// Copyright 2015 Conrad Sanderson (http://conradsanderson.id.au)
// Copyright 2015 National ICT Australia (NICTA)
// 
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
// http://www.apache.org/licenses/LICENSE-2.0
// 
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
// ------------------------------------------------------------------------


#include <armadillo>
#include "catch.hpp"

using namespace arma;


TEST_CASE("decomp_eig_gen_1")
  {
  mat A = 
    "\
     0.061198   0.201990   0.019678  -0.493936  -0.126745;\
     0.437242   0.058956  -0.149362  -0.045465   0.296153;\
    -0.492474  -0.031309   0.314156   0.419733   0.068317;\
     0.336352   0.411541   0.458476  -0.393139  -0.135040;\
     0.239585  -0.428913  -0.406953  -0.291020  -0.353768;\
    ";
  
  cx_vec eigvals1 =
    {
    cx_double(-0.431507827005653, +0.336567219978257),
    cx_double(-0.431507827005653, -0.336567219978257),
    cx_double( 0.509611570246060, +0.000000000000000),
    cx_double( 0.020403541882623, +0.255686097698784),
    cx_double( 0.020403541882623, -0.255686097698784)
    };
  
  cx_vec eigvals2 = eig_gen(A);
  
  cx_vec eigvals3;
  bool status = eig_gen(eigvals3, A);
  
  cx_vec eigvals4;
  cx_mat eigvecs4;
  eig_gen(eigvals4, eigvecs4, A);
  
  cx_vec  eigvals5;
  cx_mat leigvecs5;
  cx_mat reigvecs5;
  eig_gen(eigvals5, leigvecs5, reigvecs5, A);
  
  cx_mat B  =            eigvecs4   * diagmat(eigvals4) *   inv( eigvecs4);
  
  cx_mat Cl = inv(trans(leigvecs5)) * diagmat(eigvals5) * trans(leigvecs5);
  cx_mat Cr =           reigvecs5   * diagmat(eigvals5) *   inv(reigvecs5);
  
  REQUIRE( status == true );
  REQUIRE( accu(abs(eigvals2 - eigvals1)) == Approx(0.0).epsilon(0.0001) );
  REQUIRE( accu(abs(eigvals3 - eigvals1)) == Approx(0.0).epsilon(0.0001) );
  REQUIRE( accu(abs(eigvals4 - eigvals1)) == Approx(0.0).epsilon(0.0001) );
  REQUIRE( accu(abs(eigvals5 - eigvals1)) == Approx(0.0).epsilon(0.0001) );
  REQUIRE( accu(abs(A        - B       )) == Approx(0.0).epsilon(0.0001) );
  REQUIRE( accu(abs(A        - Cl      )) == Approx(0.0).epsilon(0.0001) );
  REQUIRE( accu(abs(A        - Cr      )) == Approx(0.0).epsilon(0.0001) );
  }



TEST_CASE("decomp_eig_gen_2")
  {
  cx_mat A = 
    { 
    { cx_double( 0.111205, +0.074101), cx_double(-0.225872, -0.068474), cx_double(-0.192660, +0.236887), cx_double( 0.355204, -0.355735) },
    { cx_double( 0.119869, +0.217667), cx_double(-0.412722, +0.366157), cx_double( 0.069916, -0.222238), cx_double( 0.234987, -0.072355) },
    { cx_double( 0.003791, +0.183253), cx_double(-0.212887, -0.172758), cx_double( 0.168689, -0.393418), cx_double( 0.008795, -0.289654) },
    { cx_double(-0.331639, -0.166660), cx_double( 0.436969, -0.313498), cx_double(-0.431574, +0.017421), cx_double(-0.104165, +0.145246) }
    };

  cx_vec eigvals1 =
    {
    cx_double(-0.47418, +0.60377),
    cx_double( 0.15084, -0.44209),
    cx_double(-0.15790, -0.35629),
    cx_double( 0.24426, +0.38670)
    };

  cx_vec eigvals2 = eig_gen(A);
  
  cx_vec eigvals3;
  bool status = eig_gen(eigvals3, A);
  
  cx_vec eigvals4;
  cx_mat eigvecs4;
  eig_gen(eigvals4, eigvecs4, A);
  
  cx_vec  eigvals5;
  cx_mat leigvecs5;
  cx_mat reigvecs5;
  eig_gen(eigvals5, leigvecs5, reigvecs5, A);
  
  cx_mat B  =            eigvecs4   * diagmat(eigvals4) *   inv( eigvecs4);

  cx_mat Cl = inv(trans(leigvecs5)) * diagmat(eigvals5) * trans(leigvecs5);
  cx_mat Cr =           reigvecs5   * diagmat(eigvals5) *   inv(reigvecs5);
  
  REQUIRE( status == true );
  REQUIRE( accu(abs(eigvals2 - eigvals1)) == Approx(0.0).epsilon(0.0001) );
  REQUIRE( accu(abs(eigvals3 - eigvals1)) == Approx(0.0).epsilon(0.0001) );
  REQUIRE( accu(abs(eigvals4 - eigvals1)) == Approx(0.0).epsilon(0.0001) );
  REQUIRE( accu(abs(eigvals5 - eigvals1)) == Approx(0.0).epsilon(0.0001) );
  REQUIRE( accu(abs(A        - B       )) == Approx(0.0).epsilon(0.0001) );
  REQUIRE( accu(abs(A        - Cl      )) == Approx(0.0).epsilon(0.0001) );
  REQUIRE( accu(abs(A        - Cr      )) == Approx(0.0).epsilon(0.0001) );
  }



TEST_CASE("decomp_eig_gen_3")
  {
  mat A(5,5,fill::randu);
  
  cx_vec eigvals(10,     fill::randu);
  cx_mat eigvecs(10, 10, fill::randu);
  
  A(0,0) = datum::inf;
  bool status = eig_gen(eigvals, eigvecs, A);
  
  REQUIRE( status         == false    );
  REQUIRE( eigvals.n_elem == uword(0) );
  REQUIRE( eigvecs.n_elem == uword(0) );
  }



TEST_CASE("decomp_eig_gen_4")
  {
  mat A(5,6,fill::randu);
  
  cx_vec eigvals;
  cx_mat eigvecs;
  
  REQUIRE_THROWS( eig_gen(eigvals, eigvecs, A) );
  }