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// SPDX-License-Identifier: Apache-2.0
//
// Copyright 2011-2017 Ryan Curtin (http://www.ratml.org/)
// Copyright 2017 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("fn_eigs_gen_odd_test")
  {
  const uword n_rows = 10;
  const uword n_eigval = 5;
  const uword n_trials = 10;
  uword count = 0;

  for(uword trial=0; trial < n_trials; ++trial)
    {
    sp_mat m;
    m.sprandu(n_rows, n_rows, 0.3);
    mat d(m);

    // Eigendecompose, getting first 5 eigenvectors.
    Col<cx_double> sp_eigval;
    Mat<cx_double> sp_eigvec;
    const bool status_sparse = eigs_gen(sp_eigval, sp_eigvec, m, n_eigval);

    // Do the same for the dense case.
    Col<cx_double> eigval;
    Mat<cx_double> eigvec;
    const bool status_dense = eig_gen(eigval, eigvec, d);

    if( (status_sparse == false) || (status_dense == false) )  { continue; }  else  { ++count; }

    uvec used(n_rows, fill::zeros);

    for(uword i=0; i < n_eigval; ++i)
      {
      // Sorting these is difficult.
      // Find which one is the likely dense eigenvalue.
      uword dense_eval = n_rows + 1;
      for(uword k = 0; k < n_rows; ++k)
        {
        if ((std::abs(cx_double(sp_eigval(i)).real() - eigval(k).real()) < 1e-4) &&
            (std::abs(cx_double(sp_eigval(i)).imag() - eigval(k).imag()) < 1e-4) &&
            (used(k) == 0))
          {
          dense_eval = k;
          used(k) = 1;
          break;
          }
        }

      REQUIRE( dense_eval != n_rows + 1 );

      REQUIRE( std::abs(sp_eigval(i)) == Approx(std::abs(eigval(dense_eval))).margin(0.1) );
      for(uword j = 0; j < n_rows; ++j)
        {
        REQUIRE( std::abs(sp_eigvec(j, i)) == Approx(std::abs(eigvec(j, dense_eval))).margin(0.1) );
        }
      }
    }

  REQUIRE(count > 0);
  }

TEST_CASE("fn_eigs_gen_even_test")
  {
  const uword n_rows = 10;
  const uword n_eigval = 4;
  const uword n_trials = 10;
  uword count = 0;

  for(uword trial=0; trial < n_trials; ++trial)
    {
    sp_mat m;
    m.sprandu(n_rows, n_rows, 0.3);
    sp_mat z(5, 5);
    z.sprandu(5, 5, 0.5);
    m.submat(2, 2, 6, 6) += 5 * z;
    mat d(m);

    // Eigendecompose, getting first 4 eigenvectors.
    Col<cx_double> sp_eigval;
    Mat<cx_double> sp_eigvec;
    const bool status_sparse = eigs_gen(sp_eigval, sp_eigvec, m, n_eigval);

    // Do the same for the dense case.
    Col<cx_double> eigval;
    Mat<cx_double> eigvec;
    const bool status_dense = eig_gen(eigval, eigvec, d);

    if( (status_sparse == false) || (status_dense == false) )  { continue; }  else  { ++count; }

    uvec used(n_rows, fill::zeros);

    for(uword i=0; i < n_eigval; ++i)
      {
      // Sorting these is difficult.
      // Find which one is the likely dense eigenvalue.
      uword dense_eval = n_rows + 1;
      for(uword k = 0; k < n_rows; ++k)
        {
        if ((std::abs(cx_double(sp_eigval(i)).real() - eigval(k).real()) < 1e-4) &&
            (std::abs(cx_double(sp_eigval(i)).imag() - eigval(k).imag()) < 1e-4) &&
            (used(k) == 0))
          {
          dense_eval = k;
          used(k) = 1;
          break;
          }
        }

      REQUIRE( dense_eval != n_rows + 1 );

      REQUIRE( std::abs(sp_eigval(i)) == Approx(std::abs(eigval(dense_eval))).margin(0.01) );
      for(uword j = 0; j < n_rows; ++j)
        {
        REQUIRE( std::abs(sp_eigvec(j, i)) == Approx(std::abs(eigvec(j, dense_eval))).margin(0.01) );
        }
      }
    }

  REQUIRE(count > 0);
  }

TEST_CASE("fn_eigs_gen_even_opts_test")
  {
  const uword n_rows = 10;
  const uword n_eigval = 4;
  const uword n_trials = 10;
  uword count = 0;

  for(uword trial=0; trial < n_trials; ++trial)
    {
    sp_mat m;
    m.sprandu(n_rows, n_rows, 0.3);
    sp_mat z(5, 5);
    z.sprandu(5, 5, 0.5);
    m.submat(2, 2, 6, 6) += 5 * z;
    mat d(m);

    // Eigendecompose, getting first 4 eigenvectors.
    Col<cx_double> sp_eigval;
    Mat<cx_double> sp_eigvec;
    eigs_opts opts{}; opts.maxiter = 10000; opts.tol = 1e-12;
    const bool status_sparse = eigs_gen(sp_eigval, sp_eigvec, m, n_eigval, "lm", opts);

    // Do the same for the dense case.
    Col<cx_double> eigval;
    Mat<cx_double> eigvec;
    const bool status_dense = eig_gen(eigval, eigvec, d);

    if( (status_sparse == false) || (status_dense == false) )  { continue; }  else  { ++count; }

    uvec used(n_rows, fill::zeros);

    for(uword i=0; i < n_eigval; ++i)
      {
      // Sorting these is difficult.
      // Find which one is the likely dense eigenvalue.
      uword dense_eval = n_rows + 1;
      for(uword k = 0; k < n_rows; ++k)
        {
        if ((std::abs(cx_double(sp_eigval(i)).real() - eigval(k).real()) < 1e-4) &&
            (std::abs(cx_double(sp_eigval(i)).imag() - eigval(k).imag()) < 1e-4) &&
            (used(k) == 0))
          {
          dense_eval = k;
          used(k) = 1;
          break;
          }
        }

      REQUIRE( dense_eval != n_rows + 1 );

      REQUIRE( std::abs(sp_eigval(i)) == Approx(std::abs(eigval(dense_eval))).margin(0.01) );
      for(uword j = 0; j < n_rows; ++j)
        {
        REQUIRE( std::abs(sp_eigvec(j, i)) == Approx(std::abs(eigvec(j, dense_eval))).margin(0.01) );
        }
      }
    }

  REQUIRE(count > 0);
  }

TEST_CASE("fn_eigs_gen_odd_sigma_test")
  {
  const uword n_rows = 10;
  const uword n_eigval = 5;
  const double sigma = 1.0;
  const uword n_trials = 10;
  uword count = 0;

  for(uword trial=0; trial < n_trials; ++trial)
    {
    sp_mat m;
    m.sprandu(n_rows, n_rows, 0.3);
    sp_mat z(5, 5);
    z.sprandu(5, 5, 0.5);
    m.submat(2, 2, 6, 6) += 5 * z;
    m += (sigma+0.001)*speye(n_rows, n_rows);
    mat d(m);

    // Eigendecompose, getting first 5 eigenvectors around 1.
    Col<cx_double> sp_eigval;
    Mat<cx_double> sp_eigvec;
    const bool status_sparse = eigs_gen(sp_eigval, sp_eigvec, m, n_eigval, sigma);

    // Do the same for the dense case.
    Col<cx_double> eigval;
    Mat<cx_double> eigvec;
    const bool status_dense = eig_gen(eigval, eigvec, d);

    if( (status_sparse == false) || (status_dense == false) )  { continue; }  else  { ++count; }

    uvec used(n_rows, fill::zeros);

    for(uword i=0; i < n_eigval; ++i)
      {
      // Sorting these is difficult.
      // Find which one is the likely dense eigenvalue.
      uword dense_eval = n_rows + 1;
      for(uword k = 0; k < n_rows; ++k)
        {
        if ((std::abs(cx_double(sp_eigval(i)).real() - eigval(k).real()) < 1e-4) &&
            (std::abs(cx_double(sp_eigval(i)).imag() - eigval(k).imag()) < 1e-4) &&
            (used(k) == 0))
          {
          dense_eval = k;
          used(k) = 1;
          break;
          }
        }

      REQUIRE( dense_eval != n_rows + 1 );

      REQUIRE( std::abs(sp_eigval(i)) == Approx(std::abs(eigval(dense_eval))).margin(0.1) );
      for(uword j = 0; j < n_rows; ++j)
        {
        REQUIRE( std::abs(sp_eigvec(j, i)) == Approx(std::abs(eigvec(j, dense_eval))).margin(0.1) );
        }
      }
    }

  REQUIRE(count > 0);
  }

TEST_CASE("fn_eigs_gen_even_sigma_test")
  {
  const uword n_rows = 10;
  const uword n_eigval = 4;
  const double sigma = 1.0;
  const uword n_trials = 10;
  uword count = 0;

  for(uword trial=0; trial < n_trials; ++trial)
    {
    sp_mat m;
    m.sprandu(n_rows, n_rows, 0.3);
    sp_mat z(5, 5);
    z.sprandu(5, 5, 0.5);
    m.submat(2, 2, 6, 6) += 5 * z;
    m += (sigma+0.001)*speye(n_rows, n_rows);
    mat d(m);

    // Eigendecompose, getting first 4 eigenvectors around 1.
    Col<cx_double> sp_eigval;
    Mat<cx_double> sp_eigvec;
    const bool status_sparse = eigs_gen(sp_eigval, sp_eigvec, m, n_eigval, sigma);

    // Do the same for the dense case.
    Col<cx_double> eigval;
    Mat<cx_double> eigvec;
    const bool status_dense = eig_gen(eigval, eigvec, d);

    if( (status_sparse == false) || (status_dense == false) )  { continue; }  else  { ++count; }

    uvec used(n_rows, fill::zeros);

    for(uword i=0; i < n_eigval; ++i)
      {
      // Sorting these is difficult.
      // Find which one is the likely dense eigenvalue.
      uword dense_eval = n_rows + 1;
      for(uword k = 0; k < n_rows; ++k)
        {
        if ((std::abs(cx_double(sp_eigval(i)).real() - eigval(k).real()) < 1e-4) &&
            (std::abs(cx_double(sp_eigval(i)).imag() - eigval(k).imag()) < 1e-4) &&
            (used(k) == 0))
          {
          dense_eval = k;
          used(k) = 1;
          break;
          }
        }

      REQUIRE( dense_eval != n_rows + 1 );

      REQUIRE( std::abs(sp_eigval(i)) == Approx(std::abs(eigval(dense_eval))).margin(0.01) );
      for(uword j = 0; j < n_rows; ++j)
        {
        REQUIRE( std::abs(sp_eigvec(j, i)) == Approx(std::abs(eigvec(j, dense_eval))).margin(0.01) );
        }
      }
    }

  REQUIRE(count > 0);
  }

TEST_CASE("fn_eigs_gen_even_sigma_opts_test")
  {
  const uword n_rows = 10;
  const uword n_eigval = 4;
  const double sigma = 1.0;
  const uword n_trials = 10;
  uword count = 0;

  for(uword trial=0; trial < n_trials; ++trial)
    {
    sp_mat m;
    m.sprandu(n_rows, n_rows, 0.3);
    sp_mat z(5, 5);
    z.sprandu(5, 5, 0.5);
    m.submat(2, 2, 6, 6) += 5 * z;
    m += (sigma+0.001)*speye(n_rows, n_rows);
    mat d(m);

    // Eigendecompose, getting first 4 eigenvectors around 1.
    Col<cx_double> sp_eigval;
    Mat<cx_double> sp_eigvec;
    eigs_opts opts{}; opts.maxiter = 10000; opts.tol = 1e-12;
    const bool status_sparse = eigs_gen(sp_eigval, sp_eigvec, m, n_eigval, sigma, opts);

    // Do the same for the dense case.
    Col<cx_double> eigval;
    Mat<cx_double> eigvec;
    const bool status_dense = eig_gen(eigval, eigvec, d);

    if( (status_sparse == false) || (status_dense == false) )  { continue; }  else  { ++count; }

    uvec used(n_rows, fill::zeros);

    for(uword i=0; i < n_eigval; ++i)
      {
      // Sorting these is difficult.
      // Find which one is the likely dense eigenvalue.
      uword dense_eval = n_rows + 1;
      for(uword k = 0; k < n_rows; ++k)
        {
        if ((std::abs(cx_double(sp_eigval(i)).real() - eigval(k).real()) < 1e-4) &&
            (std::abs(cx_double(sp_eigval(i)).imag() - eigval(k).imag()) < 1e-4) &&
            (used(k) == 0))
          {
          dense_eval = k;
          used(k) = 1;
          break;
          }
        }

      REQUIRE( dense_eval != n_rows + 1 );

      REQUIRE( std::abs(sp_eigval(i)) == Approx(std::abs(eigval(dense_eval))).margin(0.01) );
      for(uword j = 0; j < n_rows; ++j)
        {
        REQUIRE( std::abs(sp_eigvec(j, i)) == Approx(std::abs(eigvec(j, dense_eval))).margin(0.01) );
        }
      }
    }

  REQUIRE(count > 0);
  }

TEST_CASE("fn_eigs_gen_odd_sm_test")
  {
  const uword n_rows = 10;
  const uword n_eigval = 5;
  const uword n_trials = 10;
  uword count = 0;

  for(uword trial=0; trial < n_trials; ++trial)
    {
    sp_mat m;
    m.sprandu(n_rows, n_rows, 0.3);
    sp_mat z(5, 5);
    z.sprandu(5, 5, 0.5);
    m.submat(2, 2, 6, 6) += 5 * z;
    m += 0.001*speye(n_rows, n_rows);
    mat d(m);

    // Eigendecompose, getting first 5 eigenvectors.
    Col<cx_double> sp_eigval;
    Mat<cx_double> sp_eigvec;
    const bool status_sparse = eigs_gen(sp_eigval, sp_eigvec, m, n_eigval, "sm");

    // Do the same for the dense case.
    Col<cx_double> eigval;
    Mat<cx_double> eigvec;
    const bool status_dense = eig_gen(eigval, eigvec, d);

    if( (status_sparse == false) || (status_dense == false) )  { continue; }  else  { ++count; }

    uvec used(n_rows, fill::zeros);

    for(uword i=0; i < n_eigval; ++i)
      {
      // Sorting these is difficult.
      // Find which one is the likely dense eigenvalue.
      uword dense_eval = n_rows + 1;
      for(uword k = 0; k < n_rows; ++k)
        {
        if ((std::abs(cx_double(sp_eigval(i)).real() - eigval(k).real()) < 1e-4) &&
            (std::abs(cx_double(sp_eigval(i)).imag() - eigval(k).imag()) < 1e-4) &&
            (used(k) == 0))
          {
          dense_eval = k;
          used(k) = 1;
          break;
          }
        }

      REQUIRE( dense_eval != n_rows + 1 );

      REQUIRE( std::abs(sp_eigval(i)) == Approx(std::abs(eigval(dense_eval))).margin(0.1) );
      for(uword j = 0; j < n_rows; ++j)
        {
        REQUIRE( std::abs(sp_eigvec(j, i)) == Approx(std::abs(eigvec(j, dense_eval))).margin(0.1) );
        }
      }
    }

  REQUIRE(count > 0);
  }

TEST_CASE("fn_eigs_gen_even_sm_test")
  {
  const uword n_rows = 10;
  const uword n_eigval = 4;
  const uword n_trials = 10;
  uword count = 0;

  for(uword trial=0; trial < n_trials; ++trial)
    {
    sp_mat m;
    m.sprandu(n_rows, n_rows, 0.3);
    sp_mat z(5, 5);
    z.sprandu(5, 5, 0.5);
    m.submat(2, 2, 6, 6) += 5 * z;
    m += 0.001*speye(n_rows, n_rows);
    mat d(m);

    // Eigendecompose, getting first 4 eigenvectors.
    Col<cx_double> sp_eigval;
    Mat<cx_double> sp_eigvec;
    const bool status_sparse = eigs_gen(sp_eigval, sp_eigvec, m, n_eigval, "sm");

    // Do the same for the dense case.
    Col<cx_double> eigval;
    Mat<cx_double> eigvec;
    const bool status_dense = eig_gen(eigval, eigvec, d);

    if( (status_sparse == false) || (status_dense == false) )  { continue; }  else  { ++count; }

    uvec used(n_rows, fill::zeros);

    for(uword i=0; i < n_eigval; ++i)
      {
      // Sorting these is difficult.
      // Find which one is the likely dense eigenvalue.
      uword dense_eval = n_rows + 1;
      for(uword k = 0; k < n_rows; ++k)
        {
        if ((std::abs(cx_double(sp_eigval(i)).real() - eigval(k).real()) < 1e-4) &&
            (std::abs(cx_double(sp_eigval(i)).imag() - eigval(k).imag()) < 1e-4) &&
            (used(k) == 0))
          {
          dense_eval = k;
          used(k) = 1;
          break;
          }
        }

      REQUIRE( dense_eval != n_rows + 1 );

      REQUIRE( std::abs(sp_eigval(i)) == Approx(std::abs(eigval(dense_eval))).margin(0.01) );
      for(uword j = 0; j < n_rows; ++j)
        {
        REQUIRE( std::abs(sp_eigvec(j, i)) == Approx(std::abs(eigvec(j, dense_eval))).margin(0.01) );
        }
      }
    }

  REQUIRE(count > 0);
  }

TEST_CASE("fn_eigs_gen_even_sm_opts_test")
  {
  const uword n_rows = 10;
  const uword n_eigval = 4;
  const uword n_trials = 10;
  uword count = 0;

  for(uword trial=0; trial < n_trials; ++trial)
    {
    sp_mat m;
    m.sprandu(n_rows, n_rows, 0.3);
    sp_mat z(5, 5);
    z.sprandu(5, 5, 0.5);
    m.submat(2, 2, 6, 6) += 5 * z;
    m += 0.001*speye(n_rows, n_rows);
    mat d(m);

    // Eigendecompose, getting first 4 eigenvectors.
    Col<cx_double> sp_eigval;
    Mat<cx_double> sp_eigvec;
    eigs_opts opts{}; opts.maxiter = 10000; opts.tol = 1e-12;
    const bool status_sparse = eigs_gen(sp_eigval, sp_eigvec, m, n_eigval, "sm", opts);

    // Do the same for the dense case.
    Col<cx_double> eigval;
    Mat<cx_double> eigvec;
    const bool status_dense = eig_gen(eigval, eigvec, d);

    if( (status_sparse == false) || (status_dense == false) )  { continue; }  else  { ++count; }

    uvec used(n_rows, fill::zeros);

    for(uword i=0; i < n_eigval; ++i)
      {
      // Sorting these is difficult.
      // Find which one is the likely dense eigenvalue.
      uword dense_eval = n_rows + 1;
      for(uword k = 0; k < n_rows; ++k)
        {
        if ((std::abs(cx_double(sp_eigval(i)).real() - eigval(k).real()) < 1e-4) &&
            (std::abs(cx_double(sp_eigval(i)).imag() - eigval(k).imag()) < 1e-4) &&
            (used(k) == 0))
          {
          dense_eval = k;
          used(k) = 1;
          break;
          }
        }

      REQUIRE( dense_eval != n_rows + 1 );

      REQUIRE( std::abs(sp_eigval(i)) == Approx(std::abs(eigval(dense_eval))).margin(0.01) );
      for(uword j = 0; j < n_rows; ++j)
        {
        REQUIRE( std::abs(sp_eigvec(j, i)) == Approx(std::abs(eigvec(j, dense_eval))).margin(0.01) );
        }
      }
    }

  REQUIRE(count > 0);
  }

TEST_CASE("fn_eigs_gen_odd_float_test")
  {
  const uword n_rows = 10;
  const uword n_eigval = 5;
  const uword n_trials = 10;
  uword count = 0;

  for(uword trial=0; trial < n_trials; ++trial)
    {
    SpMat<float> m;
    m.sprandu(n_rows, n_rows, 0.3);
    for(uword i = 0; i < n_rows; ++i)
      {
      m(i, i) += 5 * double(i) / double(n_rows);
      }
    Mat<float> d(m);

    // Eigendecompose, getting first 5 eigenvectors.
    Col<cx_float> sp_eigval;
    Mat<cx_float> sp_eigvec;
    const bool status_sparse = eigs_gen(sp_eigval, sp_eigvec, m, n_eigval);

    // Do the same for the dense case.
    Col<cx_float> eigval;
    Mat<cx_float> eigvec;
    const bool status_dense = eig_gen(eigval, eigvec, d);

    if( (status_sparse == false) || (status_dense == false) )  { continue; }  else  { ++count; }

    uvec used(n_rows, fill::zeros);

    for(uword i=0; i < n_eigval; ++i)
      {
      // Sorting these is difficult.
      // Find which one is the likely dense eigenvalue.
      uword dense_eval = n_rows + 1;
      for(uword k = 0; k < n_rows; ++k)
        {
        if ((std::abs(cx_float(sp_eigval(i)).real() - eigval(k).real()) < 0.001) &&
            (std::abs(cx_float(sp_eigval(i)).imag() - eigval(k).imag()) < 0.001) &&
            (used(k) == 0))
          {
          dense_eval = k;
          used(k) = 1;
          break;
          }
        }

      REQUIRE( dense_eval != n_rows + 1 );

      REQUIRE( std::abs(sp_eigval(i)) == Approx(std::abs(eigval(dense_eval))).margin(0.001) );
      for(uword j = 0; j < n_rows; ++j)
        {
        REQUIRE( std::abs(sp_eigvec(j, i)) == Approx(std::abs(eigvec(j, dense_eval))).margin(0.01) );
        }
      }
    }

  REQUIRE(count > 0);
  }

TEST_CASE("fn_eigs_gen_even_float_test")
  {
  const uword n_rows = 12;
  const uword n_eigval = 8;
  const uword n_trials = 10;
  uword count = 0;

  for(uword trial=0; trial < n_trials; ++trial)
    {
    SpMat<float> m;
    m.sprandu(n_rows, n_rows, 0.3);
    for(uword i = 0; i < n_rows; ++i)
      {
      m(i, i) += 5 * double(i) / double(n_rows);
      }
    Mat<float> d(m);

    // Eigendecompose, getting first 8 eigenvectors.
    Col<cx_float> sp_eigval;
    Mat<cx_float> sp_eigvec;
    const bool status_sparse = eigs_gen(sp_eigval, sp_eigvec, m, n_eigval);

    // Do the same for the dense case.
    Col<cx_float> eigval;
    Mat<cx_float> eigvec;
    const bool status_dense = eig_gen(eigval, eigvec, d);

    if( (status_sparse == false) || (status_dense == false) )  { continue; }  else  { ++count; }

    uvec used(n_rows, fill::zeros);

    for(uword i=0; i < n_eigval; ++i)
      {
      // Sorting these is difficult.
      // Find which one is the likely dense eigenvalue.
      uword dense_eval = n_rows + 1;
      for(uword k = 0; k < n_rows; ++k)
        {
        if ((std::abs(cx_float(sp_eigval(i)).real() - eigval(k).real()) < 0.001) &&
            (std::abs(cx_float(sp_eigval(i)).imag() - eigval(k).imag()) < 0.001) &&
            (used(k) == 0))
          {
          dense_eval = k;
          used(k) = 1;
          break;
          }
        }

      REQUIRE( dense_eval != n_rows + 1 );

      REQUIRE( std::abs(sp_eigval(i)) == Approx(std::abs(eigval(dense_eval))).margin(0.01) );
      for(uword j = 0; j < n_rows; ++j)
        {
        REQUIRE( std::abs(sp_eigvec(j, i)) == Approx(std::abs(eigvec(j, dense_eval))).margin(0.01) );
        }
      }
    }

  REQUIRE(count > 0);
  }

TEST_CASE("fn_eigs_gen_even_float_opts_test")
  {
  const uword n_rows = 12;
  const uword n_eigval = 8;
  const uword n_trials = 10;
  uword count = 0;

  for(uword trial=0; trial < n_trials; ++trial)
    {
    SpMat<float> m;
    m.sprandu(n_rows, n_rows, 0.3);
    for(uword i = 0; i < n_rows; ++i)
      {
      m(i, i) += 5 * double(i) / double(n_rows);
      }
    Mat<float> d(m);

    // Eigendecompose, getting first 8 eigenvectors.
    Col<cx_float> sp_eigval;
    Mat<cx_float> sp_eigvec;
    eigs_opts opts{}; opts.maxiter = 10000; opts.tol = 1e-12;
    const bool status_sparse = eigs_gen(sp_eigval, sp_eigvec, m, n_eigval, "lm", opts);

    // Do the same for the dense case.
    Col<cx_float> eigval;
    Mat<cx_float> eigvec;
    const bool status_dense = eig_gen(eigval, eigvec, d);

    if( (status_sparse == false) || (status_dense == false) )  { continue; }  else  { ++count; }

    uvec used(n_rows, fill::zeros);

    for(uword i=0; i < n_eigval; ++i)
      {
      // Sorting these is difficult.
      // Find which one is the likely dense eigenvalue.
      uword dense_eval = n_rows + 1;
      for(uword k = 0; k < n_rows; ++k)
        {
        if ((std::abs(cx_float(sp_eigval(i)).real() - eigval(k).real()) < 0.001) &&
            (std::abs(cx_float(sp_eigval(i)).imag() - eigval(k).imag()) < 0.001) &&
            (used(k) == 0))
          {
          dense_eval = k;
          used(k) = 1;
          break;
          }
        }

      REQUIRE( dense_eval != n_rows + 1 );

      REQUIRE( std::abs(sp_eigval(i)) == Approx(std::abs(eigval(dense_eval))).margin(0.01) );
      for(uword j = 0; j < n_rows; ++j)
        {
        REQUIRE( std::abs(sp_eigvec(j, i)) == Approx(std::abs(eigvec(j, dense_eval))).margin(0.01) );
        }
      }
    }

  REQUIRE(count > 0);
  }

TEST_CASE("fn_eigs_gen_odd_float_sigma_test")
  {
  const uword n_rows = 10;
  const uword n_eigval = 5;
  const float sigma = 1.0;
  const uword n_trials = 10;
  uword count = 0;

  for(uword trial=0; trial < n_trials; ++trial)
    {
    SpMat<float> m;
    m.sprandu(n_rows, n_rows, 0.3);
    for(uword i = 0; i < n_rows; ++i)
      {
      m(i, i) += 5 * double(i) / double(n_rows);
      }
    m += (sigma+0.001)*speye<SpMat<float>>(n_rows, n_rows);
    Mat<float> d(m);

    // Eigendecompose, getting first 5 eigenvectors around 1.
    Col<cx_float> sp_eigval;
    Mat<cx_float> sp_eigvec;
    const bool status_sparse = eigs_gen(sp_eigval, sp_eigvec, m, n_eigval, sigma);

    // Do the same for the dense case.
    Col<cx_float> eigval;
    Mat<cx_float> eigvec;
    const bool status_dense = eig_gen(eigval, eigvec, d);

    if( (status_sparse == false) || (status_dense == false) )  { continue; }  else  { ++count; }

    uvec used(n_rows, fill::zeros);

    for(uword i=0; i < n_eigval; ++i)
      {
      // Sorting these is difficult.
      // Find which one is the likely dense eigenvalue.
      uword dense_eval = n_rows + 1;
      for(uword k = 0; k < n_rows; ++k)
        {
        if ((std::abs(cx_float(sp_eigval(i)).real() - eigval(k).real()) < 0.001) &&
            (std::abs(cx_float(sp_eigval(i)).imag() - eigval(k).imag()) < 0.001) &&
            (used(k) == 0))
          {
          dense_eval = k;
          used(k) = 1;
          break;
          }
        }

      REQUIRE( dense_eval != n_rows + 1 );

      REQUIRE( std::abs(sp_eigval(i)) == Approx(std::abs(eigval(dense_eval))).margin(0.001) );
      for(uword j = 0; j < n_rows; ++j)
        {
        REQUIRE( std::abs(sp_eigvec(j, i)) == Approx(std::abs(eigvec(j, dense_eval))).margin(0.01) );
        }
      }
    }

  REQUIRE(count > 0);
  }

TEST_CASE("fn_eigs_gen_even_float_sigma_test")
  {
  const uword n_rows = 12;
  const uword n_eigval = 8;
  const float sigma = 1.0;
  const uword n_trials = 10;
  uword count = 0;

  for(uword trial=0; trial < n_trials; ++trial)
    {
    SpMat<float> m;
    m.sprandu(n_rows, n_rows, 0.3);
    for(uword i = 0; i < n_rows; ++i)
      {
      m(i, i) += 5 * double(i) / double(n_rows);
      }
    m += (sigma+0.001)*speye<SpMat<float>>(n_rows, n_rows);
    Mat<float> d(m);

    // Eigendecompose, getting first 8 eigenvectors.
    Col<cx_float> sp_eigval;
    Mat<cx_float> sp_eigvec;
    const bool status_sparse = eigs_gen(sp_eigval, sp_eigvec, m, n_eigval, sigma);

    // Do the same for the dense case around 1.
    Col<cx_float> eigval;
    Mat<cx_float> eigvec;
    const bool status_dense = eig_gen(eigval, eigvec, d);

    if( (status_sparse == false) || (status_dense == false) )  { continue; }  else  { ++count; }

    uvec used(n_rows, fill::zeros);

    for(uword i=0; i < n_eigval; ++i)
      {
      // Sorting these is difficult.
      // Find which one is the likely dense eigenvalue.
      uword dense_eval = n_rows + 1;
      for(uword k = 0; k < n_rows; ++k)
        {
        if ((std::abs(cx_float(sp_eigval(i)).real() - eigval(k).real()) < 0.001) &&
            (std::abs(cx_float(sp_eigval(i)).imag() - eigval(k).imag()) < 0.001) &&
            (used(k) == 0))
          {
          dense_eval = k;
          used(k) = 1;
          break;
          }
        }

      REQUIRE( dense_eval != n_rows + 1 );

      REQUIRE( std::abs(sp_eigval(i)) == Approx(std::abs(eigval(dense_eval))).margin(0.01) );
      for(uword j = 0; j < n_rows; ++j)
        {
        REQUIRE( std::abs(sp_eigvec(j, i)) == Approx(std::abs(eigvec(j, dense_eval))).margin(0.01) );
        }
      }
    }

  REQUIRE(count > 0);
  }

TEST_CASE("fn_eigs_gen_even_float_sigma_opts_test")
  {
  const uword n_rows = 12;
  const uword n_eigval = 8;
  const float sigma = 1.0;
  const uword n_trials = 10;
  uword count = 0;

  for(uword trial=0; trial < n_trials; ++trial)
    {
    SpMat<float> m;
    m.sprandu(n_rows, n_rows, 0.3);
    for(uword i = 0; i < n_rows; ++i)
      {
      m(i, i) += 5 * double(i) / double(n_rows);
      }
    m += (sigma+0.001)*speye<SpMat<float>>(n_rows, n_rows);
    Mat<float> d(m);

    // Eigendecompose, getting first 8 eigenvectors.
    Col<cx_float> sp_eigval;
    Mat<cx_float> sp_eigvec;
    eigs_opts opts{}; opts.maxiter = 10000; opts.tol = 1e-12;
    const bool status_sparse = eigs_gen(sp_eigval, sp_eigvec, m, n_eigval, sigma, opts);

    // Do the same for the dense case around 1.
    Col<cx_float> eigval;
    Mat<cx_float> eigvec;
    const bool status_dense = eig_gen(eigval, eigvec, d);

    if( (status_sparse == false) || (status_dense == false) )  { continue; }  else  { ++count; }

    uvec used(n_rows, fill::zeros);

    for(uword i=0; i < n_eigval; ++i)
      {
      // Sorting these is difficult.
      // Find which one is the likely dense eigenvalue.
      uword dense_eval = n_rows + 1;
      for(uword k = 0; k < n_rows; ++k)
        {
        if ((std::abs(cx_float(sp_eigval(i)).real() - eigval(k).real()) < 0.001) &&
            (std::abs(cx_float(sp_eigval(i)).imag() - eigval(k).imag()) < 0.001) &&
            (used(k) == 0))
          {
          dense_eval = k;
          used(k) = 1;
          break;
          }
        }

      REQUIRE( dense_eval != n_rows + 1 );

      REQUIRE( std::abs(sp_eigval(i)) == Approx(std::abs(eigval(dense_eval))).margin(0.01) );
      for(uword j = 0; j < n_rows; ++j)
        {
        REQUIRE( std::abs(sp_eigvec(j, i)) == Approx(std::abs(eigvec(j, dense_eval))).margin(0.01) );
        }
      }
    }

  REQUIRE(count > 0);
  }

TEST_CASE("fn_eigs_gen_odd_float_sm_test")
  {
  const uword n_rows = 10;
  const uword n_eigval = 5;
  const uword n_trials = 10;
  uword count = 0;

  for(uword trial=0; trial < n_trials; ++trial)
    {
    SpMat<float> m;
    m.sprandu(n_rows, n_rows, 0.3);
    for(uword i = 0; i < n_rows; ++i)
      {
      m(i, i) += 5 * double(i) / double(n_rows);
      }
    m += 0.001*speye<SpMat<float>>(n_rows, n_rows);
    Mat<float> d(m);

    // Eigendecompose, getting first 5 eigenvectors.
    Col<cx_float> sp_eigval;
    Mat<cx_float> sp_eigvec;
    const bool status_sparse = eigs_gen(sp_eigval, sp_eigvec, m, n_eigval, "sm");

    // Do the same for the dense case.
    Col<cx_float> eigval;
    Mat<cx_float> eigvec;
    const bool status_dense = eig_gen(eigval, eigvec, d);

    if( (status_sparse == false) || (status_dense == false) )  { continue; }  else  { ++count; }

    uvec used(n_rows, fill::zeros);

    for(uword i=0; i < n_eigval; ++i)
      {
      // Sorting these is difficult.
      // Find which one is the likely dense eigenvalue.
      uword dense_eval = n_rows + 1;
      for(uword k = 0; k < n_rows; ++k)
        {
        if ((std::abs(cx_float(sp_eigval(i)).real() - eigval(k).real()) < 0.001) &&
            (std::abs(cx_float(sp_eigval(i)).imag() - eigval(k).imag()) < 0.001) &&
            (used(k) == 0))
          {
          dense_eval = k;
          used(k) = 1;
          break;
          }
        }

      REQUIRE( dense_eval != n_rows + 1 );

      REQUIRE( std::abs(sp_eigval(i)) == Approx(std::abs(eigval(dense_eval))).margin(0.001) );
      for(uword j = 0; j < n_rows; ++j)
        {
        REQUIRE( std::abs(sp_eigvec(j, i)) == Approx(std::abs(eigvec(j, dense_eval))).margin(0.01) );
        }
      }
    }

  REQUIRE(count > 0);
  }

TEST_CASE("fn_eigs_gen_even_float_sm_test")
  {
  const uword n_rows = 12;
  const uword n_eigval = 8;
  const uword n_trials = 10;
  uword count = 0;

  for(uword trial=0; trial < n_trials; ++trial)
    {
    SpMat<float> m;
    m.sprandu(n_rows, n_rows, 0.3);
    for(uword i = 0; i < n_rows; ++i)
      {
      m(i, i) += 5 * double(i) / double(n_rows);
      }
    m += 0.001*speye<SpMat<float>>(n_rows, n_rows);
    Mat<float> d(m);

    // Eigendecompose, getting first 8 eigenvectors.
    Col<cx_float> sp_eigval;
    Mat<cx_float> sp_eigvec;
    const bool status_sparse = eigs_gen(sp_eigval, sp_eigvec, m, n_eigval, "sm");

    // Do the same for the dense case.
    Col<cx_float> eigval;
    Mat<cx_float> eigvec;
    const bool status_dense = eig_gen(eigval, eigvec, d);

    if( (status_sparse == false) || (status_dense == false) )  { continue; }  else  { ++count; }

    uvec used(n_rows, fill::zeros);

    for(uword i=0; i < n_eigval; ++i)
      {
      // Sorting these is difficult.
      // Find which one is the likely dense eigenvalue.
      uword dense_eval = n_rows + 1;
      for(uword k = 0; k < n_rows; ++k)
        {
        if ((std::abs(cx_float(sp_eigval(i)).real() - eigval(k).real()) < 0.001) &&
            (std::abs(cx_float(sp_eigval(i)).imag() - eigval(k).imag()) < 0.001) &&
            (used(k) == 0))
          {
          dense_eval = k;
          used(k) = 1;
          break;
          }
        }

      REQUIRE( dense_eval != n_rows + 1 );

      REQUIRE( std::abs(sp_eigval(i)) == Approx(std::abs(eigval(dense_eval))).margin(0.01) );
      for(uword j = 0; j < n_rows; ++j)
        {
        REQUIRE( std::abs(sp_eigvec(j, i)) == Approx(std::abs(eigvec(j, dense_eval))).margin(0.01) );
        }
      }
    }

  REQUIRE(count > 0);
  }

TEST_CASE("fn_eigs_gen_even_float_sm_opts_test")
  {
  const uword n_rows = 12;
  const uword n_eigval = 8;
  const uword n_trials = 10;
  uword count = 0;

  for(uword trial=0; trial < n_trials; ++trial)
    {
    SpMat<float> m;
    m.sprandu(n_rows, n_rows, 0.3);
    for(uword i = 0; i < n_rows; ++i)
      {
      m(i, i) += 5 * double(i) / double(n_rows);
      }
    m += 0.001*speye<SpMat<float>>(n_rows, n_rows);
    Mat<float> d(m);

    // Eigendecompose, getting first 8 eigenvectors.
    Col<cx_float> sp_eigval;
    Mat<cx_float> sp_eigvec;
    eigs_opts opts{}; opts.maxiter = 10000; opts.tol = 1e-12;
    const bool status_sparse = eigs_gen(sp_eigval, sp_eigvec, m, n_eigval, "sm", opts);

    // Do the same for the dense case.
    Col<cx_float> eigval;
    Mat<cx_float> eigvec;
    const bool status_dense = eig_gen(eigval, eigvec, d);

    if( (status_sparse == false) || (status_dense == false) )  { continue; }  else  { ++count; }

    uvec used(n_rows, fill::zeros);

    for(uword i=0; i < n_eigval; ++i)
      {
      // Sorting these is difficult.
      // Find which one is the likely dense eigenvalue.
      uword dense_eval = n_rows + 1;
      for(uword k = 0; k < n_rows; ++k)
        {
        if ((std::abs(cx_float(sp_eigval(i)).real() - eigval(k).real()) < 0.001) &&
            (std::abs(cx_float(sp_eigval(i)).imag() - eigval(k).imag()) < 0.001) &&
            (used(k) == 0))
          {
          dense_eval = k;
          used(k) = 1;
          break;
          }
        }

      REQUIRE( dense_eval != n_rows + 1 );

      REQUIRE( std::abs(sp_eigval(i)) == Approx(std::abs(eigval(dense_eval))).margin(0.01) );
      for(uword j = 0; j < n_rows; ++j)
        {
        REQUIRE( std::abs(sp_eigvec(j, i)) == Approx(std::abs(eigvec(j, dense_eval))).margin(0.01) );
        }
      }
    }

  REQUIRE(count > 0);
  }

TEST_CASE("fn_eigs_gen_odd_complex_float_test")
  {
  const uword n_rows = 10;
  const uword n_eigval = 5;
  const uword n_trials = 10;
  uword count = 0;

  for(uword trial=0; trial < n_trials; ++trial)
    {
    SpMat<cx_float> m;
    m.sprandu(n_rows, n_rows, 0.3);
    Mat<cx_float> d(m);

    // Eigendecompose, getting first 5 eigenvectors.
    Col<cx_float> sp_eigval;
    Mat<cx_float> sp_eigvec;
    const bool status_sparse = eigs_gen(sp_eigval, sp_eigvec, m, n_eigval);

    // Do the same for the dense case.
    Col<cx_float> eigval;
    Mat<cx_float> eigvec;
    const bool status_dense = eig_gen(eigval, eigvec, d);

    if( (status_sparse == false) || (status_dense == false) )  { continue; }  else  { ++count; }

    uvec used(n_rows, fill::zeros);

    for(uword i=0; i < n_eigval; ++i)
      {
      // Sorting these is difficult.
      // Find which one is the likely dense eigenvalue.
      uword dense_eval = n_rows + 1;
      for(uword k = 0; k < n_rows; ++k)
        {
        if ((std::abs(cx_float(sp_eigval(i)).real() - eigval(k).real()) < 0.001) &&
            (std::abs(cx_float(sp_eigval(i)).imag() - eigval(k).imag()) < 0.001) &&
            (used(k) == 0))
          {
          dense_eval = k;
          used(k) = 1;
          break;
          }
        }

      REQUIRE( dense_eval != n_rows + 1 );

      REQUIRE( std::abs(sp_eigval(i)) == Approx(std::abs(eigval(dense_eval))).margin(0.01) );
      for(uword j = 0; j < n_rows; ++j)
        {
        REQUIRE( std::abs(sp_eigvec(j, i)) == Approx(std::abs(eigvec(j, dense_eval))).margin(0.01) );
        }
      }
    }

  REQUIRE(count > 0);
  }

TEST_CASE("fn_eigs_gen_even_complex_float_test")
  {
  const uword n_rows = 12;
  const uword n_eigval = 8;
  const uword n_trials = 10;
  uword count = 0;

  for(uword trial=0; trial < n_trials; ++trial)
    {
    SpMat<cx_float> m;
    m.sprandu(n_rows, n_rows, 0.3);
    Mat<cx_float> d(m);

    // Eigendecompose, getting first 8 eigenvectors.
    Col<cx_float> sp_eigval;
    Mat<cx_float> sp_eigvec;
    const bool status_sparse = eigs_gen(sp_eigval, sp_eigvec, m, n_eigval);

    // Do the same for the dense case.
    Col<cx_float> eigval;
    Mat<cx_float> eigvec;
    const bool status_dense = eig_gen(eigval, eigvec, d);

    if( (status_sparse == false) || (status_dense == false) )  { continue; }  else  { ++count; }

    uvec used(n_rows, fill::zeros);

    for(uword i=0; i < n_eigval; ++i)
      {
      // Sorting these is difficult.
      // Find which one is the likely dense eigenvalue.
      uword dense_eval = n_rows + 1;
      for(uword k = 0; k < n_rows; ++k)
        {
        if ((std::abs(cx_float(sp_eigval(i)).real() - eigval(k).real()) < 0.001) &&
            (std::abs(cx_float(sp_eigval(i)).imag() - eigval(k).imag()) < 0.001) &&
            (used(k) == 0))
          {
          dense_eval = k;
          used(k) = 1;
          break;
          }
        }

      REQUIRE( dense_eval != n_rows + 1 );

      REQUIRE( std::abs(sp_eigval(i)) == Approx(std::abs(eigval(dense_eval))).margin(0.01) );
      for(uword j = 0; j < n_rows; ++j)
        {
        REQUIRE( std::abs(sp_eigvec(j, i)) == Approx(std::abs(eigvec(j, dense_eval))).margin(0.01) );
        }
      }
    }

  REQUIRE(count > 0);
  }

TEST_CASE("fn_eigs_gen_even_complex_float_opts_test")
  {
  const uword n_rows = 12;
  const uword n_eigval = 8;
  const uword n_trials = 10;
  uword count = 0;

  for(uword trial=0; trial < n_trials; ++trial)
    {
    SpMat<cx_float> m;
    m.sprandu(n_rows, n_rows, 0.3);
    Mat<cx_float> d(m);

    // Eigendecompose, getting first 8 eigenvectors.
    Col<cx_float> sp_eigval;
    Mat<cx_float> sp_eigvec;
    eigs_opts opts{}; opts.maxiter = 10000; opts.tol = 1e-12;
    const bool status_sparse = eigs_gen(sp_eigval, sp_eigvec, m, n_eigval, "lm", opts);

    // Do the same for the dense case.
    Col<cx_float> eigval;
    Mat<cx_float> eigvec;
    const bool status_dense = eig_gen(eigval, eigvec, d);

    if( (status_sparse == false) || (status_dense == false) )  { continue; }  else  { ++count; }

    uvec used(n_rows, fill::zeros);

    for(uword i=0; i < n_eigval; ++i)
      {
      // Sorting these is difficult.
      // Find which one is the likely dense eigenvalue.
      uword dense_eval = n_rows + 1;
      for(uword k = 0; k < n_rows; ++k)
        {
        if ((std::abs(cx_float(sp_eigval(i)).real() - eigval(k).real()) < 0.001) &&
            (std::abs(cx_float(sp_eigval(i)).imag() - eigval(k).imag()) < 0.001) &&
            (used(k) == 0))
          {
          dense_eval = k;
          used(k) = 1;
          break;
          }
        }

      REQUIRE( dense_eval != n_rows + 1 );

      REQUIRE( std::abs(sp_eigval(i)) == Approx(std::abs(eigval(dense_eval))).margin(0.01) );
      for(uword j = 0; j < n_rows; ++j)
        {
        REQUIRE( std::abs(sp_eigvec(j, i)) == Approx(std::abs(eigvec(j, dense_eval))).margin(0.01) );
        }
      }
    }

  REQUIRE(count > 0);
  }

TEST_CASE("fn_eigs_gen_odd_complex_float_sigma_test")
  {
  const uword n_rows = 10;
  const uword n_eigval = 5;
  const cx_float sigma = 1.0;
  const uword n_trials = 10;
  uword count = 0;

  for(uword trial=0; trial < n_trials; ++trial)
    {
    SpMat<cx_float> m;
    m.sprandu(n_rows, n_rows, 0.3);
    sp_cx_fmat z(5, 5);
    z.sprandu(5, 5, 0.5);
    m.submat(2, 2, 6, 6) += 5 * z;
    m += (sigma+cx_float(0.001,0))*speye< SpMat<cx_float> >(n_rows, n_rows);
    Mat<cx_float> d(m);

    // Eigendecompose, getting first 5 eigenvectors around 1.
    Col<cx_float> sp_eigval;
    Mat<cx_float> sp_eigvec;
    const bool status_sparse = eigs_gen(sp_eigval, sp_eigvec, m, n_eigval, sigma);

    // Do the same for the dense case.
    Col<cx_float> eigval;
    Mat<cx_float> eigvec;
    const bool status_dense = eig_gen(eigval, eigvec, d);

    if( (status_sparse == false) || (status_dense == false) )  { continue; }  else  { ++count; }

    uvec used(n_rows, fill::zeros);

    for(uword i=0; i < n_eigval; ++i)
      {
      // Sorting these is difficult.
      // Find which one is the likely dense eigenvalue.
      uword dense_eval = n_rows + 1;
      for(uword k = 0; k < n_rows; ++k)
        {
        if ((std::abs(cx_float(sp_eigval(i)).real() - eigval(k).real()) < 0.001) &&
            (std::abs(cx_float(sp_eigval(i)).imag() - eigval(k).imag()) < 0.001) &&
            (used(k) == 0))
          {
          dense_eval = k;
          used(k) = 1;
          break;
          }
        }

      REQUIRE( dense_eval != n_rows + 1 );

      REQUIRE( std::abs(sp_eigval(i)) == Approx(std::abs(eigval(dense_eval))).margin(0.01) );
      for(uword j = 0; j < n_rows; ++j)
        {
        REQUIRE( std::abs(sp_eigvec(j, i)) == Approx(std::abs(eigvec(j, dense_eval))).margin(0.01) );
        }
      }
    }

  REQUIRE(count > 0);
  }

TEST_CASE("fn_eigs_gen_even_complex_float_sigma_test")
  {
  const uword n_rows = 12;
  const uword n_eigval = 8;
  const cx_float sigma = 1.0;
  const uword n_trials = 10;
  uword count = 0;

  for(uword trial=0; trial < n_trials; ++trial)
    {
    SpMat<cx_float> m;
    m.sprandu(n_rows, n_rows, 0.3);
    sp_cx_fmat z(8, 8);
    z.sprandu(8, 8, 0.5);
    m.submat(2, 2, 9, 9) += 8 * z;
    m += (sigma+cx_float(0.001,0))*speye< SpMat<cx_float> >(n_rows, n_rows);
    Mat<cx_float> d(m);

    // Eigendecompose, getting first 8 eigenvectors around 1.
    Col<cx_float> sp_eigval;
    Mat<cx_float> sp_eigvec;
    const bool status_sparse = eigs_gen(sp_eigval, sp_eigvec, m, n_eigval, sigma);

    // Do the same for the dense case.
    Col<cx_float> eigval;
    Mat<cx_float> eigvec;
    const bool status_dense = eig_gen(eigval, eigvec, d);

    if( (status_sparse == false) || (status_dense == false) )  { continue; }  else  { ++count; }

    uvec used(n_rows, fill::zeros);

    for(uword i=0; i < n_eigval; ++i)
      {
      // Sorting these is difficult.
      // Find which one is the likely dense eigenvalue.
      uword dense_eval = n_rows + 1;
      for(uword k = 0; k < n_rows; ++k)
        {
        if ((std::abs(cx_float(sp_eigval(i)).real() - eigval(k).real()) < 0.001) &&
            (std::abs(cx_float(sp_eigval(i)).imag() - eigval(k).imag()) < 0.001) &&
            (used(k) == 0))
          {
          dense_eval = k;
          used(k) = 1;
          break;
          }
        }

      REQUIRE( dense_eval != n_rows + 1 );

      REQUIRE( std::abs(sp_eigval(i)) == Approx(std::abs(eigval(dense_eval))).margin(0.01) );
      for(uword j = 0; j < n_rows; ++j)
        {
        REQUIRE( std::abs(sp_eigvec(j, i)) == Approx(std::abs(eigvec(j, dense_eval))).margin(0.01) );
        }
      }
    }

  REQUIRE(count > 0);
  }

TEST_CASE("fn_eigs_gen_even_complex_float_sigma_opts_test")
  {
  const uword n_rows = 12;
  const uword n_eigval = 8;
  const cx_float sigma = 1.0;
  const uword n_trials = 10;
  uword count = 0;

  for(uword trial=0; trial < n_trials; ++trial)
    {
    SpMat<cx_float> m;
    m.sprandu(n_rows, n_rows, 0.3);
    sp_cx_fmat z(8, 8);
    z.sprandu(8, 8, 0.5);
    m.submat(2, 2, 9, 9) += 8 * z;
    m += (sigma+cx_float(0.001,0))*speye< SpMat<cx_float> >(n_rows, n_rows);
    Mat<cx_float> d(m);

    // Eigendecompose, getting first 8 eigenvectors around 1.
    Col<cx_float> sp_eigval;
    Mat<cx_float> sp_eigvec;
    eigs_opts opts{}; opts.maxiter = 10000; opts.tol = 1e-12;
    const bool status_sparse = eigs_gen(sp_eigval, sp_eigvec, m, n_eigval, sigma, opts);

    // Do the same for the dense case.
    Col<cx_float> eigval;
    Mat<cx_float> eigvec;
    const bool status_dense = eig_gen(eigval, eigvec, d);

    if( (status_sparse == false) || (status_dense == false) )  { continue; }  else  { ++count; }

    uvec used(n_rows, fill::zeros);

    for(uword i=0; i < n_eigval; ++i)
      {
      // Sorting these is difficult.
      // Find which one is the likely dense eigenvalue.
      uword dense_eval = n_rows + 1;
      for(uword k = 0; k < n_rows; ++k)
        {
        if ((std::abs(cx_float(sp_eigval(i)).real() - eigval(k).real()) < 0.001) &&
            (std::abs(cx_float(sp_eigval(i)).imag() - eigval(k).imag()) < 0.001) &&
            (used(k) == 0))
          {
          dense_eval = k;
          used(k) = 1;
          break;
          }
        }

      REQUIRE( dense_eval != n_rows + 1 );

      REQUIRE( std::abs(sp_eigval(i)) == Approx(std::abs(eigval(dense_eval))).margin(0.01) );
      for(uword j = 0; j < n_rows; ++j)
        {
        REQUIRE( std::abs(sp_eigvec(j, i)) == Approx(std::abs(eigvec(j, dense_eval))).margin(0.01) );
        }
      }
    }

  REQUIRE(count > 0);
  }

TEST_CASE("fn_eigs_gen_odd_complex_float_sm_test")
  {
  const uword n_rows = 10;
  const uword n_eigval = 5;
  const uword n_trials = 10;
  uword count = 0;

  for(uword trial=0; trial < n_trials; ++trial)
    {
    SpMat<cx_float> m;
    m.sprandu(n_rows, n_rows, 0.3);
    sp_cx_fmat z(5, 5);
    z.sprandu(5, 5, 0.5);
    m.submat(2, 2, 6, 6) += 5 * z;
    m += cx_float(0.001,0)*speye< SpMat<cx_float> >(n_rows, n_rows);
    Mat<cx_float> d(m);

    // Eigendecompose, getting first 5 eigenvectors.
    Col<cx_float> sp_eigval;
    Mat<cx_float> sp_eigvec;
    const bool status_sparse = eigs_gen(sp_eigval, sp_eigvec, m, n_eigval, "sm");

    // Do the same for the dense case.
    Col<cx_float> eigval;
    Mat<cx_float> eigvec;
    const bool status_dense = eig_gen(eigval, eigvec, d);

    if( (status_sparse == false) || (status_dense == false) )  { continue; }  else  { ++count; }

    uvec used(n_rows, fill::zeros);

    for(uword i=0; i < n_eigval; ++i)
      {
      // Sorting these is difficult.
      // Find which one is the likely dense eigenvalue.
      uword dense_eval = n_rows + 1;
      for(uword k = 0; k < n_rows; ++k)
        {
        if ((std::abs(cx_float(sp_eigval(i)).real() - eigval(k).real()) < 0.001) &&
            (std::abs(cx_float(sp_eigval(i)).imag() - eigval(k).imag()) < 0.001) &&
            (used(k) == 0))
          {
          dense_eval = k;
          used(k) = 1;
          break;
          }
        }

      REQUIRE( dense_eval != n_rows + 1 );

      REQUIRE( std::abs(sp_eigval(i)) == Approx(std::abs(eigval(dense_eval))).margin(0.01) );
      for(uword j = 0; j < n_rows; ++j)
        {
        REQUIRE( std::abs(sp_eigvec(j, i)) == Approx(std::abs(eigvec(j, dense_eval))).margin(0.01) );
        }
      }
    }

  REQUIRE(count > 0);
  }

TEST_CASE("fn_eigs_gen_even_complex_float_sm_test")
  {
  const uword n_rows = 12;
  const uword n_eigval = 8;
  const uword n_trials = 10;
  uword count = 0;

  for(uword trial=0; trial < n_trials; ++trial)
    {
    SpMat<cx_float> m;
    m.sprandu(n_rows, n_rows, 0.3);
    sp_cx_fmat z(8, 8);
    z.sprandu(8, 8, 0.5);
    m.submat(2, 2, 9, 9) += 8 * z;
    m += cx_float(0.001,0)*speye< SpMat<cx_float> >(n_rows, n_rows);
    Mat<cx_float> d(m);

    // Eigendecompose, getting first 8 eigenvectors.
    Col<cx_float> sp_eigval;
    Mat<cx_float> sp_eigvec;
    const bool status_sparse = eigs_gen(sp_eigval, sp_eigvec, m, n_eigval, "sm");

    // Do the same for the dense case.
    Col<cx_float> eigval;
    Mat<cx_float> eigvec;
    const bool status_dense = eig_gen(eigval, eigvec, d);

    if( (status_sparse == false) || (status_dense == false) )  { continue; }  else  { ++count; }

    uvec used(n_rows, fill::zeros);

    for(uword i=0; i < n_eigval; ++i)
      {
      // Sorting these is difficult.
      // Find which one is the likely dense eigenvalue.
      uword dense_eval = n_rows + 1;
      for(uword k = 0; k < n_rows; ++k)
        {
        if ((std::abs(cx_float(sp_eigval(i)).real() - eigval(k).real()) < 0.001) &&
            (std::abs(cx_float(sp_eigval(i)).imag() - eigval(k).imag()) < 0.001) &&
            (used(k) == 0))
          {
          dense_eval = k;
          used(k) = 1;
          break;
          }
        }

      REQUIRE( dense_eval != n_rows + 1 );

      REQUIRE( std::abs(sp_eigval(i)) == Approx(std::abs(eigval(dense_eval))).margin(0.01) );
      for(uword j = 0; j < n_rows; ++j)
        {
        REQUIRE( std::abs(sp_eigvec(j, i)) == Approx(std::abs(eigvec(j, dense_eval))).margin(0.01) );
        }
      }
    }

  REQUIRE(count > 0);
  }

TEST_CASE("fn_eigs_gen_even_complex_float_sm_opts_test")
  {
  const uword n_rows = 12;
  const uword n_eigval = 8;
  const uword n_trials = 10;
  uword count = 0;

  for(uword trial=0; trial < n_trials; ++trial)
    {
    SpMat<cx_float> m;
    m.sprandu(n_rows, n_rows, 0.3);
    sp_cx_fmat z(8, 8);
    z.sprandu(8, 8, 0.5);
    m.submat(2, 2, 9, 9) += 8 * z;
    m += cx_float(0.001,0)*speye< SpMat<cx_float> >(n_rows, n_rows);
    Mat<cx_float> d(m);

    // Eigendecompose, getting first 8 eigenvectors.
    Col<cx_float> sp_eigval;
    Mat<cx_float> sp_eigvec;
    eigs_opts opts{}; opts.maxiter = 10000; opts.tol = 1e-12;
    const bool status_sparse = eigs_gen(sp_eigval, sp_eigvec, m, n_eigval, "sm", opts);

    // Do the same for the dense case.
    Col<cx_float> eigval;
    Mat<cx_float> eigvec;
    const bool status_dense = eig_gen(eigval, eigvec, d);

    if( (status_sparse == false) || (status_dense == false) )  { continue; }  else  { ++count; }

    uvec used(n_rows, fill::zeros);

    for(uword i=0; i < n_eigval; ++i)
      {
      // Sorting these is difficult.
      // Find which one is the likely dense eigenvalue.
      uword dense_eval = n_rows + 1;
      for(uword k = 0; k < n_rows; ++k)
        {
        if ((std::abs(cx_float(sp_eigval(i)).real() - eigval(k).real()) < 0.001) &&
            (std::abs(cx_float(sp_eigval(i)).imag() - eigval(k).imag()) < 0.001) &&
            (used(k) == 0))
          {
          dense_eval = k;
          used(k) = 1;
          break;
          }
        }

      REQUIRE( dense_eval != n_rows + 1 );

      REQUIRE( std::abs(sp_eigval(i)) == Approx(std::abs(eigval(dense_eval))).margin(0.01) );
      for(uword j = 0; j < n_rows; ++j)
        {
        REQUIRE( std::abs(sp_eigvec(j, i)) == Approx(std::abs(eigvec(j, dense_eval))).margin(0.01) );
        }
      }
    }

  REQUIRE(count > 0);
  }

TEST_CASE("eigs_gen_odd_complex_test")
  {
  const uword n_rows = 10;
  const uword n_eigval = 5;
  const uword n_trials = 10;
  uword count = 0;

  for(uword trial=0; trial < n_trials; ++trial)
    {
    SpMat<cx_double> m;
    m.sprandu(n_rows, n_rows, 0.3);
    Mat<cx_double> d(m);

    // Eigendecompose, getting first 5 eigenvectors.
    Col<cx_double> sp_eigval;
    Mat<cx_double> sp_eigvec;
    const bool status_sparse = eigs_gen(sp_eigval, sp_eigvec, m, n_eigval);

    // Do the same for the dense case.
    Col<cx_double> eigval;
    Mat<cx_double> eigvec;
    const bool status_dense = eig_gen(eigval, eigvec, d);

    if( (status_sparse == false) || (status_dense == false) )  { continue; }  else  { ++count; }

    uvec used(n_rows, fill::zeros);

    for(uword i=0; i < n_eigval; ++i)
      {
      // Sorting these is difficult.
      // Find which one is the likely dense eigenvalue.
      uword dense_eval = n_rows + 1;
      for(uword k = 0; k < n_rows; ++k)
        {
        if ((std::abs(cx_double(sp_eigval(i)).real() - eigval(k).real()) < 1e-10) &&
            (std::abs(cx_double(sp_eigval(i)).imag() - eigval(k).imag()) < 1e-10) &&
            (used(k) == 0))
          {
          dense_eval = k;
          used(k) = 1;
          break;
          }
        }

      REQUIRE( dense_eval != n_rows + 1 );

      REQUIRE( std::abs(sp_eigval(i)) == Approx(std::abs(eigval(dense_eval))).margin(0.01) );
      for(size_t j = 0; j < n_rows; ++j)
        {
        REQUIRE( std::abs(sp_eigvec(j, i)) == Approx(std::abs(eigvec(j, dense_eval))).margin(0.01) );
        }
      }
    }

  REQUIRE(count > 0);
  }

TEST_CASE("fn_eigs_gen_even_complex_test")
  {
  const uword n_rows = 15;
  const uword n_eigval = 6;
  const uword n_trials = 10;
  uword count = 0;

  for(uword trial=0; trial < n_trials; ++trial)
    {
    SpMat<cx_double> m;
    m.sprandu(n_rows, n_rows, 0.3);
    Mat<cx_double> d(m);

    // Eigendecompose, getting first 6 eigenvectors.
    Col<cx_double> sp_eigval;
    Mat<cx_double> sp_eigvec;
    const bool status_sparse = eigs_gen(sp_eigval, sp_eigvec, m, n_eigval);

    // Do the same for the dense case.
    Col<cx_double> eigval;
    Mat<cx_double> eigvec;
    const bool status_dense = eig_gen(eigval, eigvec, d);

    if( (status_sparse == false) || (status_dense == false) )  { continue; }  else  { ++count; }

    uvec used(n_rows, fill::zeros);

    for(uword i=0; i < n_eigval; ++i)
      {
      // Sorting these is difficult.
      // Find which one is the likely dense eigenvalue.
      uword dense_eval = n_rows + 1;
      for(uword k = 0; k < n_rows; ++k)
        {
        if ((std::abs(cx_double(sp_eigval(i)).real() - eigval(k).real()) < 1e-10) &&
            (std::abs(cx_double(sp_eigval(i)).imag() - eigval(k).imag()) < 1e-10) &&
            (used(k) == 0))
          {
          dense_eval = k;
          used(k) = 1;
          break;
          }
        }

      REQUIRE( dense_eval != n_rows + 1 );

      REQUIRE( std::abs(sp_eigval(i)) == Approx(std::abs(eigval(dense_eval))).margin(0.01) );
      for(uword j = 0; j < n_rows; ++j)
        {
        REQUIRE( std::abs(sp_eigvec(j, i)) == Approx(std::abs(eigvec(j, dense_eval))).margin(0.01) );
        }
      }
    }

  REQUIRE(count > 0);
  }

TEST_CASE("fn_eigs_gen_even_complex_opts_test")
  {
  const uword n_rows = 15;
  const uword n_eigval = 6;
  const uword n_trials = 10;
  uword count = 0;

  for(uword trial=0; trial < n_trials; ++trial)
    {
    SpMat<cx_double> m;
    m.sprandu(n_rows, n_rows, 0.3);
    Mat<cx_double> d(m);

    // Eigendecompose, getting first 6 eigenvectors.
    Col<cx_double> sp_eigval;
    Mat<cx_double> sp_eigvec;
    eigs_opts opts{}; opts.maxiter = 10000; opts.tol = 1e-12;
    const bool status_sparse = eigs_gen(sp_eigval, sp_eigvec, m, n_eigval, "lm", opts);

    // Do the same for the dense case.
    Col<cx_double> eigval;
    Mat<cx_double> eigvec;
    const bool status_dense = eig_gen(eigval, eigvec, d);

    if( (status_sparse == false) || (status_dense == false) )  { continue; }  else  { ++count; }

    uvec used(n_rows, fill::zeros);

    for(uword i=0; i < n_eigval; ++i)
      {
      // Sorting these is difficult.
      // Find which one is the likely dense eigenvalue.
      uword dense_eval = n_rows + 1;
      for(uword k = 0; k < n_rows; ++k)
        {
        if ((std::abs(cx_double(sp_eigval(i)).real() - eigval(k).real()) < 1e-10) &&
            (std::abs(cx_double(sp_eigval(i)).imag() - eigval(k).imag()) < 1e-10) &&
            (used(k) == 0))
          {
          dense_eval = k;
          used(k) = 1;
          break;
          }
        }

      REQUIRE( dense_eval != n_rows + 1 );

      REQUIRE( std::abs(sp_eigval(i)) == Approx(std::abs(eigval(dense_eval))).margin(0.01) );
      for(uword j = 0; j < n_rows; ++j)
        {
        REQUIRE( std::abs(sp_eigvec(j, i)) == Approx(std::abs(eigvec(j, dense_eval))).margin(0.01) );
        }
      }
    }

  REQUIRE(count > 0);
  }

TEST_CASE("eigs_gen_odd_complex_sigma_test")
  {
  const uword n_rows = 10;
  const uword n_eigval = 5;
  const cx_double sigma = 1.0;
  const uword n_trials = 10;
  uword count = 0;

  for(uword trial=0; trial < n_trials; ++trial)
    {
    SpMat<cx_double> m;
    m.sprandu(n_rows, n_rows, 0.3);
    sp_cx_mat z(5, 5);
    z.sprandu(5, 5, 0.5);
    m.submat(2, 2, 6, 6) += 5 * z;
    m += (sigma+cx_double(0.001,0))*speye< SpMat<cx_double> >(n_rows, n_rows);
    Mat<cx_double> d(m);

    // Eigendecompose, getting first 5 eigenvectors around 1.
    Col<cx_double> sp_eigval;
    Mat<cx_double> sp_eigvec;
    const bool status_sparse = eigs_gen(sp_eigval, sp_eigvec, m, n_eigval, sigma);

    // Do the same for the dense case.
    Col<cx_double> eigval;
    Mat<cx_double> eigvec;
    const bool status_dense = eig_gen(eigval, eigvec, d);

    if( (status_sparse == false) || (status_dense == false) )  { continue; }  else  { ++count; }

    uvec used(n_rows, fill::zeros);

    for(uword i=0; i < n_eigval; ++i)
      {
      // Sorting these is difficult.
      // Find which one is the likely dense eigenvalue.
      uword dense_eval = n_rows + 1;
      for(uword k = 0; k < n_rows; ++k)
        {
        if ((std::abs(cx_double(sp_eigval(i)).real() - eigval(k).real()) < 1e-10) &&
            (std::abs(cx_double(sp_eigval(i)).imag() - eigval(k).imag()) < 1e-10) &&
            (used(k) == 0))
          {
          dense_eval = k;
          used(k) = 1;
          break;
          }
        }

      REQUIRE( dense_eval != n_rows + 1 );

      REQUIRE( std::abs(sp_eigval(i)) == Approx(std::abs(eigval(dense_eval))).margin(0.01) );
      for(size_t j = 0; j < n_rows; ++j)
        {
        REQUIRE( std::abs(sp_eigvec(j, i)) == Approx(std::abs(eigvec(j, dense_eval))).margin(0.01) );
        }
      }
    }

  REQUIRE(count > 0);
  }

TEST_CASE("fn_eigs_gen_even_complex_sigma_test")
  {
  const uword n_rows = 15;
  const uword n_eigval = 6;
  const cx_double sigma = 1.0;
  const uword n_trials = 10;
  uword count = 0;

  for(uword trial=0; trial < n_trials; ++trial)
    {
    SpMat<cx_double> m;
    m.sprandu(n_rows, n_rows, 0.3);
    sp_cx_mat z(8, 8);
    z.sprandu(8, 8, 0.5);
    m.submat(2, 2, 9, 9) += 8 * z;
    m += (sigma+cx_double(0.001,0))*speye< SpMat<cx_double> >(n_rows, n_rows);
    Mat<cx_double> d(m);

    // Eigendecompose, getting first 6 eigenvectors around 1.
    Col<cx_double> sp_eigval;
    Mat<cx_double> sp_eigvec;
    const bool status_sparse = eigs_gen(sp_eigval, sp_eigvec, m, n_eigval, sigma);

    // Do the same for the dense case.
    Col<cx_double> eigval;
    Mat<cx_double> eigvec;
    const bool status_dense = eig_gen(eigval, eigvec, d);

    if( (status_sparse == false) || (status_dense == false) )  { continue; }  else  { ++count; }

    uvec used(n_rows, fill::zeros);

    for(uword i=0; i < n_eigval; ++i)
      {
      // Sorting these is difficult.
      // Find which one is the likely dense eigenvalue.
      uword dense_eval = n_rows + 1;
      for(uword k = 0; k < n_rows; ++k)
        {
        if ((std::abs(cx_double(sp_eigval(i)).real() - eigval(k).real()) < 1e-10) &&
            (std::abs(cx_double(sp_eigval(i)).imag() - eigval(k).imag()) < 1e-10) &&
            (used(k) == 0))
          {
          dense_eval = k;
          used(k) = 1;
          break;
          }
        }

      REQUIRE( dense_eval != n_rows + 1 );

      REQUIRE( std::abs(sp_eigval(i)) == Approx(std::abs(eigval(dense_eval))).margin(0.01) );
      for(uword j = 0; j < n_rows; ++j)
        {
        REQUIRE( std::abs(sp_eigvec(j, i)) == Approx(std::abs(eigvec(j, dense_eval))).margin(0.01) );
        }
      }
    }

  REQUIRE(count > 0);
  }

TEST_CASE("fn_eigs_gen_even_complex_sigma_opts_test")
  {
  const uword n_rows = 15;
  const uword n_eigval = 6;
  const cx_double sigma = 1.0;
  const uword n_trials = 10;
  uword count = 0;

  for(uword trial=0; trial < n_trials; ++trial)
    {
    SpMat<cx_double> m;
    m.sprandu(n_rows, n_rows, 0.3);
    sp_cx_mat z(8, 8);
    z.sprandu(8, 8, 0.5);
    m.submat(2, 2, 9, 9) += 8 * z;
    m += (sigma+cx_double(0.001,0))*speye< SpMat<cx_double> >(n_rows, n_rows);
    Mat<cx_double> d(m);

    // Eigendecompose, getting first 6 eigenvectors around 1.0.
    Col<cx_double> sp_eigval;
    Mat<cx_double> sp_eigvec;
    eigs_opts opts{}; opts.maxiter = 10000; opts.tol = 1e-12;
    const bool status_sparse = eigs_gen(sp_eigval, sp_eigvec, m, n_eigval, sigma, opts);

    // Do the same for the dense case.
    Col<cx_double> eigval;
    Mat<cx_double> eigvec;
    const bool status_dense = eig_gen(eigval, eigvec, d);

    if( (status_sparse == false) || (status_dense == false) )  { continue; }  else  { ++count; }

    uvec used(n_rows, fill::zeros);

    for(uword i=0; i < n_eigval; ++i)
      {
      // Sorting these is difficult.
      // Find which one is the likely dense eigenvalue.
      uword dense_eval = n_rows + 1;
      for(uword k = 0; k < n_rows; ++k)
        {
        if ((std::abs(cx_double(sp_eigval(i)).real() - eigval(k).real()) < 1e-10) &&
            (std::abs(cx_double(sp_eigval(i)).imag() - eigval(k).imag()) < 1e-10) &&
            (used(k) == 0))
          {
          dense_eval = k;
          used(k) = 1;
          break;
          }
        }

      REQUIRE( dense_eval != n_rows + 1 );

      REQUIRE( std::abs(sp_eigval(i)) == Approx(std::abs(eigval(dense_eval))).margin(0.01) );
      for(uword j = 0; j < n_rows; ++j)
        {
        REQUIRE( std::abs(sp_eigvec(j, i)) == Approx(std::abs(eigvec(j, dense_eval))).margin(0.01) );
        }
      }
    }

  REQUIRE(count > 0);
  }

TEST_CASE("eigs_gen_odd_complex_sm_test")
  {
  const uword n_rows = 10;
  const uword n_eigval = 5;
  const uword n_trials = 10;
  uword count = 0;

  for(uword trial=0; trial < n_trials; ++trial)
    {
    SpMat<cx_double> m;
    m.sprandu(n_rows, n_rows, 0.3);
    m += cx_double(0.001,0)*speye< SpMat<cx_double> >(n_rows, n_rows);
    Mat<cx_double> d(m);

    // Eigendecompose, getting first 5 eigenvectors.
    Col<cx_double> sp_eigval;
    Mat<cx_double> sp_eigvec;
    const bool status_sparse = eigs_gen(sp_eigval, sp_eigvec, m, n_eigval, "sm");

    // Do the same for the dense case.
    Col<cx_double> eigval;
    Mat<cx_double> eigvec;
    const bool status_dense = eig_gen(eigval, eigvec, d);

    if( (status_sparse == false) || (status_dense == false) )  { continue; }  else  { ++count; }

    uvec used(n_rows, fill::zeros);

    for(uword i=0; i < n_eigval; ++i)
      {
      // Sorting these is difficult.
      // Find which one is the likely dense eigenvalue.
      uword dense_eval = n_rows + 1;
      for(uword k = 0; k < n_rows; ++k)
        {
        if ((std::abs(cx_double(sp_eigval(i)).real() - eigval(k).real()) < 1e-10) &&
            (std::abs(cx_double(sp_eigval(i)).imag() - eigval(k).imag()) < 1e-10) &&
            (used(k) == 0))
          {
          dense_eval = k;
          used(k) = 1;
          break;
          }
        }

      REQUIRE( dense_eval != n_rows + 1 );

      REQUIRE( std::abs(sp_eigval(i)) == Approx(std::abs(eigval(dense_eval))).margin(0.01) );
      for(size_t j = 0; j < n_rows; ++j)
        {
        REQUIRE( std::abs(sp_eigvec(j, i)) == Approx(std::abs(eigvec(j, dense_eval))).margin(0.01) );
        }
      }
    }

  REQUIRE(count > 0);
  }

TEST_CASE("fn_eigs_gen_even_complex_sm_test")
  {
  const uword n_rows = 15;
  const uword n_eigval = 6;
  const uword n_trials = 10;
  uword count = 0;

  for(uword trial=0; trial < n_trials; ++trial)
    {
    SpMat<cx_double> m;
    m.sprandu(n_rows, n_rows, 0.3);
    m += cx_double(0.001,0)*speye< SpMat<cx_double> >(n_rows, n_rows);
    Mat<cx_double> d(m);

    // Eigendecompose, getting first 6 eigenvectors.
    Col<cx_double> sp_eigval;
    Mat<cx_double> sp_eigvec;
    const bool status_sparse = eigs_gen(sp_eigval, sp_eigvec, m, n_eigval, "sm");

    // Do the same for the dense case.
    Col<cx_double> eigval;
    Mat<cx_double> eigvec;
    const bool status_dense = eig_gen(eigval, eigvec, d);

    if( (status_sparse == false) || (status_dense == false) )  { continue; }  else  { ++count; }

    uvec used(n_rows, fill::zeros);

    for(uword i=0; i < n_eigval; ++i)
      {
      // Sorting these is difficult.
      // Find which one is the likely dense eigenvalue.
      uword dense_eval = n_rows + 1;
      for(uword k = 0; k < n_rows; ++k)
        {
        if ((std::abs(cx_double(sp_eigval(i)).real() - eigval(k).real()) < 1e-10) &&
            (std::abs(cx_double(sp_eigval(i)).imag() - eigval(k).imag()) < 1e-10) &&
            (used(k) == 0))
          {
          dense_eval = k;
          used(k) = 1;
          break;
          }
        }

      REQUIRE( dense_eval != n_rows + 1 );

      REQUIRE( std::abs(sp_eigval(i)) == Approx(std::abs(eigval(dense_eval))).margin(0.01) );
      for(uword j = 0; j < n_rows; ++j)
        {
        REQUIRE( std::abs(sp_eigvec(j, i)) == Approx(std::abs(eigvec(j, dense_eval))).margin(0.01) );
        }
      }
    }

  REQUIRE(count > 0);
  }

TEST_CASE("fn_eigs_gen_even_complex_sm_opts_test")
  {
  const uword n_rows = 15;
  const uword n_eigval = 6;
  const uword n_trials = 10;
  uword count = 0;

  for(uword trial=0; trial < n_trials; ++trial)
    {
    SpMat<cx_double> m;
    m.sprandu(n_rows, n_rows, 0.3);
    m += cx_double(0.001,0)*speye< SpMat<cx_double> >(n_rows, n_rows);
    Mat<cx_double> d(m);

    // Eigendecompose, getting first 6 eigenvectors.
    Col<cx_double> sp_eigval;
    Mat<cx_double> sp_eigvec;
    eigs_opts opts{}; opts.maxiter = 10000; opts.tol = 1e-12;
    const bool status_sparse = eigs_gen(sp_eigval, sp_eigvec, m, n_eigval, "sm", opts);

    // Do the same for the dense case.
    Col<cx_double> eigval;
    Mat<cx_double> eigvec;
    const bool status_dense = eig_gen(eigval, eigvec, d);

    if( (status_sparse == false) || (status_dense == false) )  { continue; }  else  { ++count; }

    uvec used(n_rows, fill::zeros);

    for(uword i=0; i < n_eigval; ++i)
      {
      // Sorting these is difficult.
      // Find which one is the likely dense eigenvalue.
      uword dense_eval = n_rows + 1;
      for(uword k = 0; k < n_rows; ++k)
        {
        if ((std::abs(cx_double(sp_eigval(i)).real() - eigval(k).real()) < 1e-10) &&
            (std::abs(cx_double(sp_eigval(i)).imag() - eigval(k).imag()) < 1e-10) &&
            (used(k) == 0))
          {
          dense_eval = k;
          used(k) = 1;
          break;
          }
        }

      REQUIRE( dense_eval != n_rows + 1 );

      REQUIRE( std::abs(sp_eigval(i)) == Approx(std::abs(eigval(dense_eval))).margin(0.01) );
      for(uword j = 0; j < n_rows; ++j)
        {
        REQUIRE( std::abs(sp_eigvec(j, i)) == Approx(std::abs(eigvec(j, dense_eval))).margin(0.01) );
        }
      }
    }

  REQUIRE(count > 0);
  }

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text:
#ifndef ASIO_CORO_EXTENSIONS_FUTURE_HPP
#define ASIO_CORO_EXTENSIONS_FUTURE_HPP

#include "detail/coroutine_holder.hpp"

#include <boost/scope_exit.hpp>
#include <boost/thread/future.hpp>

#ifdef BOOST_THREAD_PROVIDES_FUTURE_CONTINUATION

namespace asio_coro {
/// Returns an awaitable that suspends the awaiting coroutine upon the speicifed future is resolved.
///
/// The awaitable returns an instance of boost::future<ResultType> that resolves to the result of awaited future.
///
/// \param future   A future to wait for completion.
template <class ResultType> auto async_wait_future(boost::future<ResultType> &&future) {
  class awaitable {
  public:
    explicit awaitable(boost::future<ResultType> &&future) noexcept : _future(std::move(future)) {}

    constexpr bool await_ready() const noexcept { return false; }

    decltype(auto) await_resume() { return _then_future.get(); }

    void await_suspend(detail::coroutine_handle<> continuation) {
      detail::coroutine_holder<> holder(continuation);
      BOOST_SCOPE_EXIT_ALL(&) { holder.release(); };

      _future.then(boost::launch::sync, [this, holder = std::move(holder)](auto &&future) mutable {
        _then_future = std::move(future);
        holder.release().resume();
      });
    }

  private:
    boost::future<ResultType> _future;
    boost::future<ResultType> _then_future;
  };

  return awaitable(std::move(future));
}

/// Returns an awaitable that suspends the awaiting coroutine upon the future is resolved and then resumes it within the
/// context of the specified executor using boost::asio::dispatch function.
///
/// The awaitable returns an instance of boost::future<ResultType> that resolves to the result of awaited future.
///
/// \param executor   An executor to resume the awaiting coroutine in.
/// \param future     A future to wait for completion.
template <class Executor, class ResultType>
auto async_wait_future(Executor &executor, boost::future<ResultType> &&future) {
  class awaitable {
  public:
    explicit awaitable(Executor &executor, boost::future<ResultType> &&future)
        : _executor(executor), _future(std::move(future)) {}

    constexpr bool await_ready() const noexcept { return false; }

    decltype(auto) await_resume() { return _then_future.get(); }

    void await_suspend(detail::coroutine_handle<> continuation) {
      detail::coroutine_holder<> holder(continuation);
      BOOST_SCOPE_EXIT_ALL(&) { holder.release(); };

      _future.then(boost::launch::sync, [this, holder = std::move(holder)](auto &&future) mutable {
        _then_future = std::move(future);

        boost::asio::dispatch(_executor, [holder = std::move(holder)]() mutable { holder.release().resume(); });
      });
    }

  private:
    Executor &_executor;
    boost::future<ResultType> _future;
    boost::future<ResultType> _then_future;
  };

  return awaitable(executor, std::move(future));
}
} // namespace asio_coro

#endif // BOOST_THREAD_PROVIDES_FUTURE_CONTINUATION

#endif // ASIO_CORO_EXTENSIONS_FUTURE_HPP

ext: hpp


text:
// Copyright (C) 2005, 2006 Douglas Gregor.

// Use, modification and distribution is subject to the Boost Software
// License, Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
// http://www.boost.org/LICENSE_1_0.txt)

// Message Passing Interface 1.1 -- Section 4.8. All-to-all
#ifndef BOOST_MPI_ALL_TO_ALL_HPP
#define BOOST_MPI_ALL_TO_ALL_HPP

#include <boost/mpi/exception.hpp>
#include <boost/mpi/datatype.hpp>
#include <vector>
#include <boost/mpi/packed_oarchive.hpp>
#include <boost/mpi/packed_iarchive.hpp>
#include <boost/mpi/communicator.hpp>
#include <boost/mpi/environment.hpp>
#include <boost/assert.hpp>
#include <boost/mpi/collectives_fwd.hpp>
#include <boost/mpi/allocator.hpp>

namespace boost { namespace mpi {

namespace detail {
  // We're performing an all-to-all with a type that has an
  // associated MPI datatype, so we'll use MPI_Alltoall to do all of
  // the work.
  template<typename T>
  void
  all_to_all_impl(const communicator& comm, const T* in_values, int n,
                  T* out_values, mpl::true_)
  {
    MPI_Datatype type = get_mpi_datatype<T>(*in_values);
    BOOST_MPI_CHECK_RESULT(MPI_Alltoall,
                           (const_cast<T*>(in_values), n, type,
                            out_values, n, type, comm));
  }

  // We're performing an all-to-all with a type that does not have an
  // associated MPI datatype, so we'll need to serialize
  // it.
  template<typename T>
  void
  all_to_all_impl(const communicator& comm, const T* in_values, int n,
                  T* out_values, mpl::false_)
  {
    int size = comm.size();
    int rank = comm.rank();

    // The amount of data to be sent to each process
    std::vector<int> send_sizes(size);

    // The displacements for each outgoing value.
    std::vector<int> send_disps(size);

    // The buffer that will store all of the outgoing values
    std::vector<char, allocator<char> > outgoing;

    // Pack the buffer with all of the outgoing values.
    for (int dest = 0; dest < size; ++dest) {
      // Keep track of the displacements
      send_disps[dest] = outgoing.size();

      // Our own value will never be transmitted, so don't pack it.
      if (dest != rank) {
        packed_oarchive oa(comm, outgoing);
        for (int i = 0; i < n; ++i)
          oa << in_values[dest * n + i];
      }

      // Keep track of the sizes
      send_sizes[dest] = outgoing.size() - send_disps[dest];
    }

    // Determine how much data each process will receive.
    std::vector<int> recv_sizes(size);
    all_to_all(comm, send_sizes, recv_sizes);

    // Prepare a buffer to receive the incoming data.
    std::vector<int> recv_disps(size);
    int sum = 0;
    for (int src = 0; src < size; ++src) {
      recv_disps[src] = sum;
      sum += recv_sizes[src];
    }
    std::vector<char, allocator<char> > incoming(sum > 0? sum : 1);

    // Make sure we don't try to reference an empty vector
    if (outgoing.empty())
      outgoing.push_back(0);

    // Transmit the actual data
    BOOST_MPI_CHECK_RESULT(MPI_Alltoallv,
                           (&outgoing[0], &send_sizes[0],
                            &send_disps[0], MPI_PACKED,
                            &incoming[0], &recv_sizes[0],
                            &recv_disps[0], MPI_PACKED,
                            comm));

    // Deserialize data from the iarchive
    for (int src = 0; src < size; ++src) {
      if (src == rank)
        std::copy(in_values + src * n, in_values + (src + 1) * n,
                  out_values + src * n);
      else {
        packed_iarchive ia(comm, incoming, boost::archive::no_header,
                           recv_disps[src]);
        for (int i = 0; i < n; ++i)
          ia >> out_values[src * n + i];
      }
    }
  }
} // end namespace detail

template<typename T>
inline void
all_to_all(const communicator& comm, const T* in_values, T* out_values)
{
  detail::all_to_all_impl(comm, in_values, 1, out_values, is_mpi_datatype<T>());
}

template<typename T>
void
all_to_all(const communicator& comm, const std::vector<T>& in_values,
           std::vector<T>& out_values)
{
  BOOST_ASSERT((int)in_values.size() == comm.size());
  out_values.resize(comm.size());
  ::boost::mpi::all_to_all(comm, &in_values[0], &out_values[0]);
}

template<typename T>
inline void
all_to_all(const communicator& comm, const T* in_values, int n, T* out_values)
{
  detail::all_to_all_impl(comm, in_values, n, out_values, is_mpi_datatype<T>());
}

template<typename T>
void
all_to_all(const communicator& comm, const std::vector<T>& in_values, int n,
           std::vector<T>& out_values)
{
  BOOST_ASSERT((int)in_values.size() == comm.size() * n);
  out_values.resize(comm.size() * n);
  ::boost::mpi::all_to_all(comm, &in_values[0], n, &out_values[0]);
}

} } // end namespace boost::mpi

#endif // BOOST_MPI_ALL_TO_ALL_HPP

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text:
/**
 * $Id$
 *
 * Copyright (C)
 * 2015 - $Date$
 *     Martin Wolf <ndhist@martin-wolf.org>
 *
 * This file is distributed under the BSD 2-Clause Open Source License
 * (See LICENSE file).
 *
 */
#include <boost/python.hpp>

#include <ndhist/stats/expectation.hpp>

namespace bp = boost::python;

namespace ndhist {

namespace stats {

void register_expectation()
{
    bp::def("expectation"
      , &py::expectation
      , ( bp::arg("hist")
        , bp::arg("n")=1
        , bp::arg("axis")=bp::object()
        )
      , "Calculates the n'th order expectation value along the given axis of \n"
        "the given ndhist object weighted by the sum of weights in each bin. \n"
        "It generates a projection along the given axis and then calculates  \n"
        "the n'th order expectation axis value.                              \n"
        "In statistics the n'th order expectation is defined as the          \n"
        "expectation of x^n, i.e. ``E[x^n]``, where x is the bin center axis \n"
        "value in this case.                                                 \n"
        "If ``None`` is given as axis argument (the default), the n'th order \n"
        "expectation value for all individual axes of the ndhist object is   \n"
        "calculated and returned as a tuple. But if the dimensionality of    \n"
        "the histogram is 1, a scalar value is returned.                     \n"
        "                                                                    \n"
        ".. note:: This function is only defined for ndhist objects with POD \n"
        "          type axis values AND POD type weight values.              \n"
    );
}

}// namespace stats
}// namespace ndhist

ext: cpp

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