM_CXXFLAGS)
 exFit_LDFLAGS                     = -L../lib/.libs -lLatAnalyze

examples/exDWT.cpp

@@ -0,0 +1,28 @@
+#include <LatAnalyze/Numerical/DWT.hpp>
+
+using namespace std;
+using namespace Latan;
+
+int main(void)
+{
+    DVec                  data, dataRec;
+    vector<DWT::DWTLevel> dataDWT;
+    DWT                   dwt(DWTFilters::db3);
+
+    cout << "-- random data" << endl;
+    data.setRandom(16);
+    cout << data.transpose() << endl;
+    cout << "-- compute Daubechies 3 DWT" << endl;
+    dataDWT = dwt.forward(data, 4);
+    for (unsigned int l = 0; l < dataDWT.size(); ++l)
+    {
+        cout << "* level " << l << endl;
+        cout << "L= " << dataDWT[l].first.transpose() << endl;
+        cout << "H= " << dataDWT[l].second.transpose() << endl;
+    }
+    cout << "-- check inverse DWT" << endl;
+    dataRec = dwt.backward(dataDWT);
+    cout << "rel diff = " << 2.*(data - dataRec).norm()/(data + dataRec).norm() << endl;
+
+    return EXIT_SUCCESS;
+}

lib/Numerical/DWT.cpp

@@ -32,26 +32,106 @@ DWT::DWT(const DWTFilter &filter)
 {}
 
 // convolution primitive ///////////////////////////////////////////////////////
-DVec DWT::filterConvolution(const DVec &data, const DWTFilter &filter, 
+void DWT::filterConvolution(DVec &out, const DVec &data, 
-                            const Index offset)
+                            const std::vector<double> &filter, const Index offset)
 {
-    DVec res(data.size());
+    Index n = data.size(), nf = n*filter.size();
 
-    return res;
+    out.resize(n);
+    out.fill(0.);
+    for (unsigned int i = 0; i < filter.size(); ++i)
+    {
+        FOR_VEC(out, j)
+        {
+            out(j) += filter[i]*data((j + i + nf - offset) % n);
+        }
+    }
+}
+
+// downsampling/upsampling primitives //////////////////////////////////////////
+void DWT::downsample(DVec &out, const DVec &in)
+{
+    if (out.size() < in.size()/2)
+    {
+        LATAN_ERROR(Size, "output vector smaller than half the input vector size");
+    }
+    for (Index i = 0; i < in.size(); i += 2)
+    {
+        out(i/2) = in(i);
+    }
+}
+
+void DWT::upsample(DVec &out, const DVec &in)
+{
+    if (out.size() < 2*in.size())
+    {
+        LATAN_ERROR(Size, "output vector smaller than twice the input vector size");
+    }
+    out.segment(0, 2*in.size()).fill(0.);
+    for (Index i = 0; i < in.size(); i ++)
+    {
+        out(2*i) = in(i);
+    }
 }
 
 // DWT /////////////////////////////////////////////////////////////////////////
 std::vector<DWT::DWTLevel> 
 DWT::forward(const DVec &data, const unsigned int level) const
 {
-    std::vector<DWT::DWTLevel> dwt(level);
+    std::vector<DWTLevel> dwt(level);
+    DVec                  *finePt = const_cast<DVec *>(&data);
+    DVec                  tmp; 
+    Index                 n = data.size(), o = filter_.fwdL.size()/2, minSize;
+
+    minSize = 1;
+    for (unsigned int l = 0; l < level; ++l) minSize *= 2;
+    if (n < minSize)
+    {
+        LATAN_ERROR(Size, "data vector too small for a " + strFrom(level) 
+                          + "-level DWT (data size is " + strFrom(n) + ")");
+    }
+    for (unsigned int l = 0; l < level; ++l)
+    {
+        n /= 2;
+        dwt[l].first.resize(n);
+        dwt[l].second.resize(n);
+        filterConvolution(tmp, *finePt, filter_.fwdL, o);
+        downsample(dwt[l].first, tmp);
+        filterConvolution(tmp, *finePt, filter_.fwdH, o);
+        downsample(dwt[l].second, tmp);
+        finePt = &dwt[l].first;
+    }
 
     return dwt;
 }
 
 DVec DWT::backward(const std::vector<DWTLevel>& dwt) const
 {
-    DVec res;
+    unsigned int level = dwt.size();
+    Index        n = dwt.back().second.size(), o = filter_.bwdL.size()/2 - 1;
+    DVec         res, tmp, conv;
+
+    res = dwt.back().first;
+    for (int l = level - 2; l >= 0; --l)
+    {
+        n *= 2;
+        if (dwt[l].second.size() != n)
+        {
+            LATAN_ERROR(Size, "DWT result size mismatch");
+        }
+    }
+    n = dwt.back().second.size();
+    for (int l = level - 1; l >= 0; --l)
+    {
+        n *= 2;
+        tmp.resize(n);
+        upsample(tmp, res);
+        filterConvolution(conv, tmp, filter_.bwdL, o);
+        res = conv;
+        upsample(tmp, dwt[l].second);
+        filterConvolution(conv, tmp, filter_.bwdH, o);
+        res += conv;
+    }
 
     return res;
 }

lib/Numerical/DWT.hpp

@@ -38,8 +38,11 @@ public:
     // destructor
     virtual ~DWT(void) = default;
     // convolution primitive
-    static DVec filterConvolution(const DVec &data, const DWTFilter &filter,
+    static void filterConvolution(DVec &out, const DVec &data, 
-                                  const Index offset);
+                                  const std::vector<double> &filter, const Index offset);
+    // downsampling/upsampling primitives
+    static void downsample(DVec &out, const DVec &in);
+    static void upsample(DVec &out, const DVec &in);
     // DWT
     std::vector<DWTLevel> forward(const DVec &data, const unsigned int level) const;
     DVec                  backward(const std::vector<DWTLevel>& dwt) const;