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matrix_tester.cc
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matrix_tester.cc
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// Hossein Moein
// February 11, 2018
/*
Copyright (c) 2019-2022, Hossein Moein
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:
* Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the distribution.
* Neither the name of Hossein Moein and/or the Tiger nor the
names of its contributors may be used to endorse or promote products
derived from this software without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL <COPYRIGHT HOLDER> BE LIABLE FOR ANY
DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
#include <iostream>
#include <time.h>
#include <Tiger/BaseMathOperators.h>
#include <Tiger/MathOperators.h>
#include <Tiger/Complex.h>
#include <Tiger/Matrix.h>
using namespace hmma;
// ----------------------------------------------------------------------------
int main (int argCnt, char *argVctr []) {
std::cout.precision (2);
std::cout << "\nTesting the Symmetric Matrix ...\n" << std::endl;
SDMatrix smat (8, 8);
int count = 0;
for (SDMatrix::size_type r = 0; r < 8; ++r)
for (SDMatrix::size_type c = 0; c < 8; ++c)
smat (r, c) = ++count;
SDMatrix smat_tran;
smat.transpose (smat_tran);
std::cout << "Original Matrix:" << std::endl;
smat.dump (std::cout) << std::endl;
std::cout << "Is Symmetric Matrix: " << smat.is_symmetric () << std::endl;
std::cout << "Transposed Matrix:" << std::endl;
smat_tran.dump (std::cout) << std::endl;
std::cout << "\nTesting the Row Iterator:" << std::endl;
for (SDMatrix::row_const_iterator riter = smat.row_begin ();
riter != smat.row_end (); ++riter)
std::cout << *riter << " ";
std::cout << std::endl;
std::cout << "\nTesting the Column Iterator:" << std::endl;
for (SDMatrix::col_const_iterator citer = smat.col_begin ();
citer != smat.col_end (); ++citer)
std::cout << *citer << " ";
std::cout << std::endl;
std::cout << "\n-------" << std::endl;
std::cout << "\n\nTesting the Dense Matrix ...\n" << std::endl;
{
DDMatrix dmat (8, 3);
int count = 0;
for (DDMatrix::size_type i = 0; i < 8; ++i)
for (DDMatrix::size_type j = 0; j < 3; ++j)
dmat (i, j) = ++count;
dmat.dump (std::cout);
const DDMatrix::ColumnVector cv = dmat.get_column (1);
const DDMatrix::RowVector rv = dmat.get_row (4);
std::cout << "Column 1:\n";
for (DDMatrix::ColumnVector::const_iterator citer = cv.begin ();
citer != cv.end (); ++citer)
std::cout << *citer << "\n";
std::cout << "\nRow 4:\n";
for (DDMatrix::RowVector::const_iterator citer = rv.begin ();
citer != rv.end (); ++citer)
std::cout << *citer << " ";
std::cout << std::endl;
std::cout << "\nTesting the column iterator ...\n" << std::endl;
for (DDMatrix::col_const_iterator cciter = dmat.col_begin ();
cciter != dmat.col_end (); ++cciter)
std::cout << *cciter << " ";
std::cout << std::endl;
std::cout << "\nTesting the Row Iterator:" << std::endl;
for (DDMatrix::row_const_iterator rciter = dmat.row_begin ();
rciter != dmat.row_end (); ++rciter)
std::cout << *rciter << " ";
std::cout << std::endl;
std::cout << "\nTesting the transpose methods ...\n" << std::endl;
DDMatrix dmat_tran;
dmat.transpose (dmat_tran);
std::cout << "Original Matrix:" << std::endl;
dmat.dump (std::cout) << std::endl;
std::cout << "Transposed Matrix:" << std::endl;
dmat_tran.dump (std::cout) << std::endl;
std::cout << "\nTesting the set row/column methods ...\n" << std::endl;
std::vector<double> vec;
for (DDMatrix::size_type i = 0; i < 3; ++i)
vec.push_back (111.1);
dmat.set_row (vec.begin (), 7);
vec.clear ();
for (DDMatrix::size_type i = 0; i < 8; ++i)
vec.push_back (111.1);
dmat.set_column (vec.begin (), 2);
dmat.dump (std::cout);
}
std::cout << "\n-------" << std::endl;
{
std::cout << "\nTesting the transpose operator ...\n" << std::endl;
DDMatrix dmat (8, 3);
DDMatrix one_mat (3, 8);
int count = 0;
for (DDMatrix::size_type i = 0; i < 8; ++i)
for (DDMatrix::size_type j = 0; j < 3; ++j) {
dmat (i, j) = ++count;
one_mat (j, i) = 1.0;
}
const DDMatrix dmat_tran = one_mat + ~ dmat;
const DDMatrix dmat_tran2 = ~ dmat + one_mat;
const DDMatrix dmat_tran3 = one_mat + ~ dmat + one_mat;
std::cout << "Original Matrix:" << std::endl;
dmat.dump (std::cout) << std::endl;
std::cout << "Transposed Matrix:" << std::endl;
dmat_tran.dump (std::cout) << std::endl;
dmat_tran2.dump (std::cout) << std::endl;
dmat_tran3.dump (std::cout) << std::endl;
}
std::cout << "\n-------" << std::endl;
{
std::cout << "\nTesting Iterators ...\n" << std::endl;
DDMatrix dmat (3, 8);
int count = 0;
for (DDMatrix::size_type i = 0; i < 3; ++i)
for (DDMatrix::size_type j = 0; j < 8; ++j)
dmat (i, j) = ++count;
DDMatrix dmat2 (7, 10);
dmat2 = dmat;
dmat2.dump (std::cout);
std::cout << "\nTesting the Row Iterator:" << std::endl;
for (DDMatrix::row_iterator riter = dmat2.row_begin ();
riter != dmat2.row_end (); ++riter)
std::cout << *riter << " ";
std::cout << std::endl;
const DDMatrix::ColumnVector cv = dmat2.get_column (5);
const DDMatrix::RowVector rv = dmat2.get_row (2);
std::cout << "Column 5:\n";
for (DDMatrix::ColumnVector::const_iterator citer = cv.begin ();
citer != cv.end (); ++citer)
std::cout << *citer << "\n";
std::cout << "\nRow 2:\n";
for (DDMatrix::RowVector::const_iterator citer = rv.begin ();
citer != rv.end (); ++citer)
std::cout << *citer << " ";
std::cout << std::endl;
}
std::cout << "\n-------" << std::endl;
{
std::cout << "\nTesting Iterators (2) ...\n" << std::endl;
DDMatrix dmat (8, 8);
int count = 0;
for (DDMatrix::size_type i = 0; i < 8; ++i)
for (DDMatrix::size_type j = 0; j < 8; ++j)
dmat (i, j) = ++count;
const DDMatrix dmat2 = dmat;
dmat2.dump (std::cout);
std::cout << "\nTesting the Row Iterator:" << std::endl;
for (DDMatrix::row_iterator riter = dmat.row_begin ();
riter != dmat.row_end (); ++riter)
std::cout << *riter << " ";
std::cout << std::endl;
const DDMatrix::ColumnVector cv = dmat2.get_column (5);
const DDMatrix::RowVector rv = dmat2.get_row (6);
std::cout << "Column 5:\n";
for (DDMatrix::ColumnVector::const_iterator citer = cv.begin ();
citer != cv.end (); ++citer)
std::cout << *citer << "\n";
std::cout << "\nRow 6:\n";
for (DDMatrix::RowVector::const_iterator citer = rv.begin ();
citer != rv.end (); ++citer)
std::cout << *citer << " ";
std::cout << std::endl;
const int pre = std::cout.precision (8);
std::cout << "\nTesting determinant calculation ...\n" << std::endl;
std::cout << "Determinant: " << dmat.determinant () << std::endl;
std::cout << "Is singular? " << dmat.is_singular () << std::endl;
std::cout.precision (pre);
}
std::cout << "\n-------" << std::endl;
{
std::cout << "\nTesting determinant calculation ...\n" << std::endl;
const int pre = std::cout.precision (8);
DDMatrix dmat (3, 3);
DDMatrix dmat_dev (3, 3);
DDMatrix dmat_null (3, 3);
// 2*X + 3*Y + 2*Z = 13
// 3*X + 2*Y + 3*Z = 17
// 4*X - 2*Y + 2*Z = 12
//
// [2 3 2] [X] [13]
// [3 2 3] * [Y] = [17]
// [4 2 2] [Z] [12]
dmat (0, 0) = 2.0;
dmat (0, 1) = 3.0;
dmat (0, 2) = 2.0;
dmat (1, 0) = 3.0;
dmat (1, 1) = 2.0;
dmat (1, 2) = 3.0;
dmat (2, 0) = 4.0;
dmat (2, 1) = 2.0;
dmat (2, 2) = 2.0;
std::cout << "Original Matrix:" << std::endl;
dmat.dump (std::cout) << std::endl;
std::cout << "Determinant: " << dmat.determinant () << std::endl;
std::cout << "Condition#: " << dmat.condition () << std::endl;
std::cout << "Is singular? " << dmat.is_singular () << std::endl;
DDMatrix adj;
dmat.adjoint (adj);
std::cout << "The Adjoint matrix:" << std::endl;
adj.dump (std::cout) << std::endl;
dmat.scale (Multiplies<double>(), 10.0);
std::cout << "Determinant after multiplied by 10: "
<< dmat.determinant () << std::endl;
std::cout << "Condition# after multiplied by 10: "
<< dmat.condition () << std::endl;
std::cout << "Is singular? "
<< dmat.is_singular () << "\n" << std::endl;
std::cout << "Original dmat:" << std::endl;
dmat.dump (std::cout) << std::endl;
DDMatrix tmp_mtx = dmat + dmat_null;
dmat_dev = (dmat + dmat_null) / tmp_mtx;
std::cout << "After dmat / dmat:" << std::endl;
dmat_dev.dump (std::cout) << std::endl;
dmat (0, 0) = 5.0;
dmat (0, 1) = -3.0;
dmat (0, 2) = 2.0;
dmat (1, 0) = 1.0;
dmat (1, 1) = 0.0;
dmat (1, 2) = 6.0;
dmat (2, 0) = 3.0;
dmat (2, 1) = 1.0;
dmat (2, 2) = -2.0;
auto dfut = dmat.determinant_async ();
const double deter = dfut.get();
std::cout << "Determinant: " << deter << std::endl;
std::cout << "Condition#: " << dmat.condition () << std::endl;
std::cout << "Is singular? " << dmat.is_singular () << std::endl;
dmat.resize (4, 4);
dmat (0, 0) = 1.0;
dmat (0, 1) = 2.0;
dmat (0, 2) = -1.0;
dmat (0, 3) = 0.0;
dmat (1, 0) = -2.0;
dmat (1, 1) = 1.0;
dmat (1, 2) = 3.0;
dmat (1, 3) = 1.0;
dmat (2, 0) = 3.0;
dmat (2, 1) = 0.0;
dmat (2, 2) = -2.0;
dmat (2, 3) = 2.0;
dmat (3, 0) = 1.0;
dmat (3, 1) = 2.0;
dmat (3, 2) = 3.0;
dmat (3, 3) = 4.0;
std::cout << "Determinant: " << dmat.determinant () << std::endl;
std::cout << "Is singular? " << dmat.is_singular () << std::endl;
std::cout.precision (pre);
}
std::cout << "\n-------" << std::endl;
{
std::cout << "\nTesting Dense Matrix Expression math ...\n"
<< std::endl;
DDMatrix dmat1 (8, 8);
DDMatrix dmat2 (8, 8);
int count = 0;
for (DDMatrix::size_type i = 0; i < 8; ++i)
for (DDMatrix::size_type j = 0; j < 8; ++j) {
dmat1 (i, j) = ++count;
dmat2 (i, j) = 10.0;
}
std::cout << "Before Addition(1):" << std::endl;
dmat1.dump (std::cout) << std::endl;
const DDMatrix dmat3 =
(dmat1 + dmat2) - dmat2 + (dmat1 + dmat2);
std::cout << "After Addition(2):" << std::endl;
dmat3.dump (std::cout) << std::endl;
std::cout << "Before Addition:" << std::endl;
dmat1.dump (std::cout) << std::endl;
dmat2.dump (std::cout) << std::endl;
const DDMatrix dmat4 = dmat1 + dmat2;
std::cout << "After Addition(3):" << std::endl;
dmat4.dump (std::cout) << std::endl;
count = 0;
for (DDMatrix::size_type i = 0; i < 8; ++i)
for (DDMatrix::size_type j = 0; j < 8; ++j)
dmat1 (i, j) = ++count;
for (DDMatrix::size_type i = 0; i < 8; ++i)
for (DDMatrix::size_type j = 0; j < 8; ++j)
dmat2 (i, j) = --count;
std::cout << "Original Matrices:" << std::endl;
dmat1.dump (std::cout) << std::endl;
dmat2.dump (std::cout) << std::endl;
dmat2 += dmat1;
std::cout << "After dmat2 += dmat1;:" << std::endl;
dmat2.dump (std::cout) << std::endl;
count = 0;
for (DDMatrix::size_type i = 0; i < 8; ++i)
for (DDMatrix::size_type j = 0; j < 8; ++j)
dmat1 (i, j) = ++count;
for (DDMatrix::size_type i = 0; i < 8; ++i)
for (DDMatrix::size_type j = 0; j < 8; ++j)
dmat2 (i, j) = --count;
dmat2 -= dmat1;
std::cout << "After dmat2 -= dmat1;:" << std::endl;
dmat2.dump (std::cout) << std::endl;
const DDMatrix dmat5 =
(dmat1 + dmat2) - dmat2 + (dmat1 + dmat2);
std::cout << "Original Matrix:" << std::endl;
dmat5.dump (std::cout) << std::endl;
std::cout << "dmat2 += (dmat1 + dmat2) - dmat2 + (dmat1 + dmat2);:"
<< std::endl;
dmat2 += (dmat1 + dmat2) - dmat2 + (dmat1 + dmat2);
dmat2.dump (std::cout) << std::endl;
}
std::cout << "\n-------" << std::endl;
{
std::cout << "\nTesting matrix multiplication ...\n" << std::endl;
{
DDMatrix m1 (1, 4);
DDMatrix m2 (4, 1);
int count = 0;
std::cout << "\t[1 X 4] * [4 X 1] = [1 X 1]\n" << std::endl;
for (DDMatrix::size_type i = 0; i < 1; ++i)
for (DDMatrix::size_type j = 0; j < 4; ++j)
m1 (i, j) = ++count;
count = 0;
for (DDMatrix::size_type i = 0; i < 4; ++i)
for (DDMatrix::size_type j = 0; j < 1; ++j)
m2 (i, j) = ++count;
const DDMatrix m3 = m1 * m2;
std::cout << "Original Matrices:" << std::endl;
m1.dump (std::cout) << std::endl;
m2.dump (std::cout) << std::endl;
std::cout << "After m3 = m1 * m2:" << std::endl;
m3.dump (std::cout) << std::endl;
}
{
DDMatrix m1 (3, 3);
DDMatrix m2 (3, 3);
int count = 0;
std::cout << "\t[3 X 3] * [3 X 3] = [3 X 3]\n" << std::endl;
for (DDMatrix::size_type i = 0; i < 3; ++i)
for (DDMatrix::size_type j = 0; j < 3; ++j)
m1 (i, j) = ++count;
count = 0;
for (DDMatrix::size_type i = 0; i < 3; ++i)
for (DDMatrix::size_type j = 0; j < 3; ++j)
m2 (i, j) = ++count;
const DDMatrix m3 = m1 * m2;
std::cout << "Original matrices:" << std::endl;
m1.dump (std::cout) << std::endl;
m2.dump (std::cout) << std::endl;
std::cout << "After multiplication:" << std::endl;
m3.dump (std::cout) << std::endl;
}
{
DDMatrix m1 (3, 2);
DDMatrix zero_m1 (3, 2);
DDMatrix m2 (2, 3);
DDMatrix zero_m2 (2, 3);
DDMatrix m3 (3, 3);
int count = 0;
std::cout << "\t[3 X 2] * [2 X 3] = [3 X 3]\n" << std::endl;
for (DDMatrix::size_type i = 0; i < 3; ++i)
for (DDMatrix::size_type j = 0; j < 2; ++j) {
m1 (i, j) = ++count;
zero_m1 (i, j) = 0.0;
}
count = 0;
for (DDMatrix::size_type i = 0; i < 2; ++i)
for (DDMatrix::size_type j = 0; j < 3; ++j) {
m2 (i, j) = ++count;
zero_m2 (i, j) = 0.0;
}
m3 = m1 * m2;
std::cout << "Original matrices:" << std::endl;
m1.dump (std::cout) << std::endl;
m2.dump (std::cout) << std::endl;
std::cout << "After multiplication:" << std::endl;
m3.dump (std::cout) << std::endl;
std::cout << "\n-------" << std::endl;
m3 = (m1 + zero_m1) * m2;
m3.dump (std::cout) << std::endl;
m3 = m1 * (m2 + zero_m2);
m3.dump (std::cout) << std::endl;
m3 = (m1 + zero_m1) * (m2 + zero_m2);
m3.dump (std::cout) << std::endl;
std::cout << "\n-------" << std::endl;
DDMatrix m5 (3, 2);
DDMatrix m6 (2, 3);
count = 0;
for (DDMatrix::size_type i = 0; i < 3; ++i)
for (DDMatrix::size_type j = 0; j < 2; ++j)
m5 (i, j) = ++count;
for (DDMatrix::size_type i = 0; i < 2; ++i)
for (DDMatrix::size_type j = 0; j < 3; ++j)
m6 (i, j) = --count;
std::cout << "Original matrices:" << std::endl;
m5.dump (std::cout) << std::endl;
m6.dump (std::cout) << std::endl;
m5 *= m6;
std::cout << "After m5 *= m6:" << std::endl;
m5.dump (std::cout) << std::endl;
}
}
std::cout << "\n-------" << std::endl;
{
std::cout << "\nTesting comparison operators ...\n" << std::endl;
DDMatrix dmat1 (8, 8);
DDMatrix dmat2 (8, 8);
DDMatrix dmat3 (3, 8);
DDMatrix dmat4 (3, 8);
int count = 0;
for (DDMatrix::size_type i = 0; i < 8; ++i)
for (DDMatrix::size_type j = 0; j < 8; ++j)
dmat1 (i, j) = ++count;
for (DDMatrix::size_type i = 0; i < 8; ++i)
for (DDMatrix::size_type j = 0; j < 8; ++j)
dmat2 (i, j) = --count;
count = 0;
for (DDMatrix::size_type i = 0; i < 3; ++i)
for (DDMatrix::size_type j = 0; j < 8; ++j)
dmat3 (i, j) = ++count;
for (DDMatrix::size_type i = 0; i < 3; ++i)
for (DDMatrix::size_type j = 0; j < 8; ++j)
dmat4 (i, j) = --count;
if ((dmat1 + dmat2) - dmat2 + (dmat1 + dmat2) !=
(dmat1 + dmat2) - dmat2 + (dmat1 + dmat2)) {
std::cout << "ERROR: Comparison faild (1)\n" << std::endl;
return (EXIT_FAILURE);
}
if ((dmat1 + dmat2) - dmat2 + (dmat1 + dmat2) ==
(dmat1 + dmat2) - dmat2 + (dmat1 + dmat1)) {
std::cout << "ERROR: Comparison faild (2)\n" << std::endl;
return (EXIT_FAILURE);
}
if ((dmat1 + dmat2) - dmat2 + (dmat1 + dmat2) !=
(dmat1 + dmat2) - dmat2 + (dmat1 + dmat2) + (dmat1 - dmat1)) {
std::cout << "ERROR: Comparison faild (3)\n" << std::endl;
return (EXIT_FAILURE);
}
const DDMatrix x = dmat3 * dmat2;
const DDMatrix y = dmat4 * dmat1;
x.dump (std::cout) << std::endl;
y.dump (std::cout) << std::endl;
if (dmat3 * dmat2 == dmat4 * dmat1) {
std::cout << "ERROR: Comparison faild (4)\n" << std::endl;
return (EXIT_FAILURE);
}
const DDMatrix xx = dmat3 * dmat2 - x;
const DDMatrix yy = dmat4 * dmat1 - y;
xx.dump (std::cout) << std::endl;
yy.dump (std::cout) << std::endl;
if (dmat3 * dmat2 - x != dmat4 * dmat1 - y) {
std::cout << "ERROR: Comparison faild (5)\n" << std::endl;
return (EXIT_FAILURE);
}
if (x - dmat3 * dmat2 != dmat3 * dmat2 - x) {
std::cout << "ERROR: Comparison faild (6)\n" << std::endl;
return (EXIT_FAILURE);
}
std::cout << "Comparison operator testing was successfull\n"
<< std::endl;
}
std::cout << "\n-------" << std::endl;
{
std::cout << "\nTesting invert method ...\n" << std::endl;
const int pre = std::cout.precision (8);
DDMatrix dmat1 (3, 3);
DDMatrix dmat2 (3, 3);
int count = 0;
dmat1 (0, 0) = 2.0;
dmat1 (0, 1) = 3.0;
dmat1 (0, 2) = 2.0;
dmat1 (1, 0) = 3.0;
dmat1 (1, 1) = 2.0;
dmat1 (1, 2) = 3.0;
dmat1 (2, 0) = 4.0;
dmat1 (2, 1) = 2.0;
dmat1 (2, 2) = 2.0;
const DDMatrix dmat3 = ! dmat1;
std::cout << "The matrix:" << std::endl;
dmat1.dump (std::cout) << std::endl;
std::cout << "The inverted matrix:" << std::endl;
dmat3.dump (std::cout) << std::endl;
dmat2 = dmat1 * dmat3;
std::cout << "The product:" << std::endl;
dmat2.dump (std::cout) << std::endl;
std::cout.precision (pre);
}
std::cout << "\n-------" << std::endl;
{
std::cout << "\nTesting solve() method ...\n" << std::endl;
DDMatrix dmat (3, 3);
DDMatrix rhs (3, 1);
std::cout << "2*X + 3*Y + 2*Z = 13\n";
std::cout << "3*X + 2*Y + 3*Z = 17\n";
std::cout << "4*X - 2*Y + 2*Z = 12\n\n";
dmat (0, 0) = 2.0;
dmat (0, 1) = 3.0;
dmat (0, 2) = 2.0;
dmat (1, 0) = 3.0;
dmat (1, 1) = 2.0;
dmat (1, 2) = 3.0;
dmat (2, 0) = 4.0;
dmat (2, 1) = -2.0;
dmat (2, 2) = 2.0;
std::cout << "LHS:\n";
dmat.dump (std::cout) << std::endl;
rhs (0, 0) = 13.0;
rhs (1, 0) = 17.0;
rhs (2, 0) = 12.0;
std::cout << "RHS:\n";
rhs.dump (std::cout) << std::endl;
const DDMatrix sol = dmat.solve_se (rhs);
std::cout << "Solution:\n";
sol.dump (std::cout) << std::endl;
}
std::cout << "\n-------" << std::endl;
{
std::cout << "\nTesting rref() method ...\n" << std::endl;
DDMatrix dmat (3, 3);
unsigned int rank;
dmat (0, 0) = 2.0;
dmat (0, 1) = 3.0;
dmat (0, 2) = 2.0;
dmat (1, 0) = 3.0;
dmat (1, 1) = 2.0;
dmat (1, 2) = 3.0;
dmat (2, 0) = 4.0;
dmat (2, 1) = 2.0;
dmat (2, 2) = 2.0;
std::cout << "Original Matrix:\n";
dmat.dump (std::cout) << std::endl;
dmat.rref (rank);
std::cout << "Row Reduced Echelon Form with rank (" << rank << ")\n";
dmat.dump (std::cout) << std::endl;
DDMatrix dmat2 (8, 3);
double count = 0;
for (DDMatrix::size_type i = 0; i < 8; ++i)
for (DDMatrix::size_type j = 0; j < 3; ++j)
dmat2 (i, j) = ++count;
std::cout << "Original Matrix:\n";
dmat2.dump (std::cout) << std::endl;
dmat2.rref (rank);
std::cout << "Row Reduced Echelon Form with rank (" << rank << ")\n";
dmat2.dump (std::cout) << std::endl;
DDMatrix dmat3 (8, 8);
for (DDMatrix::size_type i = 0; i < 8; ++i)
for (DDMatrix::size_type j = 0; j < 8; ++j)
dmat3 (i, j) = ::rand ();
std::cout << "Original Matrix:\n";
dmat3.dump (std::cout) << std::endl;
dmat3.rref (rank);
std::cout << "Row Reduced Echelon Form with rank (" << rank << ")\n";
std::cout << "Rank: " << dmat3.rank () << "\n";
dmat3.dump (std::cout) << std::endl;
}
std::cout << "\n-------" << std::endl;
{
std::cout << "\nTesting mat_col_mean() method ...\n" << std::endl;
DDMatrix dmat (8, 4);
DDMatrix null_mat (1, 4);
DDMatrix two_mat (4, 1);
int count = 0;
for (DDMatrix::size_type i = 0; i < 8; ++i)
for (DDMatrix::size_type j = 0; j < 4; ++j)
dmat (i, j) = ++count;
for (DDMatrix::size_type i = 0; i < 4; ++i)
for (DDMatrix::size_type j = 0; j < 1; ++j)
two_mat (i, j) = 2.0;
const DDMatrix mean_mat = mat_col_mean (dmat) + null_mat;
std::cout << "Original Matrix:\n";
dmat.dump (std::cout) << std::endl;
std::cout << "Null Matrix:\n";
null_mat.dump (std::cout) << std::endl;
std::cout << "Mean Matrix:\n";
mean_mat.dump (std::cout) << std::endl;
const DDMatrix mean_mat2 = mat_col_mean (dmat) * two_mat;
const DDMatrix mean_mat3 =
null_mat + mat_col_mean (dmat) * two_mat;
std::cout << "One Matrix:\n";
two_mat.dump (std::cout) << std::endl;
std::cout << "Mean Matrix (2):\n";
mean_mat2.dump (std::cout) << std::endl;
mean_mat3.dump (std::cout) << std::endl;
}
std::cout << "\n-------" << std::endl;
{
std::cout << "\nTesting covariance() method ...\n" << std::endl;
const int pre = std::cout.precision (8);
DDMatrix dmat (5, 4);
dmat (0, 0) = 4.0;
dmat (0, 1) = 2.0;
dmat (0, 2) = 0.6;
dmat (0, 3) = 3.0;
dmat (1, 0) = 4.2;
dmat (1, 1) = 2.1;
dmat (1, 2) = 0.59;
dmat (1, 3) = 3.2;
dmat (2, 0) = 3.9;
dmat (2, 1) = 2.0;
dmat (2, 2) = 0.58;
dmat (2, 3) = 2.89;
dmat (3, 0) = 4.3;
dmat (3, 1) = 2.1;
dmat (3, 2) = 0.62;
dmat (3, 3) = 3.298;
dmat (4, 0) = 4.1;
dmat (4, 1) = 2.2;
dmat (4, 2) = 0.63;
dmat (4, 3) = 3.098;
const DDMatrix cov = dmat.covariance ();
const DDMatrix corrl = dmat.correlation ();
std::cout << "Original Matrix:\n";
dmat.dump (std::cout) << std::endl;
std::cout << "Covariance Matrix:\n";
cov.dump (std::cout) << std::endl;
std::cout << "Correlation Matrix:\n";
corrl.dump (std::cout) << std::endl;
std::cout.precision (pre);
}
std::cout << "\n-------" << std::endl;
{
std::cout << "\nTesting is_normal() method ...\n" << std::endl;
DDMatrix dmat (3, 3);
int count = 0;
for (DDMatrix::size_type i = 0; i < 3; ++i)
for (DDMatrix::size_type j = 0; j < 3; ++j)
dmat (i, j) = ++count;
std::cout << "Original Matrix:\n";
dmat.dump (std::cout);
std::cout << "Is Normal: " << dmat.is_normal () << std::endl;
std::cout << "Is Orthogonal: " << dmat.is_orthogonal ()
<< "\n" << std::endl;
dmat (0, 0) = 1;
dmat (0, 1) = 1;
dmat (0, 2) = 0;
dmat (1, 0) = 0;
dmat (1, 1) = 1;
dmat (1, 2) = 1;
dmat (2, 0) = 1;
dmat (2, 1) = 0;
dmat (2, 2) = 1;
std::cout << "Original Matrix:\n";
dmat.dump (std::cout);
std::cout << "Is Normal: " << dmat.is_normal () << std::endl;
std::cout << "Is Orthogonal: " << dmat.is_orthogonal ()
<< "\n" << std::endl;
}
std::cout << "\n-------" << std::endl;
{
const int pre = std::cout.precision (6);
std::cout << "\nTesting eigen_space() for symmetric metrices ...\n"
<< std::endl;
SDMatrix dmat (10, 10);
int count = 0;
for (DDMatrix::size_type i = 0; i < 10; ++i)
for (DDMatrix::size_type j = 0; j < 10; ++j)
dmat (i, j) = ++count;
DDMatrix eigenvals;
DDMatrix eigenvecs;
std::cout << "Original Matrix:\n";
dmat.dump (std::cout) << std::endl;
dmat.eigen_space (eigenvals, eigenvecs, true);
std::cout << "Eigen Values:\n";
eigenvals.dump (std::cout) << std::endl;
std::cout << "Eigen Vectors:\n";
eigenvecs.dump (std::cout) << std::endl;
std::cout << "\n-------\n" << std::endl;
SDMatrix dmat2 (5, 5);
count = 0;
for (DDMatrix::size_type i = 0; i < 5; ++i)
for (DDMatrix::size_type j = 0; j < 5; ++j)
dmat2 (i, j) = ++count;
std::cout << "Original Matrix:\n";
dmat2.dump (std::cout) << std::endl;
auto efut = dmat2.eigen_space_async(eigenvals, eigenvecs, true);
efut.get();
std::cout << "Eigen Values:\n";
eigenvals.dump (std::cout) << std::endl;
std::cout << "Eigen Vectors:\n";
eigenvecs.dump (std::cout) << std::endl;
std::cout.precision (pre);
}
{
const int pre = std::cout.precision (6);
std::cout << "\nTesting eigen_space() for nonsymmetric metrices ...\n"
<< std::endl;
DDMatrix dmat (10, 10);
int count = 0;
for (DDMatrix::size_type i = 0; i < 10; ++i)
for (DDMatrix::size_type j = 0; j < 10; ++j)
dmat (i, j) = ++count;
DDMatrix eigenvals;
DDMatrix eigenvecs;
std::cout << "Original Matrix:\n";
dmat.dump (std::cout) << std::endl;
dmat.eigen_space (eigenvals, eigenvecs, true);
std::cout << "Eigen Values:\n";
eigenvals.dump (std::cout) << std::endl;
std::cout << "Eigen Vectors:\n";
eigenvecs.dump (std::cout) << std::endl;
std::cout << "\n-------\n" << std::endl;
DDMatrix dmat2 (5, 5);
count = 0;
for (DDMatrix::size_type i = 0; i < 5; ++i)
for (DDMatrix::size_type j = 0; j < 5; ++j)
dmat2 (i, j) = ++count;
std::cout << "Original Matrix:\n";
dmat2.dump (std::cout) << std::endl;
dmat2.eigen_space (eigenvals, eigenvecs, false);
std::cout << "Eigen Values:\n";
eigenvals.dump (std::cout) << std::endl;
std::cout << "Eigen Vectors:\n";
eigenvecs.dump (std::cout) << std::endl;
std::cout.precision (pre);
}
std::cout << "\n-------" << std::endl;
{
const int pre = std::cout.precision (6);
std::cout << "\nTesting svd() method ...\n" << std::endl;
{
DDMatrix dmat (8, 4);
int count = 0;
for (DDMatrix::size_type i = 0; i < 8; ++i)
for (DDMatrix::size_type j = 0; j < 4; ++j)
dmat (i, j) = ++count;
DDMatrix U;
DDMatrix S;
DDMatrix V;
std::cout << "Original Matrix:\n";
dmat.dump (std::cout) << std::endl;
dmat.svd (U, S, V);
std::cout << "U:\n";
U.dump (std::cout) << std::endl;
std::cout << "S:\n";
S.dump (std::cout) << std::endl;
std::cout << "V:\n";
V.dump (std::cout) << std::endl;
const DDMatrix A = U * S * ~ V;
std::cout << "U * S * ~ V:\n";
A.dump (std::cout) << std::endl;