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test_lls.cpp
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# include <cmath>
# include <cstdlib>
# include <cstring>
# include <ctime>
# include <iomanip>
# include <iostream>
using namespace std;
# include "test_lls.hpp"
# include "r8lib.hpp"
//****************************************************************************80
double *p00_a ( int prob, int m, int n )
//****************************************************************************80
//
// Purpose:
//
// P00_A returns the matrix A for any least squares problem.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 18 April 2012
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, int PROB, the problem index.
//
// Input, int M, the number of equations.
//
// Input, int N, the number of variables.
//
// Output, double P00_A[M*N], the matrix.
//
{
double *a;
if ( prob == 1 )
{
a = p01_a ( m, n );
}
else if ( prob == 2 )
{
a = p02_a ( m, n );
}
else if ( prob == 3 )
{
a = p03_a ( m, n );
}
else if ( prob == 4 )
{
a = p04_a ( m, n );
}
else if ( prob == 5 )
{
a = p05_a ( m, n );
}
else if ( prob == 6 )
{
a = p06_a ( m, n );
}
else
{
cerr << "\n";
cerr << "P00_A - Fatal error!\n";
cerr << " Illegal value of PROB = " << prob << "\n";
exit ( 1 );
}
return a;
}
//****************************************************************************80
double *p00_b ( int prob, int m )
//****************************************************************************80
//
// Purpose:
//
// P00_B returns the right hand side B for any least squares problem.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 18 April 2012
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, int PROB, the problem index.
//
// Input, int M, the number of equations.
//
// Output, double P00_B[M], the right hand side.
//
{
double *b;
if ( prob == 1 )
{
b = p01_b ( m );
}
else if ( prob == 2 )
{
b = p02_b ( m );
}
else if ( prob == 3 )
{
b = p03_b ( m );
}
else if ( prob == 4 )
{
b = p04_b ( m );
}
else if ( prob == 5 )
{
b = p05_b ( m );
}
else if ( prob == 6 )
{
b = p06_b ( m );
}
else
{
cerr << "\n";
cerr << "P00_B - Fatal error!\n";
cerr << " Illegal value of PROB = " << prob << "\n";
exit ( 1 );
}
return b;
}
//****************************************************************************80
int p00_m ( int prob )
//****************************************************************************80
//
// Purpose:
//
// P00_M returns the number of equations M for any least squares problem.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 18 April 2012
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, int PROB, the problem index.
//
// Output, int P00_M, the number of equations.
//
{
int m;
if ( prob == 1 )
{
m = p01_m ( );
}
else if ( prob == 2 )
{
m = p02_m ( );
}
else if ( prob == 3 )
{
m = p03_m ( );
}
else if ( prob == 4 )
{
m = p04_m ( );
}
else if ( prob == 5 )
{
m = p05_m ( );
}
else if ( prob == 6 )
{
m = p06_m ( );
}
else
{
cerr << "\n";
cerr << "P00_M - Fatal error!\n";
cerr << " Illegal value of PROB = " << prob << "\n";
exit ( 1 );
}
return m;
}
//****************************************************************************80
int p00_n ( int prob )
//****************************************************************************80
//
// Purpose:
//
// P00_N returns the number of variables N for any least squares problem.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 18 April 2012
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, int PROB, the problem index.
//
// Output, int P00_N, the number of variables.
//
{
int n;
if ( prob == 1 )
{
n = p01_n ( );
}
else if ( prob == 2 )
{
n = p02_n ( );
}
else if ( prob == 3 )
{
n = p03_n ( );
}
else if ( prob == 4 )
{
n = p04_n ( );
}
else if ( prob == 5 )
{
n = p05_n ( );
}
else if ( prob == 6 )
{
n = p06_n ( );
}
else
{
cerr << "\n";
cerr << "P00_N - Fatal error!\n";
cerr << " Illegal value of PROB = " << prob << "\n";
exit ( 1 );
}
return n;
}
//****************************************************************************80
int p00_prob_num ( )
//****************************************************************************80
//
// Purpose:
//
// P00_PROB_NUM returns the number of least squares problems.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 18 April 2012
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Output, double P00_PROB_NUM, the number of problems.
//
{
int prob_num;
prob_num = 6;
return prob_num;
}
//****************************************************************************80
double *p00_x ( int prob, int n )
//****************************************************************************80
//
// Purpose:
//
// P00_X returns the least squares solution X for any least squares problem.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 18 April 2012
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, int PROB, the problem index.
//
// Input, int N, the number of variables.
//
// Output, double P00_X[N], the least squares solution.
//
{
double *x;
if ( prob == 1 )
{
x = p01_x ( n );
}
else if ( prob == 2 )
{
x = p02_x ( n );
}
else if ( prob == 3 )
{
x = p03_x ( n );
}
else if ( prob == 4 )
{
x = p04_x ( n );
}
else if ( prob == 5 )
{
x = p05_x ( n );
}
else if ( prob == 6 )
{
x = p06_x ( n );
}
else
{
cerr << "\n";
cerr << "P00_X - Fatal error!\n";
cerr << " Illegal value of PROB = " << prob << "\n";
exit ( 1 );
}
return x;
}
//****************************************************************************80
double *p01_a ( int m, int n )
//****************************************************************************80
//
// Purpose:
//
// P01_A returns the matrix A for problem 1.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 18 April 2012
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, int M, the number of equations.
//
// Input, int N, the number of variables.
//
// Output, double P01_A[M*N], the matrix.
//
{
double *a;
int i;
int j;
a = new double[m*n];
for ( i = 0; i < m; i++ )
{
a[i+0*m] = 1.0;
for ( j = 1; j < n; j++ )
{
a[i+j*m] = a[i+(j-1)*m] * ( double ) ( i + 1 );
}
}
return a;
}
//****************************************************************************80
double *p01_b ( int m )
//****************************************************************************80
//
// Purpose:
//
// P01_B returns the right hand side B for problem 1.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 18 April 2012
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, int M, the number of equations.
//
// Output, double P01_B[M], the right hand side.
//
{
double *b;
double b_save[5] = { 1.0, 2.3, 4.6, 3.1, 1.2 };
b = r8vec_copy_new ( m, b_save );
return b;
}
//****************************************************************************80
int p01_m ( )
//****************************************************************************80
//
// Purpose:
//
// P01_M returns the number of equations M for problem 1.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 18 April 2012
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Output, int P01_M, the number of equations.
//
{
int m;
m = 5;
return m;
}
//****************************************************************************80
int p01_n ( )
//****************************************************************************80
//
// Purpose:
//
// P01_N returns the number of variables N for problem 1.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 18 April 2012
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Output, int P01_N, the number of variables.
//
{
int n;
n = 3;
return n;
}
//****************************************************************************80
double *p01_x ( int n )
//****************************************************************************80
//
// Purpose:
//
// P01_X returns the least squares solution X for problem 1.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 18 April 2012
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, int N, the number of variables.
//
// Output, double P01_X[N], the least squares solution.
//
{
double *x;
double x_save[3] = { -3.0200000, 4.4914286, -0.72857143 };
x = r8vec_copy_new ( n, x_save );
return x;
}
//****************************************************************************80
double *p02_a ( int m, int n )
//****************************************************************************80
//
// Purpose:
//
// P02_A returns the matrix A for problem 2.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 18 April 2012
//
// Author:
//
// John Burkardt
//
// Reference:
//
// Cleve Moler,
// Numerical Computing with MATLAB,
// SIAM, 2004,
// ISBN13: 978-0-898716-60-3,
// LC: QA297.M625,
// ebook: http://www.mathworks.com/moler/chapters.md
//
// Parameters:
//
// Input, int M, the number of equations.
//
// Input, int N, the number of variables.
//
// Output, double P02_A[M*N], the matrix.
//
{
double *a;
int i;
int j;
a = new double[m*n];
for ( i = 0; i < m; i++ )
{
a[i+(n-1)*m] = 1.0;
for ( j = n - 2; 0 <= j; j-- )
{
a[i+j*m] = a[i+(j+1)*m] * ( double ) ( i ) / 5.0;
}
}
return a;
}
//****************************************************************************80
double *p02_b ( int m )
//****************************************************************************80
//
// Purpose:
//
// P02_B returns the right hand side B for problem 2.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 18 April 2012
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, int M, the number of equations.
//
// Output, double P02_B[M], the right hand side.
//
{
double *b;
double b_save[6] = { 150.697, 179.323, 203.212, 226.505, 249.633, 281.422 };
b = r8vec_copy_new ( m, b_save );
return b;
}
//****************************************************************************80
int p02_m ( )
//****************************************************************************80
//
// Purpose:
//
// P02_M returns the number of equations M for problem 2.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 18 April 2012
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Output, int P02_M, the number of equations.
//
{
int m;
m = 6;
return m;
}
//****************************************************************************80
int p02_n ( )
//****************************************************************************80
//
// Purpose:
//
// P02_N returns the number of variables N for problem 2.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 18 April 2012
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Output, int P02_N, the number of variables.
//
{
int n;
n = 3;
return n;
}
//****************************************************************************80
double *p02_x ( int n )
//****************************************************************************80
//
// Purpose:
//
// P02_X returns the least squares solution X for problem 2.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 18 April 2012
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, int N, the number of variables.
//
// Output, double P02_X[N], the least squares solution.
//
{
double *x;
double x_save[3] = { 5.7013, 121.1341, 152.4745 };
x = r8vec_copy_new ( n, x_save );
return x;
}
//****************************************************************************80
double *p03_a ( int m, int n )
//****************************************************************************80
//
// Purpose:
//
// P03_A returns the matrix A for problem 3.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 18 April 2012
//
// Author:
//
// John Burkardt
//
// Reference:
//
// Cleve Moler,
// Numerical Computing with MATLAB,
// SIAM, 2004,
// ISBN13: 978-0-898716-60-3,
// LC: QA297.M625,
// ebook: http://www.mathworks.com/moler/chapters.md
//
// Parameters:
//
// Input, int M, the number of equations.
//
// Input, int N, the number of variables.
//
// Output, double P03_A[M*N], the matrix.
//
{
double *a;
double a_save[5*3] = {
1.0, 4.0, 7.0, 10.0, 13.0,
2.0, 5.0, 8.0, 11.0, 14.0,
3.0, 6.0, 9.0, 12.0, 15.0 };
a = r8mat_copy_new ( m, n, a_save );
return a;
}
//****************************************************************************80
double *p03_b ( int m )
//****************************************************************************80
//
// Purpose:
//
// P03_B returns the right hand side B for problem 3.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 18 April 2012
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, int M, the number of equations.
//
// Output, double P03_B[M], the right hand side.
//
{
double *b;
double b_save[5] = { 16.0, 17.0, 18.0, 19.0, 20.0 };
b = r8vec_copy_new ( m, b_save );
return b;
}
//****************************************************************************80
int p03_m ( )
//****************************************************************************80
//
// Purpose:
//
// P03_M returns the number of equations M for problem 3.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 18 April 2012
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Output, int P03_M, the number of equations.
//
{
int m;
m = 5;
return m;
}
//****************************************************************************80
int p03_n ( )
//****************************************************************************80
//
// Purpose:
//
// P03_N returns the number of variables N for problem 3.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 18 April 2012
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Output, int P03_N, the number of variables.
//
{
int n;
n = 3;
return n;
}
//****************************************************************************80
double *p03_x ( int n )
//****************************************************************************80
//
// Purpose:
//
// P03_X returns the least squares solution X for problem 3.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 18 April 2012
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, int N, the number of variables.
//
// Output, double P03_X[N], the least squares solution.
//
{
double *x;
double x_save[3] = { -7.5555556, 0.1111111, 7.7777778 };
x = r8vec_copy_new ( n, x_save );
return x;
}
//****************************************************************************80
double *p04_a ( int m, int n )
//****************************************************************************80
//
// Purpose:
//
// P04_A returns the matrix A for problem 4.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 18 April 2012
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, int M, the number of equations.
//
// Input, int N, the number of variables.
//
// Output, double P04_A[M*N], the matrix.
//
{
double *a;
int i;
int j;
a = new double[m*n];
for ( j = 0; j < n; j++ )
{
for ( i = 0; i < m; i++ )
{
a[i+j*m] = ( double ) ( i4_power ( j + 1, i ) );
}
}
return a;
}
//****************************************************************************80
double *p04_b ( int m )
//****************************************************************************80
//
// Purpose:
//