Remez tested

tests/Grid_remez.cc

@@ -0,0 +1,103 @@
+#include <Grid.h>
+
+using namespace std;
+using namespace Grid;
+using namespace Grid::QCD;
+
+class MultiShiftFunction {
+public:
+  std::vector<double> poles;
+  std::vector<double> residues;
+  double norm;
+  double lo,hi;
+  MultiShiftFunction(int n,double _lo,double _hi): poles(n), residues(n), lo(_lo), hi(_hi) {;};
+  double approx(double x);
+  void csv(std::ostream &out);
+  void gnuplot(std::ostream &out);
+};
+double MultiShiftFunction::approx(double x)
+{
+  double a = norm;
+  for(int n=0;n<poles.size();n++){
+    a = a + residues[n]/(x+poles[n]);
+  }
+  return a;
+}
+void MultiShiftFunction::gnuplot(std::ostream &out)
+{
+  out<<"f(x) = "<<norm<<"";
+  for(int n=0;n<poles.size();n++){
+    out<<"+("<<residues[n]<<"/(x+"<<poles[n]<<"))";
+  }
+  out<<";"<<std::endl;
+}
+void MultiShiftFunction::csv(std::ostream &out)
+{
+  for (double x=lo; x<hi; x*=1.05) {
+    double f = approx(x);
+    double r = sqrt(x);
+    out<< x<<","<<r<<","<<f<<","<<r-f<<std::endl;
+  }
+  return;
+}
+
+int main (int argc, char ** argv)
+{
+  Grid_init(&argc,&argv);
+
+  std::cout << "Testing Remez"<<std::endl;
+
+  double     lo=0.01;
+  double     hi=1.0;
+  int precision=64;
+  int    degree=10;
+  AlgRemez remez(0.001,1.0,precision);
+
+  ////////////////////////////////////////
+  // sqrt and inverse sqrt
+  ////////////////////////////////////////
+  MultiShiftFunction Sqrt(degree,lo,hi);
+  MultiShiftFunction InvSqrt(degree,lo,hi);
+
+  MultiShiftFunction SqrtSqrt(degree,lo,hi);
+  MultiShiftFunction InvSqrtSqrt(degree,lo,hi);
+
+
+  std::cout << "Generating degree "<<degree<<" for x^(1/2)"<<std::endl;
+  remez.generateApprox(degree,1,2);
+  remez.getPFE (&   Sqrt.residues[0],&   Sqrt.poles[0],&   Sqrt.norm);
+  remez.getIPFE(&InvSqrt.residues[0],&InvSqrt.poles[0],&InvSqrt.norm);
+
+  std::cout << "Generating degree "<<degree<<" for x^(1/4)"<<std::endl;
+  remez.generateApprox(degree,1,4);
+  remez.getPFE (&SqrtSqrt.residues[0],&SqrtSqrt.poles[0],&SqrtSqrt.norm);
+  remez.getIPFE(&InvSqrtSqrt.residues[0],&InvSqrtSqrt.poles[0],&InvSqrtSqrt.norm);
+  
+  ofstream gnuplot(std::string("Sqrt.gnu"),std::ios::out|std::ios::trunc);
+  Sqrt.gnuplot(gnuplot);
+
+  ofstream gnuplot_inv(std::string("InvSqrt.gnu"),std::ios::out|std::ios::trunc);
+  InvSqrt.gnuplot(gnuplot);
+
+  double x=0.6789;
+  double sx=sqrt(x);
+  double ssx=sqrt(sx);
+  double isx=1.0/sx;
+  double issx=1.0/ssx;
+
+  double asx  =Sqrt.approx(x);
+  double assx =SqrtSqrt.approx(x);
+  double aisx =InvSqrt.approx(x);
+  double aissx=InvSqrtSqrt.approx(x);
+
+  std::cout << "x^(1/2) : "<<sx<<" "<<asx<<std::endl;
+  std::cout << "x^(1/4) : "<<ssx<<" "<<assx<<std::endl;
+  std::cout << "x^(-1/2): "<<isx<<" "<<aisx<<std::endl;
+  std::cout << "x^(-1/4): "<<issx<<" "<<aissx<<std::endl;
+  assert(fabs(sx-asx)<1.0e-6);
+  assert(fabs(ssx-assx)<1.0e-6);
+  assert(fabs(isx-aisx)<1.0e-6);
+  assert(fabs(issx-aissx)<1.0e-6);
+
+  Grid_finalize();
+}

tests/Makefile.am

@@ -5,7 +5,7 @@ AM_LDFLAGS = -L$(top_builddir)/lib
 #
 # Test code
 #
-bin_PROGRAMS = Grid_main Grid_stencil Grid_nersc_io Grid_cshift Grid_gamma  Grid_simd Grid_rng
+bin_PROGRAMS = Grid_main Grid_stencil Grid_nersc_io Grid_cshift Grid_gamma  Grid_simd Grid_rng Grid_remez
 
 Grid_main_SOURCES = Grid_main.cc
 Grid_main_LDADD = -lGrid
@@ -13,6 +13,9 @@ Grid_main_LDADD = -lGrid
 Grid_rng_SOURCES = Grid_rng.cc
 Grid_rng_LDADD = -lGrid
 
+Grid_remez_SOURCES = Grid_remez.cc
+Grid_remez_LDADD = -lGrid
+
 Grid_nersc_io_SOURCES = Grid_nersc_io.cc
 Grid_nersc_io_LDADD = -lGrid