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

# include "r8to.h"

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

int i4_log_10 ( int i )

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

    I4_LOG_10 returns the integer part of the logarithm base 10 of an I4.

  Example:

        I  I4_LOG_10
    -----  --------
        0    0
        1    0
        2    0
        9    0
       10    1
       11    1
       99    1
      100    2
      101    2
      999    2
     1000    3
     1001    3
     9999    3
    10000    4

  Discussion:

    I4_LOG_10 ( I ) + 1 is the number of decimal digits in I.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    23 October 2007

  Author:

    John Burkardt

  Parameters:

    Input, int I, the number whose logarithm base 10 is desired.

    Output, int I4_LOG_10, the integer part of the logarithm base 10 of
    the absolute value of X.
*/
{
  int i_abs;
  int ten_pow;
  int value;

  if ( i == 0 )
  {
    value = 0;
  }
  else
  {
    value = 0;
    ten_pow = 10;

    i_abs = abs ( i );

    while ( ten_pow <= i_abs )
    {
      value = value + 1;
      ten_pow = ten_pow * 10;
    }
  }
  return value;
}
/******************************************************************************/

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

int i4_power ( int i, int j )

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

    I4_POWER returns the value of I^J.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    23 October 2007

  Author:

    John Burkardt

  Parameters:

    Input, int I, J, the base and the power.  J should be nonnegative.

    Output, int I4_POWER, the value of I^J.
*/
{
  int k;
  int value;

  if ( j < 0 )
  {
    if ( i == 1 )
    {
      value = 1;
    }
    else if ( i == 0 )
    {
      fprintf ( stderr, "\n" );
      fprintf ( stderr, "I4_POWER - Fatal error!\n" );
      fprintf ( stderr, "  I^J requested, with I = 0 and J negative.\n" );
      exit ( 1 );
    }
    else
    {
      value = 0;
    }
  }
  else if ( j == 0 )
  {
    if ( i == 0 )
    {
      fprintf ( stderr, "\n" );
      fprintf ( stderr, "I4_POWER - Fatal error!\n" );
      fprintf ( stderr, "  I^J requested, with I = 0 and J = 0.\n" );
      exit ( 1 );
    }
    else
    {
      value = 1;
    }
  }
  else if ( j == 1 )
  {
    value = i;
  }
  else
  {
    value = 1;
    for ( k = 1; k <= j; k++ )
    {
      value = value * i;
    }
  }
  return value;
}
/******************************************************************************/

void r8ge_print ( int m, int n, double a[], char *title )

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

    R8GE_PRINT prints an R8GE matrix.

  Discussion:

    The R8GE storage format is used for a "general" M by N matrix.  
    A physical storage space is made for each logical entry.  The two 
    dimensional logical array is mapped to a vector, in which storage is 
    by columns.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    28 February 2012

  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 R8GE matrix.

    Input, char *TITLE, a title.
*/
{
  r8ge_print_some ( m, n, a, 1, 1, m, n, title );

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

void r8ge_print_some ( int m, int n, double a[], int ilo, int jlo, int ihi, 
  int jhi, char *title )

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

    R8GE_PRINT_SOME prints some of an R8GE matrix.

  Discussion:

    The R8GE storage format is used for a "general" M by N matrix.  
    A physical storage space is made for each logical entry.  The two 
    dimensional logical array is mapped to a vector, in which storage is 
    by columns.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    28 February 2012

  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 R8GE 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;

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

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

  Write the header.
*/
    printf ( "  Col:    " );
    for ( j = j2lo; j <= j2hi; j++ )
    {
      printf ( "%7d       ", j );
    }
    printf ( "\n" );
    printf ( "  Row\n" );
    printf ( "  ---\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.
*/
      printf ( "%5d  ", i );
      for ( j = j2lo; j <= j2hi; j++ )
      {
        printf ( "%12g  ", a[i-1+(j-1)*m] );
      }
      printf ( "\n" );
    }
  }
  return;
# undef INCX
}
/******************************************************************************/

double *r8to_dif2 ( int n )

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

    R8TO_DIF2 sets the second difference as an R8TO matrix.

  Discussion:

    The R8TO storage format is used for a Toeplitz matrix, which is constant
    along diagonals.  Thus, in an N by N Toeplitz matrix, there are at most 
    2*N-1 distinct entries.  The format stores the N elements of the first
    row, followed by the N-1 elements of the first column (skipping the
    entry in the first row).

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    25 September 2015

  Author:

    John Burkardt

  Parameters:

    Input, int N, the order of the matrix.
    N must be positive.

    Output, double R8TO_DIF2[2*N-1], the R8TO matrix.
*/
{
  double *a;
  int i;

  a = ( double * ) malloc ( ( 2 * n - 1 ) * sizeof ( double ) );

  for ( i = 0; i < 2 * n - 1; i++ )
  {
    a[i] = 0.0;
  }

  a[0] = 2.0;
  a[1] = -1.0;
  a[n] = -1.0;
  
  return a;
}
/******************************************************************************/

double *r8to_indicator ( int n )

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

    R8TO_INDICATOR sets up an R8TO indicator matrix.

  Discussion:

    The R8TO storage format is used for a Toeplitz matrix, which is constant
    along diagonals.  Thus, in an N by N Toeplitz matrix, there are at most 
    2*N-1 distinct entries.  The format stores the N elements of the first
    row, followed by the N-1 elements of the first column (skipping the
    entry in the first row).

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    18 February 2013

  Author:

    John Burkardt

  Parameters:

    Input, int N, the order of the matrix.
    N must be positive.

    Output, double R8TO_INDICATOR[2*N-1], the R8TO matrix.
*/
{
  double *a;
  int fac;
  int i;
  int j;
  int k;

  a = ( double * ) malloc ( ( 2 * n - 1 ) * sizeof ( double ) );

  fac = i4_power ( 10, i4_log_10 ( n ) + 1 );

  i = 1;
  k = 0;
  for ( j = 1; j <= n; j++ )
  {
    a[k] = ( double ) ( fac * i + j );
    k = k + 1;
  }

  j = 1;
  for ( i = 2; i <= n; i++ )
  {
    a[k] = ( double ) ( fac * i + j );
    k = k + 1;
  }
  
  return a;
}
/******************************************************************************/

double *r8to_mtv ( int n, double a[], double x[] )

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

    R8TO_MTV multiplies a vector times an R8TO matrix.

  Discussion:

    The R8TO storage format is used for a Toeplitz matrix, which is constant
    along diagonals.  Thus, in an N by N Toeplitz matrix, there are at most 
    2*N-1 distinct entries.  The format stores the N elements of the first
    row, followed by the N-1 elements of the first column (skipping the
    entry in the first row).

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    18 February 2013

  Author:

    John Burkardt

  Parameters:

    Input, int N, the order of the matrix.

    Input, double A[2*N-1], the R8TO matrix.

    Input, double X[N], the vector to be multiplied by A.

    Output, double R8TO_MTV[N], the product A' * X.
*/
{
  double *b;
  int i;
  int j;

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

  for ( i = 0; i < n; i++ )
  {
    b[i] = 0.0;
    for ( j = 0; j <= i; j++ )
    {
      b[i] = b[i] + a[i-j] * x[j];
    }
    for ( j = i+1; j < n; j++ )
    {
      b[i] = b[i] + a[n+j-i-1] * x[j];
    }
  }

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

double *r8to_mv ( int n, double a[], double x[] )

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

    R8TO_MV multiplies an R8TO matrix times a vector.

  Discussion:

    The R8TO storage format is used for a Toeplitz matrix, which is constant
    along diagonals.  Thus, in an N by N Toeplitz matrix, there are at most 
    2*N-1 distinct entries.  The format stores the N elements of the first
    row, followed by the N-1 elements of the first column (skipping the
    entry in the first row).

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    18 February 2013

  Author:

    John Burkardt

  Parameters:

    Input, int N, the order of the matrix.

    Input, double A[2*N-1], the R8TO matrix.

    Input, double X[N], the vector to be multiplied by A.

    Output, double R8TO_MV[N], the product A * x.
*/
{
  double *b;
  int i;
  int j;

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

  for ( i = 0; i < n; i++ )
  {
    b[i] = 0.0;
    for ( j = 0; j < i; j++ )
    {
      b[i] = b[i] + a[n+i-j-1] * x[j];
    }
    for ( j = i; j < n; j++ )
    {
      b[i] = b[i] + a[j-i] * x[j];
    }
  }

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

void r8to_print ( int n, double a[], char *title )

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

    R8TO_PRINT prints an R8TO matrix.

  Discussion:

    The R8TO storage format is used for a Toeplitz matrix, which is constant
    along diagonals.  Thus, in an N by N Toeplitz matrix, there are at most 
    2*N-1 distinct entries.  The format stores the N elements of the first
    row, followed by the N-1 elements of the first column (skipping the
    entry in the first row).

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    18 February 2013

  Author:

    John Burkardt

  Parameters:

    Input, int N, the order of the matrix.
    N must be positive.

    Input, double A[2*N-1], the R8TO matrix.

    Input, char *TITLE, a title.
*/
{
  r8to_print_some ( n, a, 1, 1, n, n, title );

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

void r8to_print_some ( int n, double a[], int ilo, int jlo, int ihi, 
  int jhi, char *title )

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

    R8TO_PRINT_SOME prints some of an R8TO matrix.

  Discussion:

    The R8TO storage format is used for a Toeplitz matrix, which is constant
    along diagonals.  Thus, in an N by N Toeplitz matrix, there are at most 
    2*N-1 distinct entries.  The format stores the N elements of the first
    row, followed by the N-1 elements of the first column (skipping the
    entry in the first row).

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    18 February 2013

  Author:

    John Burkardt

  Parameters:

    Input, int N, the order of the matrix.
    N must be positive.

    Input, double A[2*N-1], the R8TO 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;

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

    printf ( "  Col: " );

    for ( j = j2lo; j <= j2hi; j++ )
    {
      printf ( "%7d       ", j );
    }
    printf ( "\n" );
    printf ( "  Row\n" );
    printf ( "  ---\n" );
/*
  Determine the range of the rows in this strip.
*/
    i2lo = i4_max ( ilo, 1 );
    i2hi = i4_min ( ihi, n );

    for ( i = i2lo; i <= i2hi; i++ )
    {
/*
  Print out (up to) 5 entries in row I, that lie in the current strip.
*/
      printf ( "%4d  ", i );

      for ( j = j2lo; j <= j2hi; j++ )
      {
        if ( i <= j ) 
        {
          printf ( "%12g  ", a[j-i] );
        }
        else
        {
          printf ( "%12g  ", a[n+i-j-1] );
        }
      }
      printf ( "\n" );
    }
  }

  printf ( "\n" );

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

double *r8to_random ( int n, int *seed )

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

    R8TO_RANDOM randomizes an R8TO matrix.

  Discussion:

    The R8TO storage format is used for a Toeplitz matrix, which is constant
    along diagonals.  Thus, in an N by N Toeplitz matrix, there are at most 
    2*N-1 distinct entries.  The format stores the N elements of the first
    row, followed by the N-1 elements of the first column (skipping the
    entry in the first row).

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    18 February 2013

  Author:

    John Burkardt

  Parameters:

    Input, int N, the order of the matrix.
    N must be positive.

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

    Output, double R8TO_RANDOM[2*N-1], the R8TO matrix.
*/
{
  double *a;

  a = r8vec_uniform_01_new ( 2 * n - 1, seed );

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

double *r8to_sl ( int n, double a[], double b[] )

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

    R8TO_SL solves A*x=b, where A is an R8TO matrix.

  Discussion:

    The R8TO storage format is used for a Toeplitz matrix, which is constant
    along diagonals.  Thus, in an N by N Toeplitz matrix, there are at most 
    2*N-1 distinct entries.  The format stores the N elements of the first
    row, followed by the N-1 elements of the first column (skipping the
    entry in the first row).

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    25 September 2015

  Author:

    John Burkardt.

  Parameters:

    Input, int N, the order of the matrix.

    Input, double A[2*N-1], the R8TO matrix.

    Input, double B[N] the right hand side vector.

    Output, double R8TO_SL[N], the solution vector.  X and B may share the
    same storage.
*/
{
  double *c1;
  double *c2;
  int i;
  int nsub;
  double r1;
  double r2;
  double r3;
  double r5;
  double r6;
  double *x;

  if ( n < 1 )
  {
    return NULL;
  }

  x = ( double * ) malloc ( n * sizeof ( double ) );
/*
  Solve the system with the principal minor of order 1.
*/
  r1 = a[0];
  x[0] = b[0] / r1;

  if ( n == 1 )
  {
    return x;
  }

  c1 = ( double * ) malloc ( ( n - 1 ) * sizeof ( double ) );
  c2 = ( double * ) malloc ( ( n - 1 ) * sizeof ( double ) );
/*
  Recurrent process for solving the system with the Toeplitz matrix.
*/
  for ( nsub = 2; nsub <= n; nsub++ )
  {
/*
  Compute multiples of the first and last columns of the inverse of
  the principal minor of order NSUB.
*/
    r5 = a[n+nsub-2];
    r6 = a[nsub-1];

    if ( 2 < nsub )
    {
      c1[nsub-2] = r2;

      for ( i = 1; i <= nsub - 2; i++ )
      {
        r5 = r5 + a[n+i-1] * c1[nsub-i-1];
        r6 = r6 + a[i] * c2[i-1];
      }
    }

    r2 = - r5 / r1;
    r3 = - r6 / r1;
    r1 = r1 + r5 * r3;

    if ( 2 < nsub )
    {
      r6 = c2[0];
      c2[nsub-2] = 0.0;

      for ( i = 2; i <= nsub-1; i++ )
      {
        r5 = c2[i-1];
        c2[i-1] = c1[i-1] * r3 + r6;
        c1[i-1] = c1[i-1] + r6 * r2;
        r6 = r5;
      }
    }

    c2[0] = r3;
/*
  Compute the solution of the system with the principal minor of order NSUB.
*/
    r5 = 0.0;
    for ( i = nsub-1; 1 <= i; i-- )
    {
      r5 = r5 + a[n+nsub-i-1] * x[i-1];
    }

    r6 = ( b[nsub-1] - r5 ) / r1;

    for ( i = 0; i < nsub - 1; i++ )
    {
      x[i] = x[i] + c2[i] * r6;
    }
    x[nsub-1] = r6;
  }

  free ( c1 );
  free ( c2 );

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

double *r8to_slt ( int n, double a[], double b[] )

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

    R8TO_SLT solves A'*x=b, where A is an R8TO matrix.

  Discussion:

    The R8TO storage format is used for a Toeplitz matrix, which is constant
    along diagonals.  Thus, in an N by N Toeplitz matrix, there are at most 
    2*N-1 distinct entries.  The format stores the N elements of the first
    row, followed by the N-1 elements of the first column (skipping the
    entry in the first row).

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    25 September 2015

  Author:

    John Burkardt.

  Parameters:

    Input, int N, the order of the matrix.

    Input, double A[2*N-1], the R8TO matrix.

    Input, double B[N] the right hand side vector.

    Output, double R8TO_SLT[N], the solution vector.  X and B may share the
    same storage.
*/
{
  double *c1;
  double *c2;
  int i;
  int nsub;
  double r1;
  double r2;
  double r3;
  double r5;
  double r6;
  double *x;

  if ( n < 1 )
  {
    return NULL;
  }

  x = ( double * ) malloc ( n * sizeof ( double ) );
/*
  Solve the system with the principal minor of order 1.
*/
  r1 = a[0];
  x[0] = b[0] / r1;

  if ( n == 1 )
  {
    return x;
  }

  c1 = ( double * ) malloc ( ( n - 1 ) * sizeof ( double ) );
  c2 = ( double * ) malloc ( ( n - 1 ) * sizeof ( double ) );
/*
  Recurrent process for solving the system with the Toeplitz matrix.
*/
  for ( nsub = 2; nsub <= n; nsub++ )
  {
/*
  Compute multiples of the first and last columns of the inverse of
  the principal minor of order NSUB.
*/
    r5 = a[nsub-1];
    r6 = a[n+nsub-2];

    if ( 2 < nsub )
    {
      c1[nsub-2] = r2;

      for ( i = 1; i <= nsub-2; i++ )
      {
        r5 = r5 + a[i] * c1[nsub-i-1];
        r6 = r6 + a[n+i-1] * c2[i-1];
      }
    }

    r2 = - r5 / r1;
    r3 = - r6 / r1;
    r1 = r1 + r5 * r3;

    if ( 2 < nsub )
    {
      r6 = c2[0];
      c2[nsub-2] = 0.0;

      for ( i = 2; i <= nsub-1; i++ )
      {
        r5 = c2[i-1];
        c2[i-1] = c1[i-1] * r3 + r6;
        c1[i-1] = c1[i-1] + r6 * r2;
        r6 = r5;
      }
    }

    c2[0] = r3;
/*
  Compute the solution of the system with the principal minor of order NSUB.
*/
    r5 = 0.0;
    for ( i = nsub-1; 1 <= i; i-- )
    {
      r5 = r5 + a[nsub-i] * x[i-1];
    }

    r6 = ( b[nsub-1] - r5 ) / r1;

    for ( i = 0; i < nsub-1; i++ )
    {
      x[i] = x[i] + c2[i] * r6;
    }
    x[nsub-1] = r6;
  }

  free ( c1 );
  free ( c2 );

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

double *r8to_to_r8ge ( int n, double a[] )

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

    R8TO_TO_R8GE copies an R8TO matrix to an R8GE matrix.

  Discussion:

    The R8TO storage format is used for a Toeplitz matrix, which is constant
    along diagonals.  Thus, in an N by N Toeplitz matrix, there are at most 
    2*N-1 distinct entries.  The format stores the N elements of the first
    row, followed by the N-1 elements of the first column (skipping the
    entry in the first row).

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    18 February 2013

  Author:

    John Burkardt

  Parameters:

    Input, int N, the order of the matrix.

    Input, double A[2*N-1], the R8TO matrix.

    Output, double R8TO_TO_R8GE[N*N], the R8GE matrix.
*/
{
  double *b;
  int i;
  int j;

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

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

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

double *r8to_zeros ( int n )

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

    R8TO_ZEROS zeros an R8TO matrix.

  Discussion:

    The R8TO storage format is used for a Toeplitz matrix, which is constant
    along diagonals.  Thus, in an N by N Toeplitz matrix, there are at most 
    2*N-1 distinct entries.  The format stores the N elements of the first
    row, followed by the N-1 elements of the first column (skipping the
    entry in the first row).

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    18 February 2013

  Author:

    John Burkardt

  Parameters:

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

    Output, double R8TO_ZEROS[2*N-1], the R8TO matrix.
*/
{
  double *a;

  a = r8vec_zeros_new ( 2 * n - 1 );

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

double *r8vec_indicator1_new ( int n )

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

    R8VEC_INDICATOR1_NEW sets an R8VEC to the indicator1 vector {1,2,3...}.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    26 August 2008

  Author:

    John Burkardt

  Parameters:

    Input, int N, the number of elements of A.

    Output, double R8VEC_INDICATOR1_NEW[N], the array.
*/
{
  double *a;
  int i;

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

  for ( i = 0; i <= n-1; i++ ) 
  {
    a[i] = ( double ) ( i + 1 );
  }

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

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

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

    R8VEC_PRINT prints an R8VEC.

  Discussion:

    An R8VEC is a vector of R8's.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    08 April 2009

  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;

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

  for ( i = 0; i < n; i++ ) 
  {
    printf ( "  %8d  %14f\n", i, a[i] );
  }

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

double *r8vec_zeros_new ( int n )

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

    R8VEC_ZEROS_NEW creates and zeroes an R8VEC.

  Discussion:

    An R8VEC is a vector of R8's.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    25 March 2009

  Author:

    John Burkardt

  Parameters:

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

    Output, double R8VEC_ZEROS_NEW[N], a vector of zeroes.
*/
{
  double *a;
  int i;

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

  for ( i = 0; i < n; i++ )
  {
    a[i] = 0.0;
  }
  return a;
}