# include <cmath>
# include <complex>
# include <cstdlib>
# include <ctime>
# include <fstream>
# include <iomanip>
# include <iostream>

using namespace std;

# include "normal.hpp"

//****************************************************************************80

complex <float> c4_normal_01 ( int &seed )

//****************************************************************************80
//
//  Purpose:
//
//    C4_NORMAL_01 returns a unit pseudonormal C4.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    09 April 2012
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input/output, int &SEED, a seed for the random number generator.
//
//    Output, complex <float> C4_NORMAL_01, a unit pseudonormal value.
//
{
  const float r4_pi = 3.141592653589793;
  float v1;
  float v2;
  complex <float> value;
  float x_c;
  float x_r;

  v1 = r4_uniform_01 ( seed );
  v2 = r4_uniform_01 ( seed );

  x_r = sqrt ( - 2.0 * log ( v1 ) ) * cos ( 2.0 * r4_pi * v2 );
  x_c = sqrt ( - 2.0 * log ( v1 ) ) * sin ( 2.0 * r4_pi * v2 );

  value = complex <float> ( x_r, x_c );

  return value;
}
//****************************************************************************80

complex <double> c8_normal_01 ( int &seed )

//****************************************************************************80
//
//  Purpose:
//
//    C8_NORMAL_01 returns a unit pseudonormal C8.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    09 April 2012
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input/output, int &SEED, a seed for the random number generator.
//
//    Output, complex <double> C8_NORMAL_01, a unit pseudonormal value.
//
{
  const double r8_pi = 3.141592653589793;
  double v1;
  double v2;
  complex <double> value;
  double x_c;
  double x_r;

  v1 = r8_uniform_01 ( seed );
  v2 = r8_uniform_01 ( seed );

  x_r = sqrt ( - 2.0 * log ( v1 ) ) * cos ( 2.0 * r8_pi * v2 );
  x_c = sqrt ( - 2.0 * log ( v1 ) ) * sin ( 2.0 * r8_pi * v2 );

  value = complex <double> ( x_r, x_c );

  return value;
}
//****************************************************************************80

int i4_normal_ab ( double a, double b, int &seed )

//****************************************************************************80
//
//  Purpose:
//
//    I4_NORMAL_AB returns a scaled pseudonormal I4.
//
//  Discussion:
//
//    The normal probability distribution function (PDF) is sampled,
//    with mean A and standard deviation B.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    23 December 2017
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, double A, the mean of the PDF.
//
//    Input, double B, the standard deviation of the PDF.
//
//    Input/output, int &SEED, a seed for the random number generator.
//
//    Output, int I4_NORMAL_AB, a sample of the normal PDF.
//
{
  double r1;
  double r2;
  const double r8_pi = 3.141592653589793;
  int value;
  double x;

  r1 = r8_uniform_01 ( seed );
  r2 = r8_uniform_01 ( seed );
  x = sqrt ( - 2.0 * log ( r1 ) ) * cos ( 2.0 * r8_pi * r2 );

  value = ( int ) round ( a + b * x );

  return value;
}
//****************************************************************************80

void i4_normal_ab_test ( )

//****************************************************************************80
//
//  Purpose:
//
//    I4_NORMAL_AB_TEST tests I4_NORMAL_AB.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    23 December 2017
//
//  Author:
//
//    John Burkardt
//
{
  int i;
  double mu;
  int r;
  int seed;
  double sigma;

  cout << "\n";
  cout << "I4_NORMAL_AB_TEST\n";
  cout << "  I4_NORMAL_AB computes pseudonormal integer values\n";
  cout << "  with mean MU and standard deviation SIGMA.\n";

  mu = 70.0;
  sigma = 10.0;
  seed = 123456789;

  cout << "\n";
  cout << "  The mean = " << mu << "\n";
  cout << "  The standard deviation = " << sigma << "\n";
  cout << "  SEED = " << seed << "\n";
  cout << "\n";

  for ( i = 1; i <= 10; i++ )
  {
    r = i4_normal_ab ( mu, sigma, seed );
    cout << "  " << setw(8) << i
         << "  " << setw(8) << r << "\n";
  }

  return;
}
//****************************************************************************80

long long int i8_normal_ab ( double a, double b, long long int &seed )

//****************************************************************************80
//
//  Purpose:
//
//    I8_NORMAL_AB returns a scaled pseudonormal I8.
//
//  Discussion:
//
//    The normal probability distribution function (PDF) is sampled,
//    with mean A and standard deviation B.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    09 April 2012
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, double A, the mean of the PDF.
//
//    Input, double B, the standard deviation of the PDF.
//
//    Input/output, long long int &SEED, a seed for the random number generator.
//
//    Output, long long int I8_NORMAL_AB, a sample of the normal PDF.
//
{
  int seed_int;
  double value_double;
  long long int value_long_long_int;

  seed_int = ( int ) seed;

  value_double = a + b * r8_normal_01 ( seed_int );

  if ( value_double < 0.0 )
  {
    value_long_long_int = ( long long int ) ( value_double - 0.5 );
  }
  else
  {
    value_long_long_int = ( long long int ) ( value_double + 0.5 );
  }

  seed = ( long long int ) seed_int;

  return value_long_long_int;
}
//****************************************************************************80

float r4_normal_01 ( int &seed )

//****************************************************************************80
//
//  Purpose:
//
//    R4_NORMAL_01 returns a unit pseudonormal R4.
//
//  Discussion:
//
//    The standard normal probability distribution function (PDF) has
//    mean 0 and standard deviation 1.
//
//    The Box-Muller method is used, which is efficient, but
//    generates two values at a time.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    06 August 2013
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input/output, int &SEED, a seed for the random number generator.
//
//    Output, float R4_NORMAL_01, a normally distributed random value.
//
{
  const float r4_pi = 3.141592653589793;
  float r1;
  float r2;
  float x;

  r1 = r4_uniform_01 ( seed );
  r2 = r4_uniform_01 ( seed );
  x = sqrt ( - 2.0 * log ( r1 ) ) * cos ( 2.0 * r4_pi * r2 );

  return x;
}
//****************************************************************************80

float r4_normal_ab ( float a, float b, int &seed )

//****************************************************************************80
//
//  Purpose:
//
//    R4_NORMAL_AB returns a scaled pseudonormal R4.
//
//  Discussion:
//
//    The normal probability distribution function (PDF) is sampled,
//    with mean A and standard deviation B.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    09 April 2012
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, float A, the mean of the PDF.
//
//    Input, float B, the standard deviation of the PDF.
//
//    Input/output, int &SEED, a seed for the random number generator.
//
//    Output, float R4_NORMAL_AB, a sample of the normal PDF.
//
{
  float value;

  value = a + b * r4_normal_01 ( seed );

  return value;
}
//****************************************************************************80

float r4_uniform_01 ( int &seed )

//****************************************************************************80
//
//  Purpose:
//
//    R4_UNIFORM_01 returns a unit pseudorandom R4.
//
//  Discussion:
//
//    This routine implements the recursion
//
//      seed = 16807 * seed mod ( 2^31 - 1 )
//      r4_uniform_01 = seed / ( 2^31 - 1 )
//
//    The integer arithmetic never requires more than 32 bits,
//    including a sign bit.
//
//    If the initial seed is 12345, then the first three computations are
//
//      Input     Output      R4_UNIFORM_01
//      SEED      SEED
//
//         12345   207482415  0.096616
//     207482415  1790989824  0.833995
//    1790989824  2035175616  0.947702
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    09 April 2012
//
//  Author:
//
//    John Burkardt
//
//  Reference:
//
//    Paul Bratley, Bennett Fox, Linus Schrage,
//    A Guide to Simulation,
//    Springer Verlag, pages 201-202, 1983.
//
//    Pierre L'Ecuyer,
//    Random Number Generation,
//    in Handbook of Simulation
//    edited by Jerry Banks,
//    Wiley Interscience, page 95, 1998.
//
//    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.
//
//    Peter 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/output, int &SEED, the "seed" value.  Normally, this
//    value should not be 0.  On output, SEED has been updated.
//
//    Output, float R4_UNIFORM_01, a new pseudorandom variate, strictly between
//    0 and 1.
//
{
  const int i4_huge = 2147483647;
  int k;
  float r;

  k = seed / 127773;

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

  if ( seed < 0 )
  {
    seed = seed + i4_huge;
  }
//
//  Although SEED can be represented exactly as a 32 bit integer,
//  it generally cannot be represented exactly as a 32 bit real number!
//
  r = ( float ) ( seed ) * 4.656612875E-10;

  return r;
}
//****************************************************************************80

void r4mat_print ( int m, int n, float a[], string title )

//****************************************************************************80
//
//  Purpose:
//
//    R4MAT_PRINT prints an R4MAT.
//
//  Discussion:
//
//    An R4MAT is a doubly dimensioned array of R4 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 GNU LGPL license.
//
//  Modified:
//
//    10 September 2009
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int M, the number of rows in A.
//
//    Input, int N, the number of columns in A.
//
//    Input, float A[M*N], the M by N matrix.
//
//    Input, string TITLE, a title.
//
{
  r4mat_print_some ( m, n, a, 1, 1, m, n, title );

  return;
}
//****************************************************************************80

void r4mat_print_some ( int m, int n, float a[], int ilo, int jlo, int ihi,
  int jhi, string title )

//****************************************************************************80
//
//  Purpose:
//
//    R4MAT_PRINT_SOME prints some of an R4MAT.
//
//  Discussion:
//
//    An R4MAT is a doubly dimensioned array of R4 values, stored as a vector
//    in column-major order.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL 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, float 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, string TITLE, a title.
//
{
# define INCX 5

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

  cout << "\n";
  cout << title << "\n";

  if ( m <= 0 || n <= 0 )
  {
    cout << "\n";
    cout << "  (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;
    }
    cout << "\n";
//
//  For each column J in the current range...
//
//  Write the header.
//
    cout << "  Col:    ";
    for ( j = j2lo; j <= j2hi; j++ )
    {
      cout << setw(7) << j - 1 << "       ";
    }
    cout << "\n";
    cout << "  Row\n";
    cout << "\n";
//
//  Determine the range of the rows in this strip.
//
    if ( 1 < ilo )
    {
      i2lo = ilo;
    }
    else
    {
      i2lo = 1;
    }
    if ( ihi < m )
    {
      i2hi = ihi;
    }
    else
    {
      i2hi = m;
    }

    for ( i = i2lo; i <= i2hi; i++ )
    {
//
//  Print out (up to) 5 entries in row I, that lie in the current strip.
//
      cout << setw(5) << i - 1 << ": ";
      for ( j = j2lo; j <= j2hi; j++ )
      {
        cout << setw(12) << a[i-1+(j-1)*m] << "  ";
      }
      cout << "\n";
    }
  }

  return;
# undef INCX
}
//****************************************************************************80

void r4vec_print ( int n, float a[], string title )

//****************************************************************************80
//
//  Purpose:
//
//    R4VEC_PRINT prints an R4VEC.
//
//  Discussion:
//
//    An R4VEC is a vector of R4's.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    16 August 2004
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of components of the vector.
//
//    Input, float A[N], the vector to be printed.
//
//    Input, string TITLE, a title.
//
{
  int i;

  cout << "\n";
  cout << title << "\n";
  cout << "\n";
  for ( i = 0; i < n; i++ )
  {
    cout << "  " << setw(8)  << i
         << ": " << setw(14) << a[i]  << "\n";
  }

  return;
}
//****************************************************************************80

float *r4vec_uniform_01_new ( int n, int &seed )

//****************************************************************************80
//
//  Purpose:
//
//    R4VEC_UNIFORM_01_NEW returns a new unit pseudorandom R4VEC.
//
//  Discussion:
//
//    This routine implements the recursion
//
//      seed = ( 16807 * seed ) mod ( 2^31 - 1 )
//      u = seed / ( 2^31 - 1 )
//
//    The integer arithmetic never requires more than 32 bits,
//    including a sign bit.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    04 March 2015
//
//  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, float R4VEC_UNIFORM_01_NEW[N], the vector of pseudorandom values.
//
{
  int i;
  int i4_huge = 2147483647;
  int k;
  float *r;

  if ( seed == 0 )
  {
    cerr << "\n";
    cerr << "R4VEC_UNIFORM_01_NEW - Fatal error!\n";
    cerr << "  Input value of SEED = 0.\n";
    exit ( 1 );
  }

  r = new float[n];

  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] = ( float ) ( seed ) * 4.656612875E-10;
  }

  return r;
}
//****************************************************************************80

double r8_normal_01 ( int &seed )

//****************************************************************************80
//
//  Purpose:
//
//    R8_NORMAL_01 returns a unit pseudonormal R8.
//
//  Discussion:
//
//    The standard normal probability distribution function (PDF) has
//    mean 0 and standard deviation 1.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    06 August 2013
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input/output, int &SEED, a seed for the random number generator.
//
//    Output, double R8_NORMAL_01, a normally distributed random value.
//
{
  double r1;
  double r2;
  const double r8_pi = 3.141592653589793;
  double x;

  r1 = r8_uniform_01 ( seed );
  r2 = r8_uniform_01 ( seed );
  x = sqrt ( - 2.0 * log ( r1 ) ) * cos ( 2.0 * r8_pi * r2 );

  return x;
}
//****************************************************************************80

double r8_normal_ab ( double a, double b, int &seed )

//****************************************************************************80
//
//  Purpose:
//
//    R8_NORMAL_AB returns a scaled pseudonormal R8.
//
//  Discussion:
//
//    The normal probability distribution function (PDF) is sampled,
//    with mean A and standard deviation B.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    09 April 2012
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, double A, the mean of the PDF.
//
//    Input, double B, the standard deviation of the PDF.
//
//    Input/output, int &SEED, a seed for the random number generator.
//
//    Output, double R8_NORMAL_AB, a sample of the normal PDF.
//
{
  double value;

  value = a + b * r8_normal_01 ( seed );

  return value;
}
//****************************************************************************80

double r8_uniform_01 ( int &seed )

//****************************************************************************80
//
//  Purpose:
//
//    R8_UNIFORM_01 returns a unit pseudorandom R8.
//
//  Discussion:
//
//    This routine implements the recursion
//
//      seed = 16807 * seed mod ( 2^31 - 1 )
//      r8_uniform_01 = seed / ( 2^31 - 1 )
//
//    The integer arithmetic never requires more than 32 bits,
//    including a sign bit.
//
//    If the initial seed is 12345, then the first three computations are
//
//      Input     Output      R8_UNIFORM_01
//      SEED      SEED
//
//         12345   207482415  0.096616
//     207482415  1790989824  0.833995
//    1790989824  2035175616  0.947702
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    09 April 2012
//
//  Author:
//
//    John Burkardt
//
//  Reference:
//
//    Paul Bratley, Bennett Fox, Linus Schrage,
//    A Guide to Simulation,
//    Springer Verlag, pages 201-202, 1983.
//
//    Pierre L'Ecuyer,
//    Random Number Generation,
//    in Handbook of Simulation
//    edited by Jerry Banks,
//    Wiley Interscience, page 95, 1998.
//
//    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.
//
//    Peter 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/output, int &SEED, the "seed" value.  Normally, this
//    value should not be 0.  On output, SEED has been updated.
//
//    Output, double R8_UNIFORM_01, a new pseudorandom variate, strictly between
//    0 and 1.
//
{
  const int i4_huge = 2147483647;
  int k;
  double r;

  k = seed / 127773;

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

  if ( seed < 0 )
  {
    seed = seed + i4_huge;
  }
//
//  Although SEED can be represented exactly as a 32 bit integer,
//  it generally cannot be represented exactly as a 32 bit real number!
//
  r = ( double ) ( seed ) * 4.656612875E-10;

  return r;
}
//****************************************************************************80

void r8mat_normal_01 ( int m, int n, int &seed, double x[] )

//****************************************************************************80
//
//  Purpose:
//
//    R8MAT_NORMAL_01 returns a unit pseudonormal R8MAT.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    09 April 2012
//
//  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.
//
//    Peter 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 in the array.
//
//    Input/output, int &SEED, the "seed" value, which should NOT be 0.
//    On output, SEED has been updated.
//
//    Output, double X[M*N], the array of pseudonormal values.
//
{
  r8vec_normal_01 ( m*n, seed, x );

  return;
}
//****************************************************************************80

double *r8mat_normal_01_new ( int m, int n, int &seed )

//****************************************************************************80
//
//  Purpose:
//
//    R8MAT_NORMAL_01_NEW returns a unit pseudonormal R8MAT.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    09 April 2012
//
//  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.
//
//    Peter 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 in the array.
//
//    Input/output, int &SEED, the "seed" value, which should NOT be 0.
//    On output, SEED has been updated.
//
//    Output, double R8MAT_NORMAL_01_NEW[M*N], the array of pseudonormal values.
//
{
  double *r;

  r = r8vec_normal_01_new ( m * n, seed );

  return r;
}
//****************************************************************************80

void r8mat_normal_ab ( int m, int n, double a, double b, int &seed, double x[] )

//****************************************************************************80
//
//  Purpose:
//
//    R8MAT_NORMAL_AB returns a scaled pseudonormal R8MAT.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    09 April 2012
//
//  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.
//
//    Peter 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 in the array.
//
//    Input, double A, B, the mean and standard deviation.
//
//    Input/output, int &SEED, the "seed" value, which should NOT be 0.
//    On output, SEED has been updated.
//
//    Output, double X[M*N], the array of pseudonormal values.
//
{
  r8vec_normal_ab ( m * n, a, b, seed, x );

  return;
}
//****************************************************************************80

double *r8mat_normal_ab_new ( int m, int n, double a, double b, int &seed )

//****************************************************************************80
//
//  Purpose:
//
//    R8MAT_NORMAL_AB_NEW returns a scaled pseudonormal R8MAT.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    09 April 2012
//
//  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.
//
//    Peter 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 in the array.
//
//    Input, double A, B, the mean and standard deviation.
//
//    Input/output, int &SEED, the "seed" value, which should NOT be 0.
//    On output, SEED has been updated.
//
//    Output, double R8MAT_NORMAL_AB_NEW[M*N], the array of pseudonormal values.
//
{
  double *r;

  r = r8vec_normal_ab_new ( m * n, a, b, seed );

  return r;
}
//****************************************************************************80

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

//****************************************************************************80
//
//  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 GNU LGPL license.
//
//  Modified:
//
//    10 September 2009
//
//  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, string TITLE, a title.
//
{
  r8mat_print_some ( m, n, a, 1, 1, m, n, title );

  return;
}
//****************************************************************************80

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

//****************************************************************************80
//
//  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 GNU LGPL 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, string TITLE, a title.
//
{
# define INCX 5

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

  cout << "\n";
  cout << title << "\n";

  if ( m <= 0 || n <= 0 )
  {
    cout << "\n";
    cout << "  (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;
    }
    cout << "\n";
//
//  For each column J in the current range...
//
//  Write the header.
//
    cout << "  Col:    ";
    for ( j = j2lo; j <= j2hi; j++ )
    {
      cout << setw(7) << j - 1 << "       ";
    }
    cout << "\n";
    cout << "  Row\n";
    cout << "\n";
//
//  Determine the range of the rows in this strip.
//
    if ( 1 < ilo )
    {
      i2lo = ilo;
    }
    else
    {
      i2lo = 1;
    }
    if ( ihi < m )
    {
      i2hi = ihi;
    }
    else
    {
      i2hi = m;
    }

    for ( i = i2lo; i <= i2hi; i++ )
    {
//
//  Print out (up to) 5 entries in row I, that lie in the current strip.
//
      cout << setw(5) << i - 1 << ": ";
      for ( j = j2lo; j <= j2hi; j++ )
      {
        cout << setw(12) << a[i-1+(j-1)*m] << "  ";
      }
      cout << "\n";
    }
  }

  return;
# undef INCX
}
//****************************************************************************80

void r8vec_normal_01 ( int n, int &seed, double x[] )

//****************************************************************************80
//
//  Purpose:
//
//    R8VEC_NORMAL_01 returns a unit pseudonormal R8VEC.
//
//  Discussion:
//
//    The standard normal probability distribution function (PDF) has
//    mean 0 and standard deviation 1.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    06 August 2013
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of values desired.
//
//    Input/output, int &SEED, a seed for the random number generator.
//
//    Output, double X[N], a sample of the standard normal PDF.
//
//  Local parameters:
//
//    Local, double R(N+1), is used to store some uniform random values.
//    Its dimension is N+1, but really it is only needed to be the
//    smallest even number greater than or equal to N.
//
//    Local, int X_LO, X_HI, records the range of entries of
//    X that we need to compute
//
{
  int i;
  int m;
  double *r;
  const double r8_pi = 3.141592653589793;
  int x_hi;
  int x_lo;
//
//  Record the range of X we need to fill in.
//
  x_lo = 1;
  x_hi = n;
//
//  If we need just one new value, do that here to avoid null arrays.
//
  if ( x_hi - x_lo + 1 == 1 )
  {
    r = r8vec_uniform_01_new ( 2, seed );

    x[x_hi-1] = sqrt ( - 2.0 * log ( r[0] ) ) * cos ( 2.0 * r8_pi * r[1] );

    delete [] r;
  }
//
//  If we require an even number of values, that's easy.
//
  else if ( ( x_hi - x_lo + 1 ) % 2 == 0 )
  {
    m = ( x_hi - x_lo + 1 ) / 2;

    r = r8vec_uniform_01_new ( 2*m, seed );

    for ( i = 0; i <= 2 * m - 2; i = i + 2 )
    {
      x[x_lo+i-1] = sqrt ( - 2.0 * log ( r[i] ) ) * cos ( 2.0 * r8_pi * r[i+1] );
      x[x_lo+i  ] = sqrt ( - 2.0 * log ( r[i] ) ) * sin ( 2.0 * r8_pi * r[i+1] );
    }

    delete [] r;
  }
//
//  If we require an odd number of values, we generate an even number,
//  and handle the last pair specially, storing one in X(N).
//
  else
  {
    x_hi = x_hi - 1;

    m = ( x_hi - x_lo + 1 ) / 2 + 1;

    r = r8vec_uniform_01_new ( 2*m, seed );

    for ( i = 0; i <= 2 * m - 4; i = i + 2 )
    {
      x[x_lo+i-1] = sqrt ( - 2.0 * log ( r[i] ) ) * cos ( 2.0 * r8_pi * r[i+1] );
      x[x_lo+i  ] = sqrt ( - 2.0 * log ( r[i] ) ) * sin ( 2.0 * r8_pi * r[i+1] );
    }

    i = 2*m - 2;

    x[x_lo+i-1] = sqrt ( - 2.0 * log ( r[i] ) ) * cos ( 2.0 * r8_pi * r[i+1] );

    delete [] r;
  }

  return;
}
//****************************************************************************80

double *r8vec_normal_01_new ( int n, int &seed )

//****************************************************************************80
//
//  Purpose:
//
//    R8VEC_NORMAL_01_NEW returns a unit pseudonormal R8VEC.
//
//  Discussion:
//
//    The standard normal probability distribution function (PDF) has
//    mean 0 and standard deviation 1.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    06 August 2013
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of values desired.
//
//    Input/output, int &SEED, a seed for the random number generator.
//
//    Output, double R8VEC_NORMAL_01_NEW[N], a sample of the standard normal PDF.
//
//  Local parameters:
//
//    Local, double R(N+1), is used to store some uniform random values.
//    Its dimension is N+1, but really it is only needed to be the
//    smallest even number greater than or equal to N.
//
//    Local, int X_LO, X_HI, records the range of entries of
//    X that we need to compute.
//
{
  int i;
  int m;
  double *r;
  const double r8_pi = 3.141592653589793;
  double *x;
  int x_hi;
  int x_lo;

  x = new double[n];
//
//  Record the range of X we need to fill in.
//
  x_lo = 1;
  x_hi = n;
//
//  If we need just one new value, do that here to avoid null arrays.
//
  if ( x_hi - x_lo + 1 == 1 )
  {
    r = r8vec_uniform_01_new ( 2, seed );

    x[x_hi-1] = sqrt ( - 2.0 * log ( r[0] ) ) * cos ( 2.0 * r8_pi * r[1] );

    delete [] r;
  }
//
//  If we require an even number of values, that's easy.
//
  else if ( ( x_hi - x_lo + 1 ) % 2 == 0 )
  {
    m = ( x_hi - x_lo + 1 ) / 2;

    r = r8vec_uniform_01_new ( 2*m, seed );

    for ( i = 0; i <= 2 * m - 2; i = i + 2 )
    {
      x[x_lo+i-1] = sqrt ( - 2.0 * log ( r[i] ) ) * cos ( 2.0 * r8_pi * r[i+1] );
      x[x_lo+i  ] = sqrt ( - 2.0 * log ( r[i] ) ) * sin ( 2.0 * r8_pi * r[i+1] );
    }

    delete [] r;
  }
//
//  If we require an odd number of values, we generate an even number,
//  and handle the last pair specially, storing one in X(N), and
//  saving the other for later.
//
  else
  {
    x_hi = x_hi - 1;

    m = ( x_hi - x_lo + 1 ) / 2 + 1;

    r = r8vec_uniform_01_new ( 2*m, seed );

    for ( i = 0; i <= 2 * m - 4; i = i + 2 )
    {
      x[x_lo+i-1] = sqrt ( - 2.0 * log ( r[i] ) ) * cos ( 2.0 * r8_pi * r[i+1] );
      x[x_lo+i  ] = sqrt ( - 2.0 * log ( r[i] ) ) * sin ( 2.0 * r8_pi * r[i+1] );
    }

    i = 2*m - 2;

    x[x_lo+i-1] = sqrt ( - 2.0 * log ( r[i] ) ) * cos ( 2.0 * r8_pi * r[i+1] );

    delete [] r;
  }

  return x;
}
//****************************************************************************80

void r8vec_normal_ab ( int n, double b, double c, int &seed, double x[] )

//****************************************************************************80
//
//  Purpose:
//
//    R8VEC_NORMAL_AB returns a scaled pseudonormal R8VEC.
//
//  Discussion:
//
//    The scaled normal probability distribution function (PDF) has
//    mean A and standard deviation B.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    06 August 2013
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of values desired.
//
//    Input, double B, C, the mean and standard deviation.
//
//    Input/output, int &SEED, a seed for the random number generator.
//
//    Output, double X[N], a sample of the standard normal PDF.
//
//  Local parameters:
//
//    Local, double R(N+1), is used to store some uniform random values.
//    Its dimension is N+1, but really it is only needed to be the
//    smallest even number greater than or equal to N.
//
//    Local, int X_LO, X_HI, records the range of entries of
//    X that we need to compute.
//
{
  int i;
  int m;
  double *r;
  const double r8_pi = 3.141592653589793;
  int x_hi;
  int x_lo;

  x = new double[n];
//
//  Record the range of X we need to fill in.
//
  x_lo = 1;
  x_hi = n;
//
//  If we need just one new value, do that here to avoid null arrays.
//
  if ( x_hi - x_lo + 1 == 1 )
  {
    r = r8vec_uniform_01_new ( 2, seed );

    x[x_hi-1] = sqrt ( - 2.0 * log ( r[0] ) ) * cos ( 2.0 * r8_pi * r[1] );

    delete [] r;
  }
//
//  If we require an even number of values, that's easy.
//
  else if ( ( x_hi - x_lo + 1 ) % 2 == 0 )
  {
    m = ( x_hi - x_lo + 1 ) / 2;

    r = r8vec_uniform_01_new ( 2*m, seed );

    for ( i = 0; i <= 2 * m - 2; i = i + 2 )
    {
      x[x_lo+i-1] = sqrt ( - 2.0 * log ( r[i] ) ) * cos ( 2.0 * r8_pi * r[i+1] );
      x[x_lo+i  ] = sqrt ( - 2.0 * log ( r[i] ) ) * sin ( 2.0 * r8_pi * r[i+1] );
    }

    delete [] r;
  }
//
//  If we require an odd number of values, we generate an even number,
//  and handle the last pair specially, storing one in X(N).
//
  else
  {
    x_hi = x_hi - 1;

    m = ( x_hi - x_lo + 1 ) / 2 + 1;

    r = r8vec_uniform_01_new ( 2*m, seed );

    for ( i = 0; i <= 2 * m - 4; i = i + 2 )
    {
      x[x_lo+i-1] = sqrt ( - 2.0 * log ( r[i] ) ) * cos ( 2.0 * r8_pi * r[i+1] );
      x[x_lo+i  ] = sqrt ( - 2.0 * log ( r[i] ) ) * sin ( 2.0 * r8_pi * r[i+1] );
    }

    i = 2*m - 2;

    x[x_lo+i-1] = sqrt ( - 2.0 * log ( r[i] ) ) * cos ( 2.0 * r8_pi * r[i+1] );

    delete [] r;
  }

  for ( i = 0; i < n; i++ )
  {
    x[i] = b + c * x[i];
  }

  return;
}
//****************************************************************************80

double *r8vec_normal_ab_new ( int n, double b, double c, int &seed )

//****************************************************************************80
//
//  Purpose:
//
//    R8VEC_NORMAL_AB_NEW returns a scaled pseudonormal R8VEC.
//
//  Discussion:
//
//    The scaled normal probability distribution function (PDF) has
//    mean A and standard deviation B.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    06 August 2013
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of values desired.
//
//    Input, double B, C, the mean and standard deviation.
//
//    Input/output, int &SEED, a seed for the random number generator.
//
//    Output, double R8VEC_NORMAL_AB_NEW[N], a sample of the standard normal PDF.
//
//  Local parameters:
//
//    Local, double R(N+1), is used to store some uniform random values.
//    Its dimension is N+1, but really it is only needed to be the
//    smallest even number greater than or equal to N.
//
//    Local, int X_LO, X_HI, records the range of entries of
//    X that we need to compute.
//
{
  int i;
  int m;
  double *r;
  const double r8_pi = 3.141592653589793;
  double *x;
  int x_hi;
  int x_lo;

  x = new double[n];
//
//  Record the range of X we need to fill in.
//
  x_lo = 1;
  x_hi = n;
//
//  If we need just one new value, do that here to avoid null arrays.
//
  if ( x_hi - x_lo + 1 == 1 )
  {
    r = r8vec_uniform_01_new ( 2, seed );

    x[x_hi-1] = sqrt ( - 2.0 * log ( r[0] ) ) * cos ( 2.0 * r8_pi * r[1] );

    delete [] r;
  }
//
//  If we require an even number of values, that's easy.
//
  else if ( ( x_hi - x_lo + 1 ) % 2 == 0 )
  {
    m = ( x_hi - x_lo + 1 ) / 2;

    r = r8vec_uniform_01_new ( 2*m, seed );

    for ( i = 0; i <= 2 * m - 2; i = i + 2 )
    {
      x[x_lo+i-1] = sqrt ( - 2.0 * log ( r[i] ) ) * cos ( 2.0 * r8_pi * r[i+1] );
      x[x_lo+i  ] = sqrt ( - 2.0 * log ( r[i] ) ) * sin ( 2.0 * r8_pi * r[i+1] );
    }

    delete [] r;
  }
//
//  If we require an odd number of values, we generate an even number,
//  and handle the last pair specially.
//
  else
  {
    x_hi = x_hi - 1;

    m = ( x_hi - x_lo + 1 ) / 2 + 1;

    r = r8vec_uniform_01_new ( 2 * m, seed );

    for ( i = 0; i <= 2 * m - 4; i = i + 2 )
    {
      x[x_lo+i-1] = sqrt ( - 2.0 * log ( r[i] ) ) * cos ( 2.0 * r8_pi * r[i+1] );
      x[x_lo+i  ] = sqrt ( - 2.0 * log ( r[i] ) ) * sin ( 2.0 * r8_pi * r[i+1] );
    }

    i = 2*m - 2;

    x[x_lo+i-1] = sqrt ( - 2.0 * log ( r[i] ) ) * cos ( 2.0 * r8_pi * r[i+1] );

    delete [] r;
  }

  for ( i = 0; i < n; i++ )
  {
    x[i] = b + c * x[i];
  }

  return x;
}
//****************************************************************************80

void r8vec_print ( int n, double a[], string title )

//****************************************************************************80
//
//  Purpose:
//
//    R8VEC_PRINT prints an R8VEC.
//
//  Discussion:
//
//    An R8VEC is a vector of R8's.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    16 August 2004
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of components of the vector.
//
//    Input, double A[N], the vector to be printed.
//
//    Input, string TITLE, a title.
//
{
  int i;

  cout << "\n";
  cout << title << "\n";
  cout << "\n";
  for ( i = 0; i < n; i++ )
  {
    cout << "  " << setw(8)  << i
         << ": " << setw(14) << a[i]  << "\n";
  }

  return;
}
//****************************************************************************80

double *r8vec_uniform_01_new ( int n, int &seed )

//****************************************************************************80
//
//  Purpose:
//
//    R8VEC_UNIFORM_01_NEW returns a new unit pseudorandom R8VEC.
//
//  Discussion:
//
//    This routine implements the recursion
//
//      seed = ( 16807 * seed ) mod ( 2^31 - 1 )
//      u = seed / ( 2^31 - 1 )
//
//    The integer arithmetic never requires more than 32 bits,
//    including a sign bit.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    09 April 2012
//
//  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 )
  {
    cerr << "\n";
    cerr << "R8VEC_UNIFORM_01_NEW - Fatal error!\n";
    cerr << "  Input value of SEED = 0.\n";
    exit ( 1 );
  }

  r = new double[n];

  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;
}
//****************************************************************************80

void timestamp ( )

//****************************************************************************80
//
//  Purpose:
//
//    TIMESTAMP prints the current YMDHMS date as a time stamp.
//
//  Example:
//
//    31 May 2001 09:45:54 AM
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    08 July 2009
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    None
//
{
# define TIME_SIZE 40

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

  now = std::time ( NULL );
  tm_ptr = std::localtime ( &now );

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

  std::cout << time_buffer << "\n";

  return;
# undef TIME_SIZE
}