# include <math.h>
# include <stdio.h>
# include <stdlib.h>

# include "asa082.h"

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

void detq ( double a[], int n, double *d, int *ifault )

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

    detq() computes the determinant of an orthogonal matrix.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    18 January 2020

  Author:

    Original FORTRAN77 version by J C Gower.
    This C version by John Burkardt

  Reference:

    J C Gower,
    Algorithm AS 82:
    The determinant of an orthogonal matrix,
    Applied Statistics,
    Volume 24, Number 1, 1975, page 150-153.

  Input:

    double A[N*N], the orthogonal matrix stored by rows or columns.

    int N, the order of the matrix.

  Output:

    double *D, the determinant of A.

    integer *IFAULT, 
    0, no error occurred.
    1, an error was detected.
*/
{
  double *a2;
  int i;
  int j;
  int k;
  int p;
  int q;
  int r;
  int s;
  double tol;
  double x;
  double y;

  *d = 0.0;
  *ifault = 0;
  tol = 0.0001;

  if ( n <= 0 )
  {
    printf ( "\n" );
    printf ( "detq - Fatal error!\n" );
    printf ( "  n <= 0\n" );
    *ifault = 1;
    return;
  }

  a2 = ( double * ) malloc ( n * n * sizeof ( double ) );

  for ( k = 0; k < n * n; k++ )
  {
    a2[k] = a[k];
  }

  *d = 1.0;
  r = 0;

  for ( k = 2; k <= n + 1; k++ )
  {
    q = r;
    x = a2[r];
    if ( x < 0.0 )
    {
      y = - 1.0;
    }
    else
    {
      y = + 1.0;
    }
    *d = *d * y;
    y = - 1.0 / ( x + y );
    x = fabs ( x ) - 1.0;

    if ( tol < fabs ( x ) )
    {
      if ( 0.0 < x )
      {
        printf ( "\n" );
        printf ( "detq - Fatal error!\n" );
        printf ( "  x < 0.0\n" );
        printf ( "  x = %g\n", x );
        *ifault = 1;
        return;
      }

      if ( k == n + 1 )
      {
        printf ( "\n" );
        printf ( "detq - Fatal error!\n" );
        printf ( "  k == n + 1\n" );
        *ifault = 1;
        return;
      }

      for ( i = k; i <= n; i++ )
      {
        q = q + n;
        x = a2[q] * y;
        p = r;
        s = q;
        for ( j = k; j <= n; j++ )
        {
          p = p + 1;
          s = s + 1;
          a2[s] = a2[s] + x * a2[p];
        }
      }
    }
    r = r + n + 1;
  }

  free ( a2 );

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

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

  Parameters:

    Input, int M, the number of rows in A.

    Input, int N, the number of columns in A.

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

    Input, 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

  Parameters:

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

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

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

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

    Input, 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
}