zpinv

Source: tests/dense/pinv.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/dense/Matrix.h>

// Algorithms.
#include <myramath/dense/pinv.h>
#include <myramath/dense/gemm.h>
#include <myramath/dense/hermitian.h>
#include <myramath/dense/frobenius.h>

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

using namespace myra;

namespace {

template<class Number> void test(int I, int J, int K, typename ReflectPrecision<Number>::type tolerance)
  {
  myra::out() << typestring<Number>() << std::endl;
  typedef typename ReflectPrecision<Number>::type Precision;
  // Construct random A with size IxJ and rank K
  auto U = Matrix<Number>::random(I,K);
  auto V = Matrix<Number>::random(K,J);  
  auto A = U*V;
  // Compute B = pinv(A)
  auto B = pinv(A);
  // Examine the psuedoinverse properties:
  Precision error1 = frobenius(A*B*A - A);
  Precision error2 = frobenius(B*A*B - B);
  Precision error3 = frobenius(A*B - hermitian(B)*hermitian(A));
  Precision error4 = frobenius(B*A - hermitian(A)*hermitian(B));
  myra::out() << "  |A*B*A - A| = " << error1 << std::endl;
  myra::out() << "  |B*A*B - B| = " << error2 << std::endl;
  myra::out() << "  |A*B - B'A'| = " << error3 << std::endl;
  myra::out() << "  |B*A - A'B'| = " << error4 << std::endl;
  // Assert everything.
  REQUIRE(error1 < tolerance);  
  REQUIRE(error2 < tolerance);
  REQUIRE(error3 < tolerance);
  REQUIRE(error4 < tolerance);
  }

} // namespace

ADD_TEST("spinv","[dense]")
  { test<NumberS>(10,12,4,1.0e-4f); }

ADD_TEST("dpinv","[dense]")
  { test<NumberD>(10,12,4,1.0e-10); }

ADD_TEST("cpinv","[dense]")
  { test<NumberC>(10,12,4,1.0e-4f); }

ADD_TEST("zpinv","[dense]")
  { test<NumberZ>(10,12,4,1.0e-10); }

Results: [PASS]

std::complex<double>
  |A*B*A - A| = 6.26435e-15
  |B*A*B - B| = 1.90038e-16
  |A*B - B'A'| = 1.51397e-15
  |B*A - A'B'| = 4.7779e-15

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