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verification.cpp
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// This program is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, version 3 of the License.
//
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with this program. If not, see <http://www.gnu.org/licenses/>.
//
// Copyright 2016 Vegard Antun
//
#include <iostream>
#include <iomanip>
#include <cmath>
#include "hadamard.h"
#include "fxt/walsh/walshseq.h"
#include "fxt/walsh/walshpal.h"
#include "Eigen/Dense"
void insertRow(Eigen::MatrixXi & A, int *x, const int row );
void insertCol(Eigen::MatrixXi & A, int *x, const int col );
Eigen::MatrixXi createMatrix(const unsigned int N,
void (*transform)(int *, const uint32_t));
// Test of support functions
bool test_insertRowCol(bool verbose=true);
// Test of transforms
bool test_hadamard_sequency_sign_changes(bool verbose=true);
bool test_hadamardOrdinary_16(bool verbose=true);
bool test_hadamardPaley_16(bool verbose=true);
bool test_hadamardPaley_32(bool verbose=true);
bool test_sign_change_WAL( bool verbose=true);
bool test_powDyadic( bool verbose=true);
int main(int argc, char *argv[]) {
const unsigned long nu = 3;
const unsigned long N = powDyadic(nu);
test_powDyadic();
//test_sign_change_WAL();
test_hadamardOrdinary_16();
test_hadamardPaley_16();
test_hadamardPaley_32();
test_hadamard_sequency_sign_changes();
}
bool test_powDyadic( bool verbose) {
bool success = true;
unsigned long n = 1;
for (unsigned long i = 0; i < 5; i++) {
unsigned long p = powDyadic(i);
success = success and (p==n);
n *= 2;
}
if (verbose) {
const char * result = (success) ? "\e[32mPassed\e[0m" : "\e[31mFailed\e[0m";
std::cout << result << ": powDyadic" << std::endl;
}
return success;
}
bool test_sign_change_WAL( bool verbose) {
const char *result;
bool success = true;
for (unsigned int N = 4; N < 1023; N *= 2) {
// Test the number of sign changes
int *x = new int [N];
Eigen::MatrixXi X = Eigen::MatrixXi::Zero(N,N);
for (unsigned int n = 0; n < N; n++) {
for (unsigned int t = 0; t < N; t++) {
x[t] = WAL(N, n, t);
}
insertRow(X, x, n);
}
for (int row = 0; row < N; row++) {
int nbr_sign_changes = 0;
for (int i = 0; i < N-1; i++) {
if (X(row, i) != X(row, i+1)) {
nbr_sign_changes++;
}
}
//std::cout << nbr_sign_changes << std::endl;
success = success and (nbr_sign_changes == row);
}
if (verbose) {
result = (success) ? "\e[32mPassed\e[0m" : "\e[31mFailed\e[0m";
std::cout << result << ": Sequency order sign changes N = " << N << std::endl;
}
// Test of orthogonal transform
Eigen::MatrixXi I1 = X*X.transpose();
Eigen::MatrixXi I2 = X.transpose()*X;
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
if (i != j) {
success = (success and (I1(i,j) == 0));
success = (success and (I2(i,j) == 0));
} else {
success = (success and (I1(i,j) == N));
success = (success and (I2(i,j) == N));
}
}
}
if (verbose) {
result = (success) ? "\e[32mPassed\e[0m" : "\e[31mFailed\e[0m";
std::cout << result << ": Orthogonal N = " << N << std::endl;
}
delete [] x;
}
return success;
}
Eigen::MatrixXi createMatrix(const unsigned int N,
void (*transform)(int *, const uint32_t))
{
Eigen::MatrixXi A = Eigen::MatrixXi::Zero(N,N);
int *x = new int [N];
for (int i = 0; i < N; i++) {
std::memset(x, 0, sizeof(int)*N);
x[i] = 1;
transform(x, N);
insertCol(A, x, i);
}
delete [] x;
return A;
}
/*
Create the sequency ordered Hadamard matrix and testes that the correct number
of sign changes exists. In addition it tests that the resulting matrix is
orthogonal.
This is done for N = 4, 8, ..., 1024.
*/
bool test_hadamard_sequency_sign_changes(bool verbose) {
const char *result;
bool success = true;
for (int N = 4; N < 1025; N *= 2) {
int *x = new int [N];
Eigen::MatrixXi X = Eigen::MatrixXi::Zero(N,N);
for (int i = 0; i < N; i++) {
std::memset(x, 0, sizeof(int)*N);
x[i] = 1;
hadamardSequency<int>(x, N);
insertCol(X, x, i);
}
for (int row = 0; row < N; row++) {
int nbr_sign_changes = 0;
for (int i = 0; i < N-1; i++) {
if (X(row, i) != X(row, i+1)) {
nbr_sign_changes++;
}
}
success = success and (nbr_sign_changes == row);
}
if (verbose) {
result = (success) ? "\e[32mPassed\e[0m" : "\e[31mFailed\e[0m";
std::cout << result << ": Sequency order sign changes N = " << N << std::endl;
}
// Test of orthogonal transform
Eigen::MatrixXi I1 = X*X.transpose();
Eigen::MatrixXi I2 = X.transpose()*X;
for (int i = 0; i < N; i++) {
for (int j = 0; j < N; j++) {
if (i != j) {
success = (success and (I1(i,j) == 0));
success = (success and (I2(i,j) == 0));
} else {
success = (success and (I1(i,j) == N));
success = (success and (I2(i,j) == N));
}
}
}
if (verbose) {
result = (success) ? "\e[32mPassed\e[0m" : "\e[31mFailed\e[0m";
std::cout << result << ": Orthogonal N = " << N << std::endl;
}
delete [] x;
}
return success;
}
bool test_hadamardOrdinary_16(bool verbose) {
const char *result;
const unsigned int N = 16;
Eigen::MatrixXi mat1(N,N);
mat1 << 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1,
1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1,
1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1,
1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1,
1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1,
1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1,
1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1,
1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1,
1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1,
1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1,
1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1,
1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1,
1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1,
1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1,
1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1;
int x[N];
Eigen::MatrixXi X = Eigen::MatrixXi::Zero(N,N);
for (int i = 0; i < N; i++) {
std::memset(x, 0, sizeof(int)*N);
x[i] = 1;
hadamardOrdinary<int>(x, N);
insertCol(X, x, i);
}
Eigen::MatrixXi Y = mat1-X;
bool success = (Y.norm() < 1e-10);
if ( verbose ) {
result = (success) ? "\e[32mPassed\e[0m" : "\e[31mFailed\e[0m";
std::cout << result << ": hadamardOrdinary16" << std::endl;
}
return success;
}
bool test_hadamardPaley_16(bool verbose) {
const char *result;
const unsigned int N = 16;
Eigen::MatrixXi mat1(N,N);
mat1 << 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1,
1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1,
1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1,
1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1,
1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1,
1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1,
1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1,
1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1,
1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1,
1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1,
1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1,
1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1,
1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1,
1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1,
1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1;
int x[N];
Eigen::MatrixXi X = Eigen::MatrixXi::Zero(N,N);
for (int i = 0; i < N; i++) {
std::memset(x, 0, sizeof(int)*N);
x[i] = 1;
hadamardPaley<int>(x, N);
insertCol(X, x, i);
}
Eigen::MatrixXi Y = mat1-X;
bool success = (Y.norm() < 1e-10);
if ( verbose ) {
result = (success) ? "\e[32mPassed\e[0m" : "\e[31mFailed\e[0m";
std::cout << result << ": hadamardPaley16" << std::endl;
}
return success;
}
bool test_hadamardPaley_32(bool verbose) {
const char *result;
const unsigned int N = 32;
Eigen::MatrixXi mat1(N,N);
mat1 << 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1,
1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1,
1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1,
1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1,
1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1,
1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1,
1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1,
1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1,
1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1,
1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1,
1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1,
1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1,
1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1,
1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1,
1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1,
1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1,
1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1,
1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1,
1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1,
1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1,
1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1,
1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1,
1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1,
1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1,
1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1,
1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1,
1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1,
1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1,
1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1;
int x[N];
Eigen::MatrixXi X = Eigen::MatrixXi::Zero(N,N);
for (int i = 0; i < N; i++) {
std::memset(x, 0, sizeof(int)*N);
x[i] = 1;
hadamardPaley<int>(x, N);
insertCol(X, x, i);
}
Eigen::MatrixXi Y = mat1-X;
bool success = (Y.norm() < 1e-10);
if ( verbose ) {
result = (success) ? "\e[32mPassed\e[0m" : "\e[31mFailed\e[0m";
std::cout << result << ": hadamardPaley32" << std::endl;
}
return success;
}
bool test_insertRowCol(bool verbose) {
unsigned int N = 5;
const char *result;
Eigen::MatrixXi X = Eigen::MatrixXi::Zero(N,N);
// Test insertRow()
int x[N];
for (int n = 0; n < N; n++) {
for (int i = 0; i < N; i++) {
x[i] = i;
}
insertRow(X, x, n);
}
bool success1 = true;
for (int n = 0; n < N; n++) {
for (int i = 0; i < N; i++) {
success1 = success1 and ( (X(n,i) - i) == 0 );
}
}
if (verbose) {
result = (success1) ? "\e[32mPassed\e[0m" : "\e[31mFailed\e[0m";
std::cout << result << ": insertRow();" << std::endl;
}
// Test insertCol()
for (int n = 0; n < N; n++) {
for (int i = 0; i < N; i++) {
x[i] = i;
}
insertCol(X, x, n);
}
bool success2 = true;
for (int n = 0; n < N; n++) {
for (int i = 0; i < N; i++) {
success2 = success2 and ( (X(i,n) - i) == 0 );
}
}
if (verbose) {
result = (success2) ? "\e[32mPassed\e[0m" : "\e[31mFailed\e[0m";
std::cout << result << ": insertCol();" << std::endl;
}
return (success1 and success2);
}
void insertRow(Eigen::MatrixXi & A, int *x , const int row ) {
const int N = A.cols();
for (int i = 0; i < N; i++) {
A(row,i) = x[i];
}
}
void insertCol(Eigen::MatrixXi & A, int *x, const int col ) {
const int N = A.rows();
for (int i = 0; i < N; i++) {
A(i,col) = x[i];
}
}