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

# include "haar_transform.h"

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

void haar_1d ( int n, double x[] )

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

    haar_1d() computes the Haar transform of a one-dimensional array.

  Discussion:

    For the classical Haar transform, N should be a power of 2.
    However, this is not required here.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    06 March 2014

  Author:

    John Burkardt

  Parameters:

    Input, int N, the dimension of the vector.

    Input/output, double X[N], on input, the vector to be transformed.
    On output, the transformed vector.
*/
{
  int i;
  int k;
  double s;
  double *y;

  s = sqrt ( 2.0 );

  y = ( double * ) malloc ( n * sizeof ( double ) );
/*
  Initialize.
*/
  for ( i = 0; i < n; i++ )
  {
    y[i] = 0.0;
  }
/*
  Determine K, the largest power of 2 such that K <= N.
*/
  k = 1;
  while ( k * 2 <= n )
  {
    k = k * 2;
  }
  
  while ( 1 < k )
  {
    k = k / 2;
    for ( i = 0; i < k; i++ )
    {
      y[i]   = ( x[2*i] + x[2*i+1] ) / s;
      y[i+k] = ( x[2*i] - x[2*i+1] ) / s;
    }
    for ( i = 0; i < k * 2; i++ )
    {
      x[i] = y[i];
    }
  }

  free ( y );

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

void haar_1d_inverse ( int n, double x[] )

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

    haar_1d_inverse() computes the inverse Haar transform of a one-dimensional array.

  Discussion:

    For the classical Haar transform, N should be a power of 2.
    However, this is not required here.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    06 March 2014

  Author:

    John Burkardt

  Parameters:

    Input, int N, the dimension of the vector.  

    Input/output, double X[N], on input, the vector to be transformed.
    On output, the transformed vector.
*/
{
  int i;
  int k;
  double s;
  double *y;

  s = sqrt ( 2.0 );

  y = ( double * ) malloc ( n * sizeof ( double ) );
/*
  Initialize.
*/
  for ( i = 0; i < n; i++ )
  {
    y[i] = 0.0;
  }

  k = 1;
  while ( k * 2 <= n )
  {
    for ( i = 0; i < k; i++ )
    {
      y[2*i]   = ( x[i] + x[i+k] ) / s;
      y[2*i+1] = ( x[i] - x[i+k] ) / s;
    }
    for ( i = 0; i < k * 2; i++ )
    {
      x[i] = y[i];
    }
    k = k * 2;
  }

  free ( y );

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

void haar_2d ( int m, int n, double u[] )

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

    haar_2d() computes the Haar transform of an two dimensional array.

  Discussion:

    For the classical Haar transform, M and N should be a power of 2.
    However, this is not required here.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    06 March 2014

  Author:

    John Burkardt

  Parameters:

    Input, int M, N, the dimensions of the array.

    Input/output, double U[M*N], the array to be transformed.
*/
{
  int i;
  int j;
  int k;
  double s;
  double *v;

  s = sqrt ( 2.0 );

  v = ( double * ) malloc ( m * n * sizeof ( double ) );

  for ( j = 0; j < n; j++ )
  {
    for ( i = 0; i < m; i++ )
    {
      v[i+j*m] = u[i+j*m];
    }
  }
/*
  Determine K, the largest power of 2 such that K <= M.
*/
  k = 1;
  while ( k * 2 <= m )
  {
    k = k * 2;
  }
/*
  Transform all columns.
*/
  while ( 1 < k )
  {
    k = k / 2;

    for ( j = 0; j < n; j++ )
    {
      for ( i = 0; i < k; i++ )
      {
        v[i  +j*m] = ( u[2*i+j*m] + u[2*i+1+j*m] ) / s;
        v[k+i+j*m] = ( u[2*i+j*m] - u[2*i+1+j*m] ) / s;
      }
    }
    for ( j = 0; j < n; j++ )
    {
      for ( i = 0; i < 2 * k; i++ )
      {
        u[i+j*m] = v[i+j*m];
      }
    }
  }
/*
  Determine K, the largest power of 2 such that K <= N.
*/
  k = 1;
  while ( k * 2 <= n )
  {
    k = k * 2;
  }
/*
  Transform all rows.
*/
  while ( 1 < k )
  { 
    k = k / 2;

    for ( j = 0; j < k; j++ )
    {
      for ( i = 0; i < m; i++ )
      {
        v[i+(  j)*m] = ( u[i+2*j*m] + u[i+(2*j+1)*m] ) / s;
        v[i+(k+j)*m] = ( u[i+2*j*m] - u[i+(2*j+1)*m] ) / s;
      }
    }

    for ( j = 0; j < 2 * k; j++ )
    {
      for ( i = 0; i < m; i++ )
      {
        u[i+j*m] = v[i+j*m];
      }
    }
  }
  free ( v );

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

void haar_2d_inverse ( int m, int n, double u[] )

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

    haar_2d_inverse() inverts the Haar transform of a two-dimensional array.

  Discussion:

    For the classical Haar transform, M and N should be a power of 2.
    However, this is not required here.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    06 March 2014

  Author:

    John Burkardt

  Parameters:

    Input, int M, N, the dimensions of the array.

    Input/output, double U[M*N], the array to be transformed.
*/
{
  int i;
  int j;
  int k;
  double s;
  double *v;

  s = sqrt ( 2.0 );

  v = ( double * ) malloc ( m * n * sizeof ( double ) );

  for ( j = 0; j < n; j++ )
  {
    for ( i = 0; i < m; i++ )
    {
      v[i+j*m] = u[i+j*m];
    }
  }
/*
  Inverse transform of all rows.
*/
  k = 1;

  while ( k * 2 <= n )
  {
    for ( j = 0; j < k; j++ )
    {
      for ( i = 0; i < m; i++ )
      {
        v[i+(2*j  )*m] = ( u[i+j*m] + u[i+(k+j)*m] ) / s;
        v[i+(2*j+1)*m] = ( u[i+j*m] - u[i+(k+j)*m] ) / s;
      }
    }

    for ( j = 0; j < 2 * k; j++ )
    {
      for ( i = 0; i < m; i++ )
      {
        u[i+j*m] = v[i+j*m];
      }
    }
    k = k * 2;
  }
/*
  Inverse transform of all columns.
*/
  k = 1;

  while ( k * 2 <= m )
  {
    for ( j = 0; j < n; j++ )
    {
      for ( i = 0; i < k; i++ )
      {
        v[2*i  +j*m] = ( u[i+j*m] + u[k+i+j*m] ) / s;
        v[2*i+1+j*m] = ( u[i+j*m] - u[k+i+j*m] ) / s;
      }
    }

    for ( j = 0; j < n; j++ )
    {
      for ( i = 0; i < 2 * k; i++ )
      {
        u[i+j*m] = v[i+j*m];
      }
    }
    k = k * 2;
  }
  free ( v );

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

int i4_max ( int i1, int i2 )

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

    I4_MAX returns the maximum of two I4's.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    29 August 2006

  Author:

    John Burkardt

  Parameters:

    Input, int I1, I2, are two integers to be compared.

    Output, int I4_MAX, the larger of I1 and I2.
*/
{
  int value;

  if ( i2 < i1 )
  {
    value = i1;
  }
  else
  {
    value = i2;
  }
  return value;
}
/******************************************************************************/

int i4_min ( int i1, int i2 )

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

    I4_MIN returns the smaller of two I4's.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    29 August 2006

  Author:

    John Burkardt

  Parameters:

    Input, int I1, I2, two integers to be compared.

    Output, int I4_MIN, the smaller of I1 and I2.
*/
{
  int value;

  if ( i1 < i2 )
  {
    value = i1;
  }
  else
  {
    value = i2;
  }
  return value;
}
/******************************************************************************/

double *r8mat_copy_new ( int m, int n, double a1[] )

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

    R8MAT_COPY_NEW copies one R8MAT to a "new" R8MAT.

  Discussion:

    An R8MAT is a doubly dimensioned array of R8's, which
    may be stored as a vector in column-major order.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    26 July 2008

  Author:

    John Burkardt

  Parameters:

    Input, int M, N, the number of rows and columns.

    Input, double A1[M*N], the matrix to be copied.

    Output, double R8MAT_COPY_NEW[M*N], the copy of A1.
*/
{
  double *a2;
  int i;
  int j;

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

  for ( j = 0; j < n; j++ )
  {
    for ( i = 0; i < m; i++ )
    {
      a2[i+j*m] = a1[i+j*m];
    }
  }

  return a2;
}
/******************************************************************************/

double r8mat_dif_fro ( int m, int n, double a[], double b[] )

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

    R8MAT_DIF_FRO returns the Frobenius norm of the difference of R8MAT's.

  Discussion: 							    

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

    The Frobenius norm is defined as

      R8MAT_NORM_FRO = sqrt (
        sum ( 1 <= I <= M ) sum ( 1 <= j <= N ) A(I,J)^2 )

    The matrix Frobenius norm is not derived from a vector norm, but
    is compatible with the vector L2 norm, so that:

      r8vec_norm_l2 ( A * x ) <= r8mat_norm_fro ( A ) * r8vec_norm_l2 ( x ).

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    19 June 2012

  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], double B[M*N], the matrices for which we
    want the Frobenius norm of the difference.

    Output, double R8MAT_DIF_FRO, the Frobenius norm of ( A - B ).
*/
{
  int i;
  int j;
  double value;

  value = 0.0;
  for ( j = 0; j < n; j++ )
  {
    for ( i = 0; i < m; i++ )
    {
      value = value + pow ( a[i+j*m] - b[i+j*m], 2 );
    }
  }
  value = sqrt ( value );

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

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's, which
    may be 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's, which
    may be stored as a vector in column-major order.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    20 August 2010

  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;
    j2hi = i4_min ( j2hi, n );
    j2hi = i4_min ( 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.
*/
    i2lo = i4_max ( ilo, 1 );
    i2hi = i4_min ( ihi, m );

    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, "  %14f", a[i-1+(j-1)*m] );
      }
      fprintf ( stdout, "\n" );
    }
  }

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

double *r8mat_uniform_01_new ( int m, int n, int *seed )

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

    R8MAT_UNIFORM_01_NEW fills an R8MAT with unit pseudorandom values.

  Discussion:

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

    This routine implements the recursion

      seed = 16807 * seed mod ( 2^31 - 1 )
      unif = seed / ( 2^31 - 1 )

    The integer arithmetic never requires more than 32 bits,
    including a sign bit.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    30 June 2009

  Author:

    John Burkardt

  Reference:

    Paul Bratley, Bennett Fox, Linus Schrage,
    A Guide to Simulation,
    Springer Verlag, pages 201-202, 1983.

    Bennett Fox,
    Algorithm 647:
    Implementation and Relative Efficiency of Quasirandom
    Sequence Generators,
    ACM Transactions on Mathematical Software,
    Volume 12, Number 4, pages 362-376, 1986.

    Philip Lewis, Allen Goodman, James Miller,
    A Pseudo-Random Number Generator for the System/360,
    IBM Systems Journal,
    Volume 8, pages 136-143, 1969.

  Parameters:

    Input, int M, N, the number of rows and columns.

    Input/output, int *SEED, the "seed" value.  Normally, this
    value should not be 0, otherwise the output value of SEED
    will still be 0, and R8_UNIFORM will be 0.  On output, SEED has
    been updated.

    Output, double R8MAT_UNIFORM_01_NEW[M*N], a matrix of pseudorandom values.
*/
{
  int i;
  int j;
  int k;
  double *r;

  r = ( double * ) malloc ( m * n * sizeof ( double ) );

  for ( j = 0; j < n; j++ )
  {
    for ( i = 0; i < m; i++ )
    {
      k = *seed / 127773;

      *seed = 16807 * ( *seed - k * 127773 ) - k * 2836;

      if ( *seed < 0 )
      {
        *seed = *seed + 2147483647;
      }
/*
  Although SEED can be represented exactly as a 32 bit integer,
  it generally cannot be represented exactly as a 32 bit real number
*/
      r[i+j*m] = ( double ) ( *seed ) * 4.656612875E-10;
    }
  }

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

double *r8vec_copy_new ( int n, double a1[] )

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

    R8VEC_COPY_NEW copies an R8VEC.

  Discussion:

    An R8VEC is a vector of R8's.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    26 August 2008

  Author:

    John Burkardt

  Parameters:

    Input, int N, the number of entries in the vectors.

    Input, double A1[N], the vector to be copied.

    Output, double R8VEC_COPY_NEW[N], the copy of A1.
*/
{
  double *a2;
  int i;

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

  for ( i = 0; i < n; i++ )
  {
    a2[i] = a1[i];
  }
  return a2;
}
/******************************************************************************/

double r8vec_diff_norm ( int n, double a[], double b[] )

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

    R8VEC_DIFF_NORM returns the L2 norm of the difference of R8VEC's.

  Discussion:

    An R8VEC is a vector of R8's.

    The vector L2 norm is defined as:

      R8VEC_NORM_L2 = sqrt ( sum ( 1 <= I <= N ) A(I)^2 ).

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    24 June 2011

  Author:

    John Burkardt

  Parameters:

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

    Input, double A[N], B[N], the vectors.

    Output, double R8VEC_DIFF_NORM, the L2 norm of A - B.
*/
{
  int i;
  double value;

  value = 0.0;

  for ( i = 0; i < n; i++ )
  {
    value = value + ( a[i] - b[i] ) * ( a[i] - b[i] );
  }
  value = sqrt ( value );

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

double *r8vec_linspace_new ( int n, double a_first, double a_last )

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

    R8VEC_LINSPACE_NEW creates a vector of linearly spaced values.

  Discussion:

    An R8VEC is a vector of R8's.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    14 March 2011

  Author:

    John Burkardt

  Parameters:

    Input, int N, the number of entries in the vector.

    Input, double A_FIRST, A_LAST, the first and last entries.

    Output, double R8VEC_ONES_NEW[N], a vector of linearly spaced data.
*/
{
  double *a;
  int i;

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

  if ( n == 1 )
  {
    a[0] = ( a_first + a_last ) / 2.0;
  }
  else
  {
    for ( i = 0; i < n; i++ )
    {
      a[i] = ( ( double ) ( n - 1 - i ) * a_first 
             + ( double ) (         i ) * a_last ) 
             / ( double ) ( n - 1     );
    }
  }
  return a;
}
/******************************************************************************/

double *r8vec_ones_new ( int n )

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

    R8VEC_ONES_NEW creates a vector of 1's.

  Discussion:

    An R8VEC is a vector of R8's.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    14 March 2011

  Author:

    John Burkardt

  Parameters:

    Input, int N, the number of entries in the vector.

    Output, double R8VEC_ONES_NEW[N], a vector of 1's.
*/
{
  double *a;
  int i;

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

  for ( i = 0; i < n; i++ )
  {
    a[i] = 1.0;
  }
  return a;
}
/******************************************************************************/

void r8vec_transpose_print ( int n, double a[], char *title )

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

    R8VEC_TRANSPOSE_PRINT prints an R8VEC "transposed".

  Discussion:

    An R8VEC is a vector of R8's.

  Example:

    A = (/ 1.0, 2.1, 3.2, 4.3, 5.4, 6.5, 7.6, 8.7, 9.8, 10.9, 11.0 /)
    TITLE = 'My vector:  '

    My vector:

        1.0    2.1    3.2    4.3    5.4
        6.5    7.6    8.7    9.8   10.9
       11.0

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    12 November 2010

  Author:

    John Burkardt

  Parameters:

    Input, int N, the number of components of the vector.

    Input, double A[N], the vector to be printed.

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

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

  if ( n <= 0 )
  {
    printf ( "  (Empty)\n" );
    return;
  }

  for ( ilo = 0; ilo < n; ilo = ilo + 5 )
  {
    ihi = i4_min ( ilo + 5, n );
    for ( i = ilo; i < ihi; i++ )
    {
      printf ( "  %12f", a[i] );
    }
    printf ( "\n" );
  }

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

double *r8vec_uniform_01_new ( int n, int *seed )

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

    R8VEC_UNIFORM_01_NEW returns a unit pseudorandom R8VEC.

  Discussion:

    This routine implements the recursion

      seed = 16807 * seed mod ( 2^31 - 1 )
      unif = seed / ( 2^31 - 1 )

    The integer arithmetic never requires more than 32 bits,
    including a sign bit.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    19 August 2004

  Author:

    John Burkardt

  Reference:

    Paul Bratley, Bennett Fox, Linus Schrage,
    A Guide to Simulation,
    Second Edition,
    Springer, 1987,
    ISBN: 0387964673,
    LC: QA76.9.C65.B73.

    Bennett Fox,
    Algorithm 647:
    Implementation and Relative Efficiency of Quasirandom
    Sequence Generators,
    ACM Transactions on Mathematical Software,
    Volume 12, Number 4, December 1986, pages 362-376.

    Pierre L'Ecuyer,
    Random Number Generation,
    in Handbook of Simulation,
    edited by Jerry Banks,
    Wiley, 1998,
    ISBN: 0471134031,
    LC: T57.62.H37.

    Peter Lewis, Allen Goodman, James Miller,
    A Pseudo-Random Number Generator for the System/360,
    IBM Systems Journal,
    Volume 8, Number 2, 1969, pages 136-143.

  Parameters:

    Input, int N, the number of entries in the vector.

    Input/output, int *SEED, a seed for the random number generator.

    Output, double R8VEC_UNIFORM_01_NEW[N], the vector of pseudorandom values.
*/
{
  int i;
  int i4_huge = 2147483647;
  int k;
  double *r;

  if ( *seed == 0 )
  {
    fprintf ( stderr, "\n" );
    fprintf ( stderr, "R8VEC_UNIFORM_01_NEW - Fatal error!\n" );
    fprintf ( stderr, "  Input value of SEED = 0.\n" );
    exit ( 1 );
  }

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

  for ( i = 0; i < n; i++ )
  {
    k = *seed / 127773;

    *seed = 16807 * ( *seed - k * 127773 ) - k * 2836;

    if ( *seed < 0 )
    {
      *seed = *seed + i4_huge;
    }

    r[i] = ( double ) ( *seed ) * 4.656612875E-10;
  }

  return r;
}