Python r8vec_uniform_ab.r8vec_uniform_ab函数代码示例

def uvwp_ethier_test ( ):

#*****************************************************************************80
#
## UVWP_ETHIER_TEST samples the solution at the initial time.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    17 January 2015
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  from r8vec_uniform_ab import r8vec_uniform_ab

  a = np.pi / 4.0
  d = np.pi / 2.0

  print ''
  print 'UVWP_ETHIER_TEST'
  print '  Estimate the range of velocity and pressure'
  print '  at the initial time T = 0, using a region that is'
  print '  the cube centered at (0,0,0) with "radius" 1.0,'
  print '  Parameter A = %g' % ( a )
  print '  Parameter D = %g' % ( d )

  n = 1000
  x_lo = -1.0
  x_hi = +1.0
  seed = 123456789
  x, seed = r8vec_uniform_ab ( n, x_lo, x_hi, seed )
  y, seed = r8vec_uniform_ab ( n, x_lo, x_hi, seed )
  z, seed = r8vec_uniform_ab ( n, x_lo, x_hi, seed )
  t = 0.0

  u, v, w, p = uvwp_ethier ( a, d, n, x, y, z, t )

  print ''
  print '           Minimum       Maximum'
  print ''
  print '  U:  %14.6g  %14.6g' % ( np.min ( u ), np.max ( u ) )
  print '  V:  %14.6g  %14.6g' % ( np.min ( v ), np.max ( v ) )
  print '  W:  %14.6g  %14.6g' % ( np.min ( w ), np.max ( w ) )
  print '  P:  %14.6g  %14.6g' % ( np.min ( p ), np.max ( p ) )

  print ''
  print 'UVWP_ETHIER_TEST:'
  print '  Normal end of execution.'

  return

def resid_ethier_test ( ):

#*****************************************************************************80
#
## RESID_ETHIER_TEST samples the residual at the initial time.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    17 January 2015
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  from r8vec_uniform_ab import r8vec_uniform_ab

  a = np.pi / 4.0;
  d = np.pi / 2.0;

  print ''
  print 'RESID_ETHIER_TEST'
  print '  Sample the Navier-Stokes residuals'
  print '  at the initial time T = 0, using a region that is'
  print '  the cube centered at (0,0,0) with "radius" 1.0,'
  print '  Parameter A = %g' % ( a )
  print '  Parameter D = %g' % ( d )

  n = 1000
  x_lo = -1.0
  x_hi = +1.0
  seed = 123456789
  x, seed = r8vec_uniform_ab ( n, x_lo, x_hi, seed )
  y, seed = r8vec_uniform_ab ( n, x_lo, x_hi, seed )
  z, seed = r8vec_uniform_ab ( n, x_lo, x_hi, seed )
  t = 0.0

  ur, vr, wr, pr = resid_ethier ( a, d, n, x, y, z, t )

  print ''
  print '           Minimum       Maximum'
  print ''
  print '  Ur:  %14.6g  %14.6g' % ( np.min ( np.abs ( ur ) ), np.max ( np.abs ( ur ) ) )
  print '  Vr:  %14.6g  %14.6g' % ( np.min ( np.abs ( vr ) ), np.max ( np.abs ( vr ) ) )
  print '  Wr:  %14.6g  %14.6g' % ( np.min ( np.abs ( wr ) ), np.max ( np.abs ( wr ) ) )
  print '  Pr:  %14.6g  %14.6g' % ( np.min ( np.abs ( pr ) ), np.max ( np.abs ( pr ) ) )

  print ''
  print 'RESID_ETHIER_TEST:'
  print '  Normal end of execution.'

  return

def rhs_taylor_test ( ):

#*****************************************************************************80
#
## RHS_TAYLOR_TEST samples the right hand sides at the initial time.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    30 January 2015
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  from r8vec_uniform_ab import r8vec_uniform_ab

  nu = 1.0
  rho = 1.0

  print ''
  print 'RHS_TAYLOR_TEST'
  print '  Taylor Vortex Flow:'
  print '  Sample the Navier-Stokes right hand sides'
  print '  at the initial time T = 0, using a region that is'
  print '  the square centered at (1.5,1.5) with "radius" 1.0,'
  print '  Kinematic viscosity NU = %g' % ( nu )
  print '  Fluid density RHO = %g' % ( rho )

  n = 1000
  x_lo = 0.5
  x_hi = +2.5
  seed = 123456789
  x, seed = r8vec_uniform_ab ( n, x_lo, x_hi, seed )
  y, seed = r8vec_uniform_ab ( n, x_lo, x_hi, seed )
  t = 0.0

  f, g, h = rhs_taylor ( nu, rho, n, x, y, t )

  print ''
  print '           Minimum       Maximum'
  print ''
  print '  Ur:  %14.6g  %14.6g' % ( np.min ( f ), np.max ( f ) )
  print '  Vr:  %14.6g  %14.6g' % ( np.min ( g ), np.max ( g ) )
  print '  Pr:  %14.6g  %14.6g' % ( np.min ( h ), np.max ( h ) )

  print ''
  print 'RHS_TAYLOR_TEST:'
  print '  Normal end of execution.'

  return

def uvp_spiral_test ( ):

#*****************************************************************************80
#
## UVP_SPIRAL_TEST samples the Spiral Flow solution at the initial time.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    29 January 2015
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  from r8vec_uniform_ab import r8vec_uniform_ab

  nu = 1.0
  rho = 1.0

  print ''
  print 'UVP_SPIRAL_TEST'
  print '  Spiral Flow:'
  print '  Estimate the range of velocity and pressure'
  print '  at the initial time T = 0, over the unit square.'
  print '  Kinematic viscosity NU = %g' % ( nu )
  print '  Fluid density RHO = %g' % ( rho )

  n = 1000
  x_lo = 0.0
  x_hi = +1.0
  seed = 123456789
  x, seed = r8vec_uniform_ab ( n, x_lo, x_hi, seed )
  y, seed = r8vec_uniform_ab ( n, x_lo, x_hi, seed )
  t = 0.0

  u, v, p = uvp_spiral ( nu, rho, n, x, y, t )

  print ''
  print '           Minimum       Maximum'
  print ''
  print '  U:  %14.6g  %14.6g' % ( np.min ( u ), np.max ( u ) )
  print '  V:  %14.6g  %14.6g' % ( np.min ( v ), np.max ( v ) )
  print '  P:  %14.6g  %14.6g' % ( np.min ( p ), np.max ( p ) )

  print ''
  print 'UVP_SPIRAL_TEST:'
  print '  Normal end of execution.'

  return

def uvp_taylor_test ( ):

#*****************************************************************************80
#
## UVP_TAYLOR_TEST samples the solution at the initial time.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    22 January 2015
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  from r8vec_uniform_ab import r8vec_uniform_ab

  nu = 1.0
  rho = 1.0

  print ''
  print 'UVP_TAYLOR_TEST'
  print '  Estimate the range of velocity and pressure'
  print '  at the initial time T = 0, using a region that is'
  print '  the square centered at (1.5,1.5) with "radius" 1.0,'
  print '  Kinematic viscosity NU = %g' % ( nu )
  print '  Fluid density RHO = %g' % ( rho )

  n = 1000
  x_lo = 0.5
  x_hi = +2.5
  seed = 123456789
  x, seed = r8vec_uniform_ab ( n, x_lo, x_hi, seed )
  y, seed = r8vec_uniform_ab ( n, x_lo, x_hi, seed )
  t = 0.0

  u, v, p = uvp_taylor ( nu, rho, n, x, y, t )

  print ''
  print '           Minimum       Maximum'
  print ''
  print '  U:  %14.6g  %14.6g' % ( np.min ( u ), np.max ( u ) )
  print '  V:  %14.6g  %14.6g' % ( np.min ( v ), np.max ( v ) )
  print '  P:  %14.6g  %14.6g' % ( np.min ( p ), np.max ( p ) )

  print ''
  print 'UVP_TAYLOR_TEST:'
  print '  Normal end of execution.'

  return

def resid_spiral_test ( ):

#*****************************************************************************80
#
## RESID_SPIRAL_TEST samples the residuals at the initial time.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    30 January 2015
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  from r8vec_uniform_ab import r8vec_uniform_ab

  nu = 1.0
  rho = 1.0

  print ''
  print 'RESID_SPIRAL_TEST'
  print '  Spiral Flow:'
  print '  Sample the Navier-Stokes residuals'
  print '  at the initial time T = 0, over the unit square.'
  print '  Kinematic viscosity NU = %g' % ( nu )
  print '  Fluid density RHO = %g' % ( rho )

  n = 1000
  x_lo = 0.0
  x_hi = 1.0
  seed = 123456789
  x, seed = r8vec_uniform_ab ( n, x_lo, x_hi, seed )
  y, seed = r8vec_uniform_ab ( n, x_lo, x_hi, seed )
  t = 0.0

  ur, vr, pr = resid_spiral ( nu, rho, n, x, y, t )

  print ''
  print '           Minimum       Maximum'
  print ''
  print '  Ur:  %14.6g  %14.6g' % ( np.min ( np.abs ( ur ) ), np.max ( np.abs ( ur ) ) )
  print '  Vr:  %14.6g  %14.6g' % ( np.min ( np.abs ( vr ) ), np.max ( np.abs ( vr ) ) )
  print '  Pr:  %14.6g  %14.6g' % ( np.min ( np.abs ( pr ) ), np.max ( np.abs ( pr ) ) )

  print ''
  print 'RESID_SPIRAL_TEST:'
  print '  Normal end of execution.'

  return

def rhs_lucas_test ( ):

#*****************************************************************************80
#
## RHS_LUCAS_TEST samples the right hand sides at the initial time.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    07 March 2015
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  from r8vec_uniform_ab import r8vec_uniform_ab

  nu = 1.0
  rho = 1.0

  print ''
  print 'RHS_LUCAS_TEST'
  print '  Lucas Bystricky Flow'
  print '  Sample the Navier-Stokes right hand sides'
  print '  at the initial time T = 0, over the unit square.'
  print '  Kinematic viscosity NU = %g' % ( nu )
  print '  Fluid density RHO = %g' % ( rho )

  n = 1000
  r8_lo = 0.0
  r8_hi = 1.0
  seed = 123456789
  x, seed = r8vec_uniform_ab ( n, r8_lo, r8_hi, seed )
  y, seed = r8vec_uniform_ab ( n, r8_lo, r8_hi, seed )
  t = 0.0

  f, g, h = rhs_lucas ( nu, rho, n, x, y, t )

  print ''
  print '           Minimum       Maximum'
  print ''
  print '  Ur:  %14.6g  %14.6g' % ( np.min ( f ), np.max ( f ) )
  print '  Vr:  %14.6g  %14.6g' % ( np.min ( g ), np.max ( g ) )
  print '  Pr:  %14.6g  %14.6g' % ( np.min ( h ), np.max ( h ) )

  print ''
  print 'RHS_LUCAS_TEST:'
  print '  Normal end of execution.'

  return

def ortega_determinant_test ( ):

#*****************************************************************************80
#
## ORTEGA_DETERMINANT_TEST tests ORTEGA_DETERMINANT.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    20 February 2015
#
#  Author:
#
#    John Burkardt
#
  from ortega import ortega
  from r8mat_print import r8mat_print
  from r8vec_uniform_ab import r8vec_uniform_ab
 
  print ''
  print 'ORTEGA_DETERMINANT_TEST'
  print '  ORTEGA_DETERMINANT computes the determinant of the ORTEGA matrix.'
  print ''

  m = 5
  n = m
  r8_lo = -5.0
  r8_hi = +5.0
  seed = 123456789
  v1, seed = r8vec_uniform_ab ( n, r8_lo, r8_hi, seed )
  v2, seed = r8vec_uniform_ab ( n, r8_lo, r8_hi, seed )
  v3, seed = r8vec_uniform_ab ( n, r8_lo, r8_hi, seed )

  a = ortega ( n, v1, v2, v3 )

  r8mat_print ( m, n, a, '  ORTEGA matrix:' )

  value = ortega_determinant ( n )

  print ''
  print '  Value =  %g' % ( value )

  print ''
  print 'ORTEGA_DETERMINANT_TEST'
  print '  Normal end of execution.'

  return

def uv_spiral_test ( ):

#*****************************************************************************80
#
## UV_SPIRAL_TEST generates a field and estimates its range.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    20 January 2015
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  from r8vec_uniform_ab import r8vec_uniform_ab

  nu = 1.0
  rho = 1.0

  print ''
  print 'UV_SPIRAL_TEST'
  print '  Sample a spiral velocity field and estimate'
  print '  the range of the solution values.'

  n = 1000
  x_lo = 0.0
  x_hi = +1.0
  seed = 123456789
  x, seed = r8vec_uniform_ab ( n, x_lo, x_hi, seed )
  y, seed = r8vec_uniform_ab ( n, x_lo, x_hi, seed )

  c = 1.0
  u, v = uv_spiral ( n, x, y, c )

  print ''
  print '           Minimum       Maximum'
  print ''
  print '  U:  %14.6g  %14.6g' % ( np.min ( u ), np.max ( u ) )
  print '  V:  %14.6g  %14.6g' % ( np.min ( v ), np.max ( v ) )

  print ''
  print 'UV_SPIRAL_TEST:'
  print '  Normal end of execution.'

  return

def rhs_stokes2_test ( ):

#*****************************************************************************80
#
## RHS_STOKES2_TEST samples the right hand sides.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    25 January 2015
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  from r8vec_uniform_ab import r8vec_uniform_ab

  print ''
  print 'RHS_STOKES2_TEST'
  print '  Exact Stokes solution #2.'
  print '  Estimate the range of the right hand side functions'
  print '  using a region that is the unit square.'

  n = 1000
  x_lo = 0.0
  x_hi = +1.0
  seed = 123456789
  x, seed = r8vec_uniform_ab ( n, x_lo, x_hi, seed )
  y, seed = r8vec_uniform_ab ( n, x_lo, x_hi, seed )

  f, g, h = rhs_stokes2 ( n, x, y )

  print ''
  print '           Minimum       Maximum'
  print ''
  print '  U:  %14.6g  %14.6g' % ( np.min ( f ), np.max ( f ) )
  print '  V:  %14.6g  %14.6g' % ( np.min ( g ), np.max ( g ) )
  print '  P:  %14.6g  %14.6g' % ( np.min ( h ), np.max ( h ) )

  print ''
  print 'RHS_STOKES2_TEST:'
  print '  Normal end of execution.'

  return

def uvp_stokes1_test ( ):

#*****************************************************************************80
#
## UVP_STOKES1_TEST samples the solution.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    25 January 2015
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  from r8vec_uniform_ab import r8vec_uniform_ab

  print ''
  print 'UVP_STOKES1_TEST'
  print '  Exact Stokes solution #1.'
  print '  Estimate the range of velocity and pressure'
  print '  using a region that is the unit square.'

  n = 1000
  x_lo = 0.0
  x_hi = +1.0
  seed = 123456789
  x, seed = r8vec_uniform_ab ( n, x_lo, x_hi, seed )
  y, seed = r8vec_uniform_ab ( n, x_lo, x_hi, seed )

  u, v, p = uvp_stokes1 ( n, x, y )

  print ''
  print '           Minimum       Maximum'
  print ''
  print '  U:  %14.6g  %14.6g' % ( np.min ( u ), np.max ( u ) )
  print '  V:  %14.6g  %14.6g' % ( np.min ( v ), np.max ( v ) )
  print '  P:  %14.6g  %14.6g' % ( np.min ( p ), np.max ( p ) )

  print ''
  print 'UVP_STOKES1_TEST:'
  print '  Normal end of execution.'

  return

def triv_determinant_test ( ):

#*****************************************************************************80
#
## TRIV_DETERMINANT_TEST tests TRIV_DETERMINANT.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    26 February 2015
#
#  Author:
#
#    John Burkardt
#
  from triv import triv
  from r8vec_uniform_ab import r8vec_uniform_ab
  from r8mat_print import r8mat_print

  print ''
  print 'TRIV_DETERMINANT_TEST'
  print '  TRIV_DETERMINANT computes the TRIV determinant.'

  m = 5
  n = m
  r8_lo = -5.0
  r8_hi = +5.0
  seed = 123456789
  x, seed = r8vec_uniform_ab ( n - 1, r8_lo, r8_hi, seed )
  y, seed = r8vec_uniform_ab ( n, r8_lo, r8_hi, seed )
  z, seed = r8vec_uniform_ab ( n - 1, r8_lo, r8_hi, seed )
  a = triv ( n, x, y, z )

  r8mat_print ( m, n, a, '  TRIV matrix:' )

  value = triv_determinant ( n, x, y, z )

  print ''
  print '  Value =  %g' % ( value )

  print ''
  print 'TRIV_DETERMINANT_TEST'
  print '  Normal end of execution.'

  return

def resid_stokes3_test ( ):

#*****************************************************************************80
#
## RESID_STOKES3_TEST samples the residuals.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    12 February 2015
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  from r8vec_uniform_ab import r8vec_uniform_ab

  print ''
  print 'RESID_STOKES3_TEST'
  print '  Exact Stokes solution #3.'
  print '  Sample the Stokes residuals.'

  n = 1000
  x_lo = -1.0
  x_hi = +1.0
  seed = 123456789
  x, seed = r8vec_uniform_ab ( n, x_lo, x_hi, seed )
  y, seed = r8vec_uniform_ab ( n, x_lo, x_hi, seed )

  ur, vr, pr = resid_stokes3 ( n, x, y )

  print ''
  print '           Minimum       Maximum'
  print ''
  print '  Ur:  %14.6g  %14.6g' % ( np.min ( np.abs ( ur ) ), np.max ( np.abs ( ur ) ) )
  print '  Vr:  %14.6g  %14.6g' % ( np.min ( np.abs ( vr ) ), np.max ( np.abs ( vr ) ) )
  print '  Pr:  %14.6g  %14.6g' % ( np.min ( np.abs ( pr ) ), np.max ( np.abs ( pr ) ) )

  print ''
  print 'RESID_STOKES3_TEST:'
  print '  Normal end of execution.'

  return

def schur_block_test ( ):

#*****************************************************************************80
#
## SCHUR_BLOCK_TEST tests SCHUR_BLOCK.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    28 March 2015
#
#  Author:
#
#    John Burkardt
#
  from r8mat_print import r8mat_print
  from r8vec_uniform_ab import r8vec_uniform_ab

  print ''
  print 'SCHUR_BLOCK_TEST'
  print '  SCHUR_BLOCK computes the SCHUR_BLOCK matrix.'

  m = 5
  n = m
  r8_lo = -5.0
  r8_hi = +5.0
  seed = 123456789
  x_n = ( ( n + 1 ) // 2 )
  x, seed = r8vec_uniform_ab ( x_n, r8_lo, r8_hi, seed )
  y_n = ( n // 2 )
  y, seed = r8vec_uniform_ab ( y_n, r8_lo, r8_hi, seed )
  a = schur_block ( n, x, y )

  r8mat_print ( n, n, a, '  SCHUR_BLOCK matrix:' )

  print ''
  print 'SCHUR_BLOCK_TEST'
  print '  Normal end of execution.'

  return

def clement2_determinant_test ( ):

#*****************************************************************************80
#
## CLEMENT2_DETERMINANT_TEST tests CLEMENT2_DETERMINANT.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    27 December 2014
#
#  Author:
#
#    John Burkardt
#
  from clement2 import clement2
  from r8mat_print import r8mat_print
  from r8vec_uniform_ab import r8vec_uniform_ab

  print ''
  print 'CLEMENT2_DETERMINANT_TEST'
  print '  CLEMENT2_DETERMINANT computes the CLEMENT2 determinant.'

  m = 4
  n = m
  seed = 123456789
  x, seed = r8vec_uniform_ab ( n-1, -5.0, +5.0, seed )
  y, seed = r8vec_uniform_ab ( n-1, -5.0, +5.0, seed )

  a = clement2 ( n, x, y )
  r8mat_print ( m, n, a, '  CLEMENT2 matrix:' )

  value = clement2_determinant ( n, x, y )
  print '  Value =  %g' % ( value )

  print ''
  print 'CLEMENT2_DETERMINANT_TEST'
  print '  Normal end of execution.'

  return