#*****************************************************************************80
#
## gradient_vector makes a vector plot of the gradient of a function f(x,y).
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    06 September 2020
#
#  Author:
#
#    John Burkardt
#
library ( OceanView )
library ( pracma )

cat ( "\n" )
cat ( "gradient_vector:\n" )
cat ( " ", version$version.string, "\n" )
cat ( "  Plot the gradient vector field of a function f(x,y).\n" )
#
#  Define the grid.
#
x <- seq ( from = -2.0, to = +2.0, length.out = 31 )
y <- seq ( from = -2.0, to = +2.0, length.out = 31 )
XY <- meshgrid ( x, y )
X <- XY$X
Y <- XY$Y
#
#  Create the data.
#
Z <-        2.0 * X^2 - 1.05 * X^4 + X^6 / 6.0 + X * Y + Y^2
dZdX <- - ( 4.0 * X   - 4.20 * X^3 + X^5 + Y )
dZdY <- - (                                     X     + 2.0 * Y )
#
#  Plot.
#
filename = 'gradient_vector.png'
png ( filename )

quiver2D ( dZdX, dZdY, X, Y, 
  arr.max = 0.4,
  type = "triangle",
  scale = 4.0,
  contour = list ( z = Z, x = x, y = y, levels = seq ( 0.0, 10.0, by = 0.5 ) ),
  main = "Gradient vector field" )

cat ( "\n" )
cat ( "  Graphics saved as '", filename, "'\n" )
#
#  Terminate.
#
cat ( "\n" )
cat ( "gradient_vector:\n" )
cat ( "  Normal end of execution.\n" )

quit ( )