zrotate1

Source: tests/dense/rotate1.cpp

// ========================================================================= //
// This file is part of MyraMath, copyright (c) 2014-2019 by Ryan A Chilton  //
// and distributed by MyraCore, LLC. See LICENSE.txt for license terms.      //
// ========================================================================= //

// Containers.
#include <myramath/utility/Number.h>
#include <myramath/dense/Matrix.h>
#include <myramath/dense/Vector.h>
#include <myramath/dense/VectorRange.h>
#include <myramath/dense/MatrixRange.h>

// Algorithms.
#include <myramath/dense/gemv.h>
#include <myramath/dense/gemm.h>
#include <myramath/dense/rotate.h>
#include <myramath/dense/frobenius.h>

// Reporting.
#include <tests/myratest.h>

using namespace myra;

namespace {

template<class Number> void test(typename ReflectPrecision<Number>::type tolerance) 
  {
  // Form random vector x, then compute a givens1() rotation to zero x(1).
  typedef typename ReflectPrecision<Number>::type Precision;
  auto x = Vector<Number>::random(2);
  std::pair<Number,Number> cs = rotate1(x(0),x(1));
  Number c = cs.first;
  Number s = cs.second;
  // Form G = [c s; -s' c], apply rotation y=G*x.
  auto G = Matrix<Number>::fill_rmajor(2,2, {c,s,-conjugate(s),c});
  auto I = Matrix<Number>::identity(2);
  auto y = G*x;
  // Verify G'G is identity.  
  Precision G_error = frobenius(gemm(G,'H',G)-I);
  myra::out() << "|G'G-I| = " << G_error << std::endl;  
  REQUIRE(G_error < tolerance);
  // Verify y(1) is zero. 
  Precision y_error = scalar_norm1(y(1));
  myra::out() << "|(G*x)(1)| = " << y_error << std::endl;
  REQUIRE(y_error < tolerance);
  }

} // namespace

ADD_TEST("srotate1","[dense][lapack]")
  { test<NumberS>(1.0e-5f); }
  
ADD_TEST("drotate1","[dense][lapack]")
  { test<NumberD>(1.0e-10); }

ADD_TEST("crotate1","[dense][lapack]")
  { test<NumberC>(1.0e-5f); }

ADD_TEST("zrotate1","[dense][lapack]")
  { test<NumberZ>(1.0e-10); }

Results: [PASS]

|G'G-I| = 3.6015e-18
|(G*x)(1)| = 1.14439e-16

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