# include <stdbool.h>
# include <stdio.h>
# include <stdlib.h>
# include <time.h>

# include "rref2.h"

int main ( );
void is_rref_test ( );
void rref_compute_test ( );
void rref_columns_test ( );
void rref_determinant_test ( );
void rref_inverse_test ( );
void rref_rank_test ( );
void rref_solve_test ( );
void i4vec_print ( int n, int a[], char *title );
double *r8mat_mm_new ( int n1, int n2, int n3, double a[], double b[] );
void r8mat_print ( int m, int n, double a[], char *title );
void r8mat_print_some ( int m, int n, double a[], int ilo, int jlo, int ihi,
  int jhi, char *title );
void timestamp ( );

/******************************************************************************/

int main ( )

/******************************************************************************/
/*
  Purpose:

    rref2_test() tests rref2().

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    15 December 2024

  Author:

    John Burkardt
*/
{
  timestamp ( );
  printf ( "\n" );
  printf ( "rref2_test():\n" );
  printf ( "  C version\n" );
  printf ( "  Test rref(), which analyzes matrices using the\n" );
  printf ( "  reduced row echelon form (RREF)\n" );

  is_rref_test ( );
  rref_compute_test ( );
  rref_columns_test ( );
  rref_determinant_test ( );
  rref_inverse_test ( );
  rref_rank_test ( );
  rref_solve_test ( );
/*
  Terminate.
*/
  printf ( "\n" );
  printf ( "rref2_test():\n" );
  printf ( "  Normal end of execution.\n" );
  printf ( "\n" );
  timestamp ( );

  return 0;
}
/******************************************************************************/

void is_rref_test ( )

/******************************************************************************/
/*
  Purpose:

    is_rref_test() tests is_rref().

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    15 December 2024

  Author:
[ 
    John Burkardt
*/
{
  int m = 4;
  int n = 5;
/*
  Zero rows must come last.
*/
  double A0[4*5] = {
    1, 0, 0, 0, 
    0, 0, 0, 0, 
    0, 1, 0, 0, 
    9, 0, 0, 1, 
    4, 8, 0, 0  };
/*
  First nonzero must be to right of first nonzero in previous row.
*/
  double A1[4*5] = {
    1, 0, 0, 0, 
    0, 0, 0, 0, 
    0, 0, 1, 0, 
    9, 1, 0, 1, 
    4, 0, 8, 0  };
/*
  First nonzero must be a 1.
*/
  double A2[4*5] = {
    1, 0, 0, 0, 
    0, 1, 0, 0, 
    0, 0, 3, 0, 
    9, 2, 0, 0, 
    4, 8, 0, 0  };
/*
  First nonzero must only nonzero in its column.
*/
  double A3[4*5] = {
    1, 0, 0, 0, 
    0, 1, 0, 0, 
    3, 0, 1, 0, 
    9, 2, 0, 0, 
    4, 8, 0, 0 };
/*
  RREF example.
*/
  double A4[4*5] = {
    1, 0, 0, 0, 
    0, 1, 0, 0, 
    3, 2, 0, 0, 
    0, 0, 1, 0, 
    4, 8, 0, 0 };

  printf ( "\n" );
  printf ( "is_rref_test():\n" );
  printf ( "  is_rref() reports if a matrix is in reduced row echelon format.\n" );

  r8mat_print ( m, n, A0, "  Matrix A0:" );
  printf ( "  is_rref(A0) = %d\n", is_rref ( m, n, A0 ) );

  r8mat_print ( m, n, A1, "  Matrix A1:" );
  printf ( "  is_rref(A1) = %d\n", is_rref ( m, n, A1 ) );

  r8mat_print ( m, n, A2, "  Matrix A2:" );
  printf ( "  is_rref(A2) = %d\n", is_rref ( m, n, A2 ) );

  r8mat_print ( m, n, A3, "  Matrix A3:" );
  printf ( "  is_rref(A3) = %d\n", is_rref ( m, n, A3 ) );

  r8mat_print ( m, n, A4, "  Matrix A4:" );
  printf ( "  is_rref(A4) = %d\n", is_rref ( m, n, A4 ) );

  return;
}
/******************************************************************************/

void rref_columns_test ( )

/******************************************************************************/
/*
  Purpose:

    rref_columns_test() tests rref_columns().

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    08 December 2024

  Author:

    John Burkardt
*/
{
  double A[7*4] = {
    1,  2,  3,  4,  5,  6,  7, 
    2,  4,  6,  8, 10, 12, 14, 
    3,  9,  0,  0,  6,  6,  2, 
    1,  3,  0,  2,  6,  3,  1 };
  int *a_cols;
  double *A_COLUMNS;
  double *A_RREF;
  int i;
  int j;
  int j2;
  int j3;
  int m = 7;
  int n = 4;
  int n2;

  printf ( "\n" );
  printf ( "rref_columns_test():\n" );
  printf ( "  rref_columns() uses the reduced row echelon form (RREF)\n" );
  printf ( "  of a matrix to find the linearly independent columns.\n" );

  r8mat_print ( m, n, A, "  Matrix A:" );

  A_RREF = ( double * ) malloc ( m * n * sizeof ( double ) );
  a_cols = ( int * ) malloc ( n * sizeof ( int ) );
  rref_compute ( m, n, A, A_RREF, a_cols );

  n2 = 0;
  for ( j = 0; j < n; j++ )
  {
    if ( 0 <= a_cols[j] )
    {
      n2 = n2 + 1;
    }
  }

  printf ( "\n" );
  printf ( "  Number of independent columns is %d\n", n2 );

  i4vec_print ( n2, a_cols, "  Independent column indices" );

  A_COLUMNS = ( double * ) malloc ( m * n2 * sizeof ( double ) );

  j2 = 0;
  for ( j = 0; j < n; j++ )
  {
    if ( a_cols[j] != -1 )
    {
      for ( i = 0; i < m; i++ )
      {
        j3 = a_cols[j];
        A_COLUMNS[i+j2*m] = A[i+j3*m];
      }
      j2 = j2 + 1;
    }
  }

  r8mat_print ( m, n2, A_COLUMNS, "  Independent columns:" );

  free ( A_RREF );
  free ( a_cols );
  free ( A_COLUMNS );

  return;
}
/******************************************************************************/

void rref_compute_test ( )

/******************************************************************************/
/*
  Purpose:

    ref_compute_test() tests rref_compute().

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    08 December 2024

  Author:

    John Burkardt
*/
{
  double A[4*7] = {
    1, -2,  3, -1, 
    3, -6,  9, -3, 
    0,  0,  0,  0, 
    2, -2,  0,  1, 
    6, -8,  6,  0, 
    3,  3,  6,  9, 
    1,  1,  2,  3 };
  int *a_cols;
  double *A_RREF;
  int m = 4;
  int n = 7;

  printf ( "\n" );
  printf ( "rref_compute_test():\n" );
  printf ( "  rref_compute() is a user-written code to compute the\n" );
  printf ( "  reduced row echelon form (RREF) of a matrix.\n" );

  r8mat_print ( m, n, A, "  Matrix A:" );

  A_RREF = ( double * ) malloc ( m * n * sizeof ( double ) );
  a_cols = ( int * ) malloc ( n * sizeof ( int ) );

  rref_compute ( m, n, A, A_RREF, a_cols );

  r8mat_print ( m, n, A_RREF, "  rref_compute(A):" );

  i4vec_print ( n, a_cols, "  Column indices" );

  free ( A_RREF );
  free ( a_cols );

  return;
}
/******************************************************************************/

void rref_determinant_test ( )

/******************************************************************************/
/*
  Purpose:

    rref_determinant_test() tests rref_determinant().

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    08 December 2024

  Author:

    John Burkardt
*/
{
  double A[4*4] = {
    5,  7,  6,  5, 
    7, 10,  8,  7, 
    6,  8, 10,  9, 
    5,  7,  9, 10 };
  double a_det;
  int n = 4;

  printf ( "\n" );
  printf ( "rref_determinant_test():\n" );
  printf ( "  rref_determinant() uses the reduced row echelon form \n" );
  printf ( "  of a square matrix to compute the determinant.\n" );

  r8mat_print ( n, n, A, "  matrix A:" );

  a_det = rref_determinant ( n, A );
  printf ( "\n" );
  printf ( "  Estimated determinant of A = %g\n", a_det );

  return;
}
/******************************************************************************/

void rref_inverse_test ( )

/******************************************************************************/
/*
  Purpose:

    rref_inverse_test() tests rref_inverse().

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    08 December 2024

  Author:

    John Burkardt
*/
{
  double A[4*4] = {
    5,  7,  6,  5, 
    7, 10,  8,  7, 
    6,  8, 10,  9, 
    5,  7,  9, 10 };
  double *A_INV;
  int n = 4;
  double *P;

  printf ( "\n" );
  printf ( "rref_inverse_test():\n" );
  printf ( "  rref_inverse() uses the reduced row echelon form\n" );
  printf ( "  of a square matrix to compute its inverse.\n" );

  r8mat_print ( n, n, A, "  matrix A:" );

  A_INV = rref_inverse ( n, A );

  r8mat_print ( n, n, A_INV, "  Estimated inverse A_inv:" );

  P = r8mat_mm_new ( n, n, n, A_INV, A );

  r8mat_print ( n, n, P, "  Product A_inv * A:" );

  free ( A_INV );
  free ( P );

  return;
}
/******************************************************************************/

void rref_rank_test ( )

/******************************************************************************/
/*
  Purpose:

    rref_rank_test() tests rref_rank().

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    08 December 2024

  Author:

    John Burkardt

*/
{
  double A[4*7] = {
    1, -2,  3, -1, 
    3, -6,  9, -3, 
    0,  0,  0,  0, 
    2, -2,  0,  1, 
    6, -8,  6,  0, 
    3,  3,  6,  9, 
    1,  1,  2,  3 };
  int a_rank;
  int m = 4;
  int n = 7;

  printf ( "\n" );
  printf ( "rref_rank_test():\n" );
  printf ( "  rref_rank() uses the reduced row echelon form\n" );
  printf ( "  of a matrix to estimate its rank.\n" );

  r8mat_print ( m, n, A, "  matrix A:" );

  a_rank = rref_rank ( m, n, A );
  printf ( "\n" );
  printf ( "  A has rank %d\n", a_rank );

  return;
}
/******************************************************************************/

void rref_solve_test ( )

/******************************************************************************/
/*
  Purpose:

    rref_solve_test() tests rref_solve().

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    08 December 2024

  Author:

    John Burkardt
*/
{
  double A[4*4] = {
    5,  7,  6,  5, 
    7, 10,  8,  7, 
    6,  8, 10,  9, 
    5,  7,  9, 10 };
  double *b;
  double *b2;
  int m = 4;
  int n = 4;
  int nb = 1;
  double x[4*1] = { 1, 2, 3, 4 };
  double *x2;

  printf ( "\n" );
  printf ( "rref_solve_test():\n" );
  printf ( "  rref_solve() uses the reduced row echelon form\n" );
  printf ( "  of a square matrix to solve a linear system.\n" );

  r8mat_print ( m, n, A, "  matrix A:" );

  b = r8mat_mm_new ( m, n, nb, A, x );
  r8mat_print ( m, nb, b,  "  Right hand side b:" );

  x2 = rref_solve ( m, n, A, nb, b );

  r8mat_print ( n, nb, x2,  "  Estimated solution:" );

  b2 = r8mat_mm_new ( m, n, nb, A, x2 );
  r8mat_print ( m, nb, b2,  "  Product A * x:" );

  free ( b );
  free ( b2 );
  free ( x2 );

  return;
}
/******************************************************************************/

void i4vec_print ( int n, int a[], char *title )

/******************************************************************************/
/*
  Purpose:

    i4vec_print() prints an I4VEC.

  Discussion:

    An I4VEC is a vector of I4"s.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    14 November 2003

  Author:

    John Burkardt

  Input:

    int N, the number of components of the vector.

    int A[N], the vector to be printed.

    char *TITLE, a title.
*/
{
  int i;

  fprintf ( stdout, "\n" );
  fprintf ( stdout, "%s\n", title );
  fprintf ( stdout, "\n" );

  for ( i = 0; i < n; i++ )
  {
    fprintf ( stdout, "  %6d: %8d\n", i, a[i] );
  }
  return;
}
/******************************************************************************/

double *r8mat_mm_new ( int n1, int n2, int n3, double a[], double b[] )

/******************************************************************************/
/*
  Purpose:

    r8mat_mm_new() multiplies two matrices.

  Discussion:

    An R8MAT is a doubly dimensioned array of R8 values, stored as a vector
    in column-major order.

    For this routine, the result is returned as the function value.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    08 April 2009

  Author:

    John Burkardt

  Input:

    int N1, N2, N3, the order of the matrices.

    double A[N1*N2], double B[N2*N3], the matrices to multiply.

  Output:

    double R8MAT_MM_NEW[N1*N3], the product matrix C = A * B.
*/
{
  double *c;
  int i;
  int j;
  int k;

  c = ( double * ) malloc ( n1 * n3 * sizeof ( double ) );

  for ( i = 0; i < n1; i++ )
  {
    for ( j = 0; j < n3; j++ )
    {
      c[i+j*n1] = 0.0;
      for ( k = 0; k < n2; k++ )
      {
        c[i+j*n1] = c[i+j*n1] + a[i+k*n1] * b[k+j*n2];
      }
    }
  }

  return c;
}
/******************************************************************************/

void r8mat_print ( int m, int n, double a[], char *title )

/******************************************************************************/
/*
  Purpose:

    r8mat_print() prints an R8MAT.

  Discussion:

    An R8MAT is a doubly dimensioned array of R8 values, stored as a vector
    in column-major order.

    Entry A(I,J) is stored as A[I+J*M]

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    28 May 2008

  Author:

    John Burkardt

  Input:

    int M, the number of rows in A.

    int N, the number of columns in A.

    double A[M*N], the M by N matrix.

    char *TITLE, a title.
*/
{
  r8mat_print_some ( m, n, a, 1, 1, m, n, title );

  return;
}
/******************************************************************************/

void r8mat_print_some ( int m, int n, double a[], int ilo, int jlo, int ihi,
  int jhi, char *title )

/******************************************************************************/
/*
  Purpose:

    r8mat_print_some() prints some of an R8MAT.

  Discussion:

    An R8MAT is a doubly dimensioned array of R8 values, stored as a vector
    in column-major order.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    26 June 2013

  Author:

    John Burkardt

  Input:

    int M, the number of rows of the matrix.
    M must be positive.

    int N, the number of columns of the matrix.
    N must be positive.

    double A[M*N], the matrix.

    int ILO, JLO, IHI, JHI, designate the first row and
    column, and the last row and column to be printed.

    char *TITLE, a title.
*/
{
# define INCX 5

  int i;
  int i2hi;
  int i2lo;
  int j;
  int j2hi;
  int j2lo;

  fprintf ( stdout, "\n" );
  fprintf ( stdout, "%s\n", title );

  if ( m <= 0 || n <= 0 )
  {
    fprintf ( stdout, "\n" );
    fprintf ( stdout, "  (None)\n" );
    return;
  }
/*
  Print the columns of the matrix, in strips of 5.
*/
  for ( j2lo = jlo; j2lo <= jhi; j2lo = j2lo + INCX )
  {
    j2hi = j2lo + INCX - 1;
    if ( n < j2hi )
    {
      j2hi = n;
    }
    if ( jhi < j2hi )
    {
      j2hi = jhi;
    }

    fprintf ( stdout, "\n" );
/*
  For each column J in the current range...

  Write the header.
*/
    fprintf ( stdout, "  Col:  ");
    for ( j = j2lo; j <= j2hi; j++ )
    {
      fprintf ( stdout, "  %7d     ", j - 1 );
    }
    fprintf ( stdout, "\n" );
    fprintf ( stdout, "  Row\n" );
    fprintf ( stdout, "\n" );
/*
  Determine the range of the rows in this strip.
*/
    if ( 1 < ilo )
    {
      i2lo = ilo;
    }
    else
    {
      i2lo = 1;
    }
    if ( m < ihi )
    {
      i2hi = m;
    }
    else
    {
      i2hi = ihi;
    }

    for ( i = i2lo; i <= i2hi; i++ )
    {
/*
  Print out (up to) 5 entries in row I, that lie in the current strip.
*/
      fprintf ( stdout, "%5d:", i - 1 );
      for ( j = j2lo; j <= j2hi; j++ )
      {
        fprintf ( stdout, "  %14g", a[i-1+(j-1)*m] );
      }
      fprintf ( stdout, "\n" );
    }
  }

  return;
# undef INCX
}
/******************************************************************************/

void timestamp ( )

/******************************************************************************/
/*
  Purpose:
 
    timestamp() prints the current YMDHMS date as a time stamp.

  Example:

    17 June 2014 09:45:54 AM

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    01 May 2021

  Author:

    John Burkardt
*/
{
# define TIME_SIZE 40

  static char time_buffer[TIME_SIZE];
  const struct tm *tm;
  time_t now;

  now = time ( NULL );
  tm = localtime ( &now );

  strftime ( time_buffer, TIME_SIZE, "%d %B %Y %I:%M:%S %p", tm );

  printf ( "%s\n", time_buffer );

  return;
# undef TIME_SIZE
}