linpack_bench.cpp

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

using namespace std;

int main ( void );
double cpu_time ( void );
double r8_abs ( double x );
double r8_epsilon ( void );
double *r8_matgen ( int lda, int n );
double r8_max ( double x, double y );
double r8_random ( int iseed[4] );
void daxpy ( int n, double da, double dx[], int incx, double dy[], int incy );
double ddot ( int n, double dx[], int incx, double dy[], int incy );
int dgefa ( double a[], int lda, int n, int ipvt[] );
void dgesl ( double a[], int lda, int n, int ipvt[], double b[], int job );
void dscal ( int n, double sa, double x[], int incx );
int idamax ( int n, double dx[], int incx );
void timestamp ( void );

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

int main ( void )

//****************************************************************************80
//
//  Purpose:
//
//    LINPACK_BENCH drives the double precision LINPACK benchmark program.
//
{
# define N 1000
# define LDA ( N + 1 )

  double *a;
  double a_max;
  double *b;
  double b_max;
  double cray = 0.056;
  double eps;
  int i;
  int info;
  int *ipvt;
  int j;
  int job;
  double ops;
  double *resid;
  double resid_max;
  double residn;
  double *rhs;
  double t1;
  double t2;
  double time[6];
  double total;
  double *x;
//
//  This program was updated on 10/12/92 to correct a
//  problem with the random number generator. The previous
//  random number generator had a short period and produced
//  singular matrices occasionally.
//
  timestamp ( );
  cout << "\n";
  cout << "LINPACK_BENCH\n";
  cout << "  The LINPACK benchmark.\n";
  cout << "  Language: C++\n";
  cout << "  Datatype: Double\n";

  ops = ( double ) ( 2 * N * N * N ) / 3.0 + 2.0 * ( double ) ( N * N );

  a = r8_matgen ( LDA, N );
  b = new double[N];
  ipvt = new int[N];
  resid = new double[N];
  rhs = new double[N];
  x = new double[N];

  a_max = 0.0;
  for ( j = 1; j <= N; j++ )
  {
    for ( i = 1; i <= N; i++ )
    {
      a_max = r8_max ( a_max, a[i-1+(j-1)*LDA] );
    }
  }

  for ( i = 1; i <= N; i++ )
  {
    x[i-1] = 1.0;
  }

  for ( i = 1; i <= N; i++ )
  {
    b[i-1] = 0.0;
    for ( j = 1; j <= N; j++ )
    {
      b[i-1] = b[i-1] + a[i-1+(j-1)*LDA] * x[j-1];
    }
  }
//
//  DEBUG:
//
  b_max = 0.0;
  for ( i = 1; i <= N; i++ )
  {
    b_max = r8_max ( b_max, r8_abs ( b[i-1] ) );
  }
  t1 = cpu_time ( );

  info = dgefa ( a, LDA, N, ipvt );

  if ( info != 0 )
  {
    cout << "\n";
    cout << "LINPACK_BENCH - Fatal error!\n";
    cout << "  The matrix A is apparently singular.\n";
    cout << "  Abnormal end of execution.\n";
    return 1;
  }

  t2 = cpu_time ( );
  time[0] = t2 - t1;

  t1 = cpu_time ( );

  job = 0;
  dgesl ( a, LDA, N, ipvt, b, job );

  t2 = cpu_time ( );
  time[1] = t2 - t1;

  total = time[0] + time[1];

  delete [] a;
//
//  Compute a residual to verify results.
//
  a = r8_matgen ( LDA, N );

  for ( i = 1; i <= N; i++ )
  {
    x[i-1] = 1.0;
  }

  for ( i = 1; i <= N; i++ )
  {
    rhs[i-1] = 0.0;
    for ( j = 1; j <= N; j++ )
    {
      rhs[i-1] = rhs[i-1] + a[i-1+(j-1)*LDA] * x[j-1];
    }
  }

  for ( i = 1; i <= N; i++ )
  {
    resid[i-1] = -rhs[i-1];
    for ( j = 1; j <= N; j++ )
    {
      resid[i-1] = resid[i-1] + a[i-1+(j-1)*LDA] * b[j-1];
    }
  }

  resid_max = 0.0;
  for ( i = 1; i <= N; i++ )
  {
    resid_max = r8_max ( resid_max, r8_abs ( resid[i-1] ) );
  }

  b_max = 0.0;
  for ( i = 1; i <= N; i++ )
  {
    b_max = r8_max ( b_max, r8_abs ( b[i-1] ) );
  }

  eps = r8_epsilon ( );

  residn = resid_max /  ( ( double ) N * a_max * b_max * eps );

  time[2] = total;
  if ( 0.0 < total )
  {
    time[3] = ops / ( 1.0E+06 * total );
  }
  else
  {
    time[3] = -1.0;
  }
  time[4] = 2.0 / time[3];
  time[5] = total / cray;

  cout << "\n";
  cout << "     Norm. Resid      Resid           MACHEP         X[1]          X[N]\n";
  cout << "\n";
  cout << setw(14) << residn << "  "
       << setw(14) << resid_max << "  "
       << setw(14) << eps       << "  "
       << setw(14) << b[0] << "  "
       << setw(14) << b[N-1] << "\n";
  cout << "\n";
  cout << "  Times are reported for matrices of order N = " << N << "\n";
  cout << "  with leading array dimension of LDA = " << LDA << "\n";
  cout << "\n";
  cout << "      Factor     Solve      Total     MFLOPS       Unit      Ratio\n";
  cout << "\n";
  cout << setw(9) << time[0] << "  "
       << setw(9) << time[1] << "  "
       << setw(9) << time[2] << "  "
       << setw(9) << time[3] << "  "
       << setw(9) << time[4] << "  "
       << setw(9) << time[5] << "\n";
  cout << "\n";
  cout << "  End of tests -- This version dated 10/12/92.\n";

  delete [] a;
  delete [] b;
  delete [] ipvt;
  delete [] resid;
  delete [] rhs;
  delete [] x;

  cout << "\n";
  cout << "LINPACK_BENCH\n";
  cout << "  Normal end of execution.\n";

  cout << "\n";
  timestamp ( );

  return 0;
# undef LDA
# undef N
}
//****************************************************************************80

double cpu_time ( void )

//****************************************************************************80
//
//  Purpose:
//
//    CPU_TIME returns the current reading on the CPU clock.
//
//  Modified:
//
//    06 June 2005
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Output, double CPU_TIME, the current reading of the CPU clock, in seconds.
//
{
  double value;

  value = ( double ) ( clock ( ) / CLOCKS_PER_SEC );

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

double r8_abs ( double x )

//****************************************************************************80
//
//  Purpose:
//
//    R8_ABS returns the absolute value of a double precision number.
//
//  Modified:
//
//    02 April 2005
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, double X, the quantity whose absolute value is desired.
//
//    Output, double R8_ABS, the absolute value of X.
//
{
  if ( 0.0 <= x )
  {
    return x;
  } 
  else
  {
    return ( -x );
  }
}
//****************************************************************************80

double r8_epsilon ( void )

//****************************************************************************80
//
//  Purpose:
//
//    R8_EPSILON returns the round off unit for double precision arithmetic.
//
//  Discussion:
//
//    R8_EPSILON is a number R which is a power of 2 with the property that,
//    to the precision of the computer's arithmetic,
//      1 < 1 + R
//    but 
//      1 = ( 1 + R / 2 )
//
//  Modified:
//
//    01 July 2004
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Output, double R8_EPSILON, the double precision round-off unit.
//
{
  double r;

  r = 1.0E+00;

  while ( 1.0E+00 < ( double ) ( 1.0E+00 + r )  )
  {
    r = r / 2.0E+00;
  }

  return ( 2.0E+00 * r );
}
//****************************************************************************80

double *r8_matgen ( int lda, int n )

//****************************************************************************80
//
//  Purpose:
//
//    R8_MATGEN generates a random matrix.
//
//  Modified:
//
//    06 June 2005
//
//  Parameters:
//
//    Input, integer LDA, the leading dimension of the matrix.
//
//    Input, integer N, the order of the matrix.
//
//    Output, double R8_MATGEN[LDA*N], the N by N matrix.
//
{
  double *a;
  int i;
  int init[4] = { 1, 2, 3, 1325 };
  int j;

  a = new double[lda*n];

  for ( j = 1; j <= n; j++ )
  {
    for ( i = 1; i <= n; i++ )
    {
      a[i-1+(j-1)*lda] = r8_random ( init ) - 0.5;
    }
  }

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

double r8_max ( double x, double y )

//****************************************************************************80
//
//  Purpose:
//
//    R8_MAX returns the maximum of two double precision values.
//
//  Modified:
//
//    18 August 2004
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, double X, Y, the quantities to compare.
//
//    Output, double R8_MAX, the maximum of X and Y.
//
{
  if ( y < x )
  {
    return x;
  } 
  else
  {
    return y;
  }
}
//****************************************************************************80

double r8_random ( int iseed[4] )

//****************************************************************************80
//
//  Purpose:
//
//    R8_RANDOM returns a uniformly distributed random number between 0 and 1.
//
//  Discussion:
//
//    This routine uses a multiplicative congruential method with modulus
//    2**48 and multiplier 33952834046453 (see G.S.Fishman,
//    'Multiplicative congruential random number generators with modulus
//    2**b: an exhaustive analysis for b = 32 and a partial analysis for
//    b = 48', Math. Comp. 189, pp 331-344, 1990).
//
//    48-bit integers are stored in 4 integer array elements with 12 bits
//    per element. Hence the routine is portable across machines with
//    integers of 32 bits or more.
//
//  Parameters:
//
//    Input/output, integer ISEED(4).
//    On entry, the seed of the random number generator; the array
//    elements must be between 0 and 4095, and ISEED(4) must be odd.
//    On exit, the seed is updated.
//
//    Output, double R8_RANDOM, the next pseudorandom number.
//
{
  int ipw2 = 4096;
  int it1;
  int it2;
  int it3;
  int it4;
  int m1 = 494;
  int m2 = 322;
  int m3 = 2508;
  int m4 = 2549;
  double one = 1.0;
  double r = 1.0 / 4096.0;
  double value;
//
//  Multiply the seed by the multiplier modulo 2**48.
//
  it4 = iseed[3] * m4;
  it3 = it4 / ipw2;
  it4 = it4 - ipw2 * it3;
  it3 = it3 + iseed[2] * m4 + iseed[3] * m3;
  it2 = it3 / ipw2;
  it3 = it3 - ipw2 * it2;
  it2 = it2 + iseed[1] * m4 + iseed[2] * m3 + iseed[3] * m2;
  it1 = it2 / ipw2;
  it2 = it2 - ipw2 * it1;
  it1 = it1 + iseed[0] * m4 + iseed[1] * m3 + iseed[2] * m2 + iseed[3] * m1;
  it1 = ( it1 % ipw2 );
//
//  Return updated seed
//
  iseed[0] = it1;
  iseed[1] = it2;
  iseed[2] = it3;
  iseed[3] = it4;
//
//  Convert 48-bit integer to a real number in the interval (0,1)
//
  value = 
      r * ( ( double ) ( it1 ) 
    + r * ( ( double ) ( it2 ) 
    + r * ( ( double ) ( it3 ) 
    + r * ( ( double ) ( it4 ) ) ) ) );

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

void daxpy ( int n, double da, double dx[], int incx, double dy[], int incy )

//****************************************************************************80
//
//  Purpose:
//
//    DAXPY computes constant times a vector plus a vector.
//
//  Discussion:
//
//    This routine uses unrolled loops for increments equal to one.
//
//  Modified:
//
//    02 May 2005
//
//  Author:
//
//    Jack Dongarra
//
//  Reference:
//
//    Dongarra, Moler, Bunch, Stewart,
//    LINPACK User's Guide,
//    SIAM, 1979.
//
//    Lawson, Hanson, Kincaid, Krogh,
//    Basic Linear Algebra Subprograms for Fortran Usage,
//    Algorithm 539, 
//    ACM Transactions on Mathematical Software, 
//    Volume 5, Number 3, September 1979, pages 308-323.
//
//  Parameters:
//
//    Input, int N, the number of elements in DX and DY.
//
//    Input, double DA, the multiplier of DX.
//
//    Input, double DX[*], the first vector.
//
//    Input, int INCX, the increment between successive entries of DX.
//
//    Input/output, double DY[*], the second vector.
//    On output, DY[*] has been replaced by DY[*] + DA * DX[*].
//
//    Input, int INCY, the increment between successive entries of DY.
//
{
  int i;
  int ix;
  int iy;
  int m;

  if ( n <= 0 )
  {
    return;
  }

  if ( da == 0.0 )
  {
    return;
  }
//
//  Code for unequal increments or equal increments
//  not equal to 1.
//
  if ( incx != 1 || incy != 1 )
  {
    if ( 0 <= incx )
    {
      ix = 0;
    }
    else
    {
      ix = ( - n + 1 ) * incx;
    }

    if ( 0 <= incy )
    {
      iy = 0;
    }
    else
    {
      iy = ( - n + 1 ) * incy;
    }

    for ( i = 0; i < n; i++ )
    {
      dy[iy] = dy[iy] + da * dx[ix];
      ix = ix + incx;
      iy = iy + incy;
    }
  }
//
//  Code for both increments equal to 1.
//
  else
  {
    m = n % 4;

    for ( i = 0; i < m; i++ )
    {
      dy[i] = dy[i] + da * dx[i];
    }

    for ( i = m; i < n; i = i + 4 )
    {
      dy[i  ] = dy[i  ] + da * dx[i  ];
      dy[i+1] = dy[i+1] + da * dx[i+1];
      dy[i+2] = dy[i+2] + da * dx[i+2];
      dy[i+3] = dy[i+3] + da * dx[i+3];
    }

  }

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

double ddot ( int n, double dx[], int incx, double dy[], int incy )

//****************************************************************************80
//
//  Purpose:
//
//    DDOT forms the dot product of two vectors.
//
//  Discussion:
//
//    This routine uses unrolled loops for increments equal to one.
//
//  Modified:
//
//    02 May 2005
//
//  Author:
//
//    Jack Dongarra
//
//  Reference:
//
//    Dongarra, Moler, Bunch, Stewart,
//    LINPACK User's Guide,
//    SIAM, 1979.
//
//    Lawson, Hanson, Kincaid, Krogh,
//    Basic Linear Algebra Subprograms for Fortran Usage,
//    Algorithm 539, 
//    ACM Transactions on Mathematical Software, 
//    Volume 5, Number 3, September 1979, pages 308-323.
//
//  Parameters:
//
//    Input, int N, the number of entries in the vectors.
//
//    Input, double DX[*], the first vector.
//
//    Input, int INCX, the increment between successive entries in DX.
//
//    Input, double DY[*], the second vector.
//
//    Input, int INCY, the increment between successive entries in DY.
//
//    Output, double DDOT, the sum of the product of the corresponding
//    entries of DX and DY.
//
{
  double dtemp;
  int i;
  int ix;
  int iy;
  int m;

  dtemp = 0.0;

  if ( n <= 0 )
  {
    return dtemp;
  }
//
//  Code for unequal increments or equal increments
//  not equal to 1.
//
  if ( incx != 1 || incy != 1 )
  {
    if ( 0 <= incx )
    {
      ix = 0;
    }
    else
    {
      ix = ( - n + 1 ) * incx;
    }

    if ( 0 <= incy )
    {
      iy = 0;
    }
    else
    {
      iy = ( - n + 1 ) * incy;
    }

    for ( i = 0; i < n; i++ )
    {
      dtemp = dtemp + dx[ix] * dy[iy];
      ix = ix + incx;
      iy = iy + incy;
    }
  }
//
//  Code for both increments equal to 1.
//
  else
  {
    m = n % 5;

    for ( i = 0; i < m; i++ )
    {
      dtemp = dtemp + dx[i] * dy[i];
    }

    for ( i = m; i < n; i = i + 5 )
    {
      dtemp = dtemp + dx[i  ] * dy[i  ] 
                    + dx[i+1] * dy[i+1] 
                    + dx[i+2] * dy[i+2] 
                    + dx[i+3] * dy[i+3] 
                    + dx[i+4] * dy[i+4];
    }

  }

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

int dgefa ( double a[], int lda, int n, int ipvt[] )

//****************************************************************************80
//
//  Purpose:
//
//    DGEFA factors a real general matrix.
//
//  Modified:
//
//    16 May 2005
//
//  Author:
//
//    C++ translation by John Burkardt.
//
//  Reference:
//
//    Dongarra, Moler, Bunch and Stewart,
//    LINPACK User's Guide,
//    SIAM, (Society for Industrial and Applied Mathematics),
//    3600 University City Science Center,
//    Philadelphia, PA, 19104-2688.
//    ISBN 0-89871-172-X
//
//  Parameters:
//
//    Input/output, double A[LDA*N].
//    On intput, the matrix to be factored.
//    On output, an upper triangular matrix and the multipliers used to obtain
//    it.  The factorization can be written A=L*U, where L is a product of
//    permutation and unit lower triangular matrices, and U is upper triangular.
//
//    Input, int LDA, the leading dimension of A.
//
//    Input, int N, the order of the matrix A.
//
//    Output, int IPVT[N], the pivot indices.
//
//    Output, int DGEFA, singularity indicator.
//    0, normal value.
//    K, if U(K,K) == 0.  This is not an error condition for this subroutine,
//    but it does indicate that DGESL or DGEDI will divide by zero if called.
//    Use RCOND in DGECO for a reliable indication of singularity.
//
{
  int info;
  int j;
  int k;
  int l;
  double t;
//
//  Gaussian elimination with partial pivoting.
//
  info = 0;

  for ( k = 1; k <= n-1; k++ )
  {
//
//  Find L = pivot index.
//
    l = idamax ( n-k+1, a+(k-1)+(k-1)*lda, 1 ) + k - 1;
    ipvt[k-1] = l;
//
//  Zero pivot implies this column already triangularized.
//
    if ( a[l-1+(k-1)*lda] == 0.0 )
    {
      info = k;
      continue;
    }
//
//  Interchange if necessary.
//
    if ( l != k )
    {
      t = a[l-1+(k-1)*lda];
      a[l-1+(k-1)*lda] = a[k-1+(k-1)*lda];
      a[k-1+(k-1)*lda] = t;
    }
//
//  Compute multipliers.
//
    t = -1.0 / a[k-1+(k-1)*lda];

    dscal ( n-k, t, a+k+(k-1)*lda, 1 );
//
//  Row elimination with column indexing.
//
    for ( j = k+1; j <= n; j++ )
    {
      t = a[l-1+(j-1)*lda];
      if ( l != k )
      {
        a[l-1+(j-1)*lda] = a[k-1+(j-1)*lda];
        a[k-1+(j-1)*lda] = t;
      }
      daxpy ( n-k, t, a+k+(k-1)*lda, 1, a+k+(j-1)*lda, 1 );
    }

  }

  ipvt[n-1] = n;

  if ( a[n-1+(n-1)*lda] == 0.0 )
  {
    info = n;
  }

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

void dgesl ( double a[], int lda, int n, int ipvt[], double b[], int job )

//****************************************************************************80
//
//  Purpose:
//
//    DGESL solves a real general linear system A * X = B.
//
//  Discussion:
//
//    DGESL can solve either of the systems A * X = B or A' * X = B.
//
//    The system matrix must have been factored by DGECO or DGEFA.
//
//    A division by zero will occur if the input factor contains a
//    zero on the diagonal.  Technically this indicates singularity
//    but it is often caused by improper arguments or improper
//    setting of LDA.  It will not occur if the subroutines are
//    called correctly and if DGECO has set 0.0 < RCOND
//    or DGEFA has set INFO == 0.
//
//  Modified:
//
//    16 May 2005
//
//  Author:
//
//    C++ translation by John Burkardt.
//
//  Reference:
//
//    Dongarra, Moler, Bunch and Stewart,
//    LINPACK User's Guide,
//    SIAM, (Society for Industrial and Applied Mathematics),
//    3600 University City Science Center,
//    Philadelphia, PA, 19104-2688.
//    ISBN 0-89871-172-X
//
//  Parameters:
//
//    Input, double A[LDA*N], the output from DGECO or DGEFA.
//
//    Input, int LDA, the leading dimension of A.
//
//    Input, int N, the order of the matrix A.
//
//    Input, int IPVT[N], the pivot vector from DGECO or DGEFA.
//
//    Input/output, double B[N].
//    On input, the right hand side vector.
//    On output, the solution vector.
//
//    Input, int JOB.
//    0, solve A * X = B;
//    nonzero, solve A' * X = B.
//
{
  int k;
  int l;
  double t;
//
//  Solve A * X = B.
//
  if ( job == 0 )
  {
    for ( k = 1; k <= n-1; k++ )
    {
      l = ipvt[k-1];
      t = b[l-1];

      if ( l != k )
      {
        b[l-1] = b[k-1];
        b[k-1] = t;
      }

      daxpy ( n-k, t, a+k+(k-1)*lda, 1, b+k, 1 );

    }

    for ( k = n; 1 <= k; k-- )
    {
      b[k-1] = b[k-1] / a[k-1+(k-1)*lda];
      t = -b[k-1];
      daxpy ( k-1, t, a+0+(k-1)*lda, 1, b, 1 );
    }
  }
//
//  Solve A' * X = B.
//
  else
  {
    for ( k = 1; k <= n; k++ )
    {
      t = ddot ( k-1, a+0+(k-1)*lda, 1, b, 1 );
      b[k-1] = ( b[k-1] - t ) / a[k-1+(k-1)*lda];
    }

    for ( k = n-1; 1 <= k; k-- )
    {
      b[k-1] = b[k-1] + ddot ( n-k, a+k+(k-1)*lda, 1, b+k, 1 );
      l = ipvt[k-1];

      if ( l != k )
      {
        t = b[l-1];
        b[l-1] = b[k-1];
        b[k-1] = t;
      }
    }
  }
  return;
}
//****************************************************************************80

void dscal ( int n, double sa, double x[], int incx )

//****************************************************************************80
//
//  Purpose:
//
//    DSCAL scales a vector by a constant.
//
//  Modified:
//
//    02 May 2005
//
//  Author:
//
//    Jack Dongarra
//
//  Reference:
//
//    Dongarra, Moler, Bunch, Stewart,
//    LINPACK User's Guide,
//    SIAM, 1979.
//
//    Lawson, Hanson, Kincaid, Krogh,
//    Basic Linear Algebra Subprograms for Fortran Usage,
//    Algorithm 539,
//    ACM Transactions on Mathematical Software,
//    Volume 5, Number 3, September 1979, pages 308-323.
//
//  Parameters:
//
//    Input, int N, the number of entries in the vector.
//
//    Input, double SA, the multiplier.
//
//    Input/output, double X[*], the vector to be scaled.
//
//    Input, int INCX, the increment between successive entries of X.
//
{
  int i;
  int ix;
  int m;

  if ( n <= 0 )
  {
  }
  else if ( incx == 1 )
  {
    m = n % 5;

    for ( i = 0; i < m; i++ )
    {
      x[i] = sa * x[i];
    }

    for ( i = m; i < n; i = i + 5 )
    {
      x[i]   = sa * x[i];
      x[i+1] = sa * x[i+1];
      x[i+2] = sa * x[i+2];
      x[i+3] = sa * x[i+3];
      x[i+4] = sa * x[i+4];
    }
  }
  else
  {
    if ( 0 <= incx )
    {
      ix = 0;
    }
    else
    {
      ix = ( - n + 1 ) * incx;
    }

    for ( i = 0; i < n; i++ )
    {
      x[ix] = sa * x[ix];
      ix = ix + incx;
    }

  }

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

int idamax ( int n, double dx[], int incx )

//****************************************************************************80
//
//  Purpose:
//
//    IDAMAX finds the index of the vector element of maximum absolute value.
//
//  Modified:
//
//    02 May 2005
//
//  Reference:
//
//    Dongarra, Moler, Bunch, Stewart,
//    LINPACK User's Guide,
//    SIAM, 1979.
//
//    Lawson, Hanson, Kincaid, Krogh,
//    Basic Linear Algebra Subprograms for Fortran Usage,
//    Algorithm 539,
//    ACM Transactions on Mathematical Software,
//    Volume 5, Number 3, September 1979, pages 308-323.
//
//  Parameters:
//
//    Input, int N, the number of entries in the vector.
//
//    Input, double X[*], the vector to be examined.
//
//    Input, int INCX, the increment between successive entries of SX.
//
//    Output, int IDAMAX, the index of the element of maximum
//    absolute value.
//
{
  double dmax;
  int i;
  int ix;
  int value;

  value = 0;

  if ( n < 1 || incx <= 0 )
  {
    return value;
  }

  value = 1;

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

  if ( incx == 1 )
  {
    dmax = r8_abs ( dx[0] );

    for ( i = 1; i < n; i++ )
    {
      if ( dmax < r8_abs ( dx[i] ) )
      {
        value = i + 1;
        dmax = r8_abs ( dx[i] );
      }
    }
  }
  else
  {
    ix = 0;
    dmax = r8_abs ( dx[0] );
    ix = ix + incx;

    for ( i = 1; i < n; i++ )
    {
      if ( dmax < r8_abs ( dx[ix] ) )
      {
        value = i + 1;
        dmax = r8_abs ( dx[ix] );
      }
      ix = ix + incx;
    }
  }

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

void timestamp ( void )

//****************************************************************************80
//
//  Purpose:
//
//    TIMESTAMP prints the current YMDHMS date as a time stamp.
//
//  Example:
//
//    May 31 2001 09:45:54 AM
//
//  Modified:
//
//    24 September 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    None
//
{
# define TIME_SIZE 40

  static char time_buffer[TIME_SIZE];
  const struct tm *tm;
  size_t len;
  time_t now;

  now = time ( NULL );
  tm = localtime ( &now );

  len = strftime ( time_buffer, TIME_SIZE, "%d %B %Y %I:%M:%S %p", tm );

  cout << time_buffer << "\n";

  return;
# undef TIME_SIZE
}