# include <cmath>
# include <cstdlib>
# include <ctime>
# include <iomanip>
# include <iostream>
# include <fstream>
# include <sstream>
# include <string>

using namespace std;

int main ( int argc, char *argv[] );
double *multinormal_sample ( int m, int n, double a[], double mu[] );
void r8mat_print ( int m, int n, double a[], string title );
void r8mat_print_some ( int m, int n, double a[], int ilo, int jlo, int ihi, 
  int jhi, string title );
void r8mat_write ( string output_filename, int m, int n, double table[] );
double *r8po_fa ( int n, double a[] );
double *r8vec_normal_01_new ( int n );
void r8vec_print ( int n, double a[], string title );
void timestamp ( );

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

int main ( int argc, char *argv[] )

//****************************************************************************80
//
//  Purpose:
//
//    normal_dataset() generates a dataset of multivariate normal random values.
//
//  Usage:
//
//    normal_dataset m n mu a
//
//    where
//
//    * M, the spatial dimension,
//    * N, the number of points to generate,
//    * MU, the mean vector.
//    * A, the MxM variance-covariance matrix.
//
//    creates an M by N multivariate normal random dataset and writes it 
//    to the file "normal_M_N.txt"./
//
//  Licensing:
//
//    This information is distributed under the MIT license. 
//
//  Modified:
//
//    15 May 2024
//
//  Author:
//
//    John Burkardt
//
{
  double *a;
  string output_filename;
  int i;
  int j;
  int k;
  int m;
  double *mu;
  ostringstream m_ostring;
  int n;
  ostringstream n_ostring;
  double *x;

  timestamp ( );

  srand48 ( time ( NULL ) );

  cout << "\n";
  cout << "normal_dataset():\n";
  cout << "  C++ version\n";
  cout << "  Generate a multivariate normal random dataset.\n";
  cout << "\n";
  cout << "  The program requests input values from the user:\n";
  cout << "\n";
  cout << "  * M, the spatial dimension,\n";
  cout << "  * N, the number of points to generate,\n";
  cout << "  * MU, the mean vector of length M.\n";
  cout << "  * A, the MxM variance-covariance matrix.\n";
  cout << "\n";
  cout << "  The program generates the data, writes it to the file\n";
  cout << "\n";
  cout << "    normal_M_N.txt\n";
  cout << "\n";
  cout << "  where ""M"" and ""N"" are the numeric values specified\n";
  cout << "  by the user.\n";
//
//  Get the spatial dimension.
//
  if ( 1 < argc )
  {
    m = atoi ( argv[1] );
  }
  else
  {
    cout << "\n";
    cout << "  Enter the value of M\n";
    cin >> m;
  }

  cout << "\n";
  cout << "  Spatial dimension M = " << m << "\n";
//
//  Get the number of points.
//
  if ( 2 < argc )
  {
    n = atoi ( argv[2] );
  }
  else
  {
    cout << "\n";
    cout << "  Enter the number of points N\n";
    cin >> n;
  }

  cout << "\n";
  cout << "  Number of points N = " << n << "\n";
//
//  Get the mean.
//
  mu = new double[m];

  k = 3;

  if ( 3 < argc )
  {
    for ( i = 0; i < m; i++ )
    {    
      mu[i] = atof ( argv[k] );
      k = k + 1;
    }
  }
  else
  {
    cout << "\n";
    cout << "  Enter MU:\n";
    for ( i = 0; i < m; i++ )
    {
      cin >> mu[i];
    }
  }

  r8vec_print ( m, mu, "  The mean vector M:" );
//
//  Get the variance-covariance matrix.
//
  a = new double[m*m];

  if ( 4 < argc )
  {
    for ( i = 0; i < m; i++ )
    {    
      for ( j = 0; j < m; j++ )
      {
        a[i+j*m] = atof ( argv[k] );
        k = k + 1;
      }
    }
  }
  else
  {
    cout << "\n";
    cout << "  Enter A:\n";
    for ( i = 0; i < m; i++ )
    {
      for ( j = 0; j < m; j++ )
      {
        cin >> a[i+j*m];
      }
    }
  }

  r8mat_print ( m, m, a, "  The variance-covariance matrix A:" );
//
//  Compute the data.
//
  x = multinormal_sample ( m, n, a, mu );
//
//  Write it to a file.
//
  m_ostring << m;
  n_ostring << n;

  output_filename = "normal_" + m_ostring.str ( ) + "_" 
    + n_ostring.str ( ) + ".txt";

  r8mat_write ( output_filename, m, n, x );

  cout << "\n";
  cout << "  The data was written to the file \"" 
    << output_filename << "\".\n";
//
//  Terminate.
//
  delete [] a;
  delete [] mu;
  delete [] x;

  cout << "\n";
  cout << "normal_dataset():\n";
  cout << "  Normal end of execution.\n";
  cout << "\n";
  timestamp ( );

  return 0;
}
//****************************************************************************80

double *multinormal_sample ( int m, int n, double a[], double mu[] )

//****************************************************************************80
//
//  Purpose:
//
//    multinormal_sample() samples a multivariate normal distribution.
//
//  Discussion:
//
//    The multivariate normal distribution for the M dimensional vector X
//    has the form:
//
//      pdf(X) = (2*pi*det(A))**(-M/2) * exp(-0.5*(X-MU)'*inverse(A)*(X-MU))
//
//    where MU is the mean vector, and A is a positive definite symmetric
//    matrix called the variance-covariance matrix.
//
//  Licensing:
//
//    This information is distributed under the MIT license. 
//
//  Modified:
//
//    15 May 2024
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    int M, the dimension of the space.
//
//    int N, the number of points.
//
//    double A[M*M], the variance-covariance 
//    matrix.  A must be symmetric positive definite.
//
//    double MU[M], the mean vector.
//
//  Output:
//
//    double MULTINORMAL_SAMPLE[M*N], the points.
//
{
  int i;
  int j;
  int k;
  double *r;
  double *x;
  double *y;
//
//  Compute the upper triangular Cholesky factor R of the variance-covariance
//  matrix.
//
  r = r8po_fa ( m, a );

  if ( !r )
  {
    cout << "\n";
    cout << "multinormal_sample(): Fatal error!\n";
    cout << "  The variance-covariance matrix is not positive definite symmetric.\n";
    exit ( 1 );
  }
//
//  Y = MxN matrix of samples of the 1D normal distribution with mean 0
//  and variance 1.  
//
  y = r8vec_normal_01_new ( m*n );
//
//  Compute X = MU + R' * Y.
//
  x = new double[m*n];

  for ( j = 0; j < n; j++ )
  {
    for ( i = 0; i < m; i++ )
    {
      x[i+j*m] = mu[i];
      for ( k = 0; k < m; k++ )
      {
        x[i+j*m] = x[i+j*m] + r[k+i*m] * y[k+j*m];
      }
    }
  }        

  delete [] r;
  delete [] y;

  return x;
}
//****************************************************************************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 information is distributed under the MIT license. 
//
//  Modified:
//
//    15 May 2024
//
//  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.
//
//    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 information is distributed under the MIT license. 
//
//  Modified:
//
//    15 May 2024
//
//  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.
//
//    string TITLE, a title.
//
{
# define INCX 5

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

  cout << "\n";
  cout << title << "\n";
//
//  Print the columns of the matrix, in strips of 5.
//
  for ( j2lo = jlo; j2lo <= jhi; j2lo = j2lo + INCX )
  {
    j2hi = j2lo + INCX - 1;
    j2hi = min ( j2hi, n );
    j2hi = min ( 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 << "       ";
    }
    cout << "\n";
    cout << "  Row\n";
    cout << "\n";
//
//  Determine the range of the rows in this strip.
//
    i2lo = max ( ilo, 1 );
    i2hi = min ( ihi, 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 << "  ";
      for ( j = j2lo; j <= j2hi; j++ )
      {
        cout << setw(12) << a[i-1+(j-1)*m] << "  ";
      }
      cout << "\n";
    }
  }

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

void r8mat_write ( string output_filename, int m, int n, double table[] )

//****************************************************************************80
//
//  Purpose:
//
//    r8mat_write() writes an R8MAT file with no header.
//
//  Licensing:
//
//    This information is distributed under the MIT license. 
//
//  Modified:
//
//    15 May 2024
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    string OUTPUT_FILENAME, the output filename.
//
//    int M, the spatial dimension.
//
//    int N, the number of points.
//
//    double TABLE[M*N], the table data.
//
{
  int i;
  int j;
  ofstream output;
//
//  Open the file.
//
  output.open ( output_filename.c_str ( ) );

  if ( !output )
  {
    cerr << "\n";
    cerr << "r8mat_write(): Fatal error!\n";
    cerr << "  Could not open the output file.\n";
    return;
  }
//
//  Write the data.
//
  for ( j = 0; j < n; j++ )
  {
    for ( i = 0; i < m; i++ )
    {
      output << "  " << setw(24) << setprecision(16) << table[i+j*m];
    }
    output << "\n";
  }
//
//  Close the file.
//
  output.close ( );

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

double *r8po_fa ( int n, double a[] )

//****************************************************************************80
//
//  Purpose:
//
//    r8po_fa() factors a R8PO matrix.
//
//  Discussion:
//
//    The R8PO storage format is appropriate for a symmetric positive definite 
//    matrix and its inverse.  (The Cholesky factor of a R8PO matrix is an
//    upper triangular matrix, so it will be in R8GE storage format.)
//
//    Only the diagonal and upper triangle of the square array are used.
//    This same storage format is used when the matrix is factored by
//    R8PO_FA, or inverted by R8PO_INVERSE.  For clarity, the lower triangle
//    is set to zero.
//
//    The positive definite symmetric matrix A has a Cholesky factorization
//    of the form:
//
//      A = R' * R
//
//    where R is an upper triangular matrix with positive elements on
//    its diagonal.  
//
//  Licensing:
//
//    This information is distributed under the MIT license. 
//
//  Modified:
//
//    15 May 2024
//
//  Author:
//
//    Original FORTRAN77 version by Dongarra, Bunch, Moler, Stewart.
//    This version by John Burkardt.
//
//  Reference:
//
//    Jack Dongarra, Jim Bunch, Cleve Moler, Pete Stewart,
//    LINPACK User's Guide,
//    SIAM, 1979,
//    ISBN13: 978-0-898711-72-1,
//    LC: QA214.L56.
//
//  Input:
//
//    int N, the order of the matrix.
//
//    double A[N*N], the matrix in R8PO storage.
//
//  Output:
//
//    double R8PO_FA[N*N], the Cholesky factor in SGE
//    storage, or NULL if there was an error.
//
{
  double *b;
  int i;
  int j;
  int k;
  double s;

  b = new double[n*n];

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

  for ( j = 0; j < n; j++ )
  {
    for ( k = 0; k <= j-1; k++ )
    {
      for ( i = 0; i <= k-1; i++ )
      {
        b[k+j*n] = b[k+j*n] - b[i+k*n] * b[i+j*n];
      }
      b[k+j*n] = b[k+j*n] / b[k+k*n];
    }

    s = b[j+j*n];
    for ( i = 0; i <= j-1; i++ )
    {
      s = s - b[i+j*n] * b[i+j*n];
    }

    if ( s <= 0.0 )
    {
      delete [] b;
      return NULL;
    }

    b[j+j*n] = sqrt ( s );
  }
//
//  Since the Cholesky factor is in R8GE format, zero out the lower triangle.
//
  for ( i = 0; i < n; i++ )
  {
    for ( j = 0; j < i; j++ )
    {
      b[i+j*n] = 0.0;
    }
  }

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

double *r8vec_normal_01_new ( int n )

//****************************************************************************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.
//
//    This routine can generate a vector of values on one call.
//
//  Licensing:
//
//    This information is distributed under the MIT license. 
//
//  Modified:
//
//    09 December 2024
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    int N, the number of values desired.
//
//  Output:
//
//    double R8VEC_NORMAL_01_NEW[N], a sample of the standard normal PDF.
//
{
  int i;
  double r1;
  double r2;
  static double r8_pi = 3.141592653589793;
  double *x;

  x = new double[n];

  for ( i = 0; i < n; i++ )
  {
    r1 = drand48 ( );
    r2 = drand48 ( );
    x[i] = sqrt ( - 2.0 * log ( r1 ) ) * cos ( 2.0 * r8_pi * r2 );
  }

  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 information is distributed under the MIT license. 
//
//  Modified:
//
//    15 May 2024
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    int N, the number of components of the vector.
//
//    double A[N], the vector to be printed.
//
//    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

void timestamp ( )

//****************************************************************************80
//
//  Purpose:
//
//    timestamp() prints the current YMDHMS date as a time stamp.
//
//  Example:
//
//    31 May 2001 09:45:54 AM
//
//  Licensing:
//
//    This information is distributed under the MIT license. 
//
//  Modified:
//
//    15 May 2024
//
//  Author:
//
//    John Burkardt
//
{
# 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
}