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use sympy to find gradient and plot vector field

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0

I wrote some code to use sympy to find the gradient of a function f(x,y) = x*y**2, and then to plot the vector field from the gradient. See Below:

%matplotlib inline
import matplotlib.pyplot as plt
import sympy as sp
import numpy as np

sp.init_printing()
x,y = sp.symbols('x y')

def gradient(f):
 return (f.diff(x), f.diff(y))

f = x*y**2
g = gradient(f)
g

X,Y = np.meshgrid(np.linspace(-3,3,15), np.linspace(-3,3,15))

U=[g[0].subs(x:x1, y:y1) for (x1,y1) in zip(X,Y)]
V=[g[1].subs(x:x1, y:y1) for (x1,y1) in zip(X,Y)]

plt.quiver(X,Y,U,V, linewidth=1)
plt.title("vector field")
plt.show()

What i'm wondering about is why the sympy "subs" function is not working in this code. Its just returns the expression without inserting a value of X and Y to evaluate to a numerical value, instead its just returning the sympy object without any subsitution.

python matplotlib sympy

share|improve this question

asked Mar 25 at 0:23

DiscreteMathDiscreteMath

84

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  stackoverflow.com/questions/36013063/…
  
  – DiscreteMath
  Mar 25 at 1:17
  

  
  
  
  

add a comment | 

0

I wrote some code to use sympy to find the gradient of a function f(x,y) = x*y**2, and then to plot the vector field from the gradient. See Below:

%matplotlib inline
import matplotlib.pyplot as plt
import sympy as sp
import numpy as np

sp.init_printing()
x,y = sp.symbols('x y')

def gradient(f):
 return (f.diff(x), f.diff(y))

f = x*y**2
g = gradient(f)
g

X,Y = np.meshgrid(np.linspace(-3,3,15), np.linspace(-3,3,15))

U=[g[0].subs(x:x1, y:y1) for (x1,y1) in zip(X,Y)]
V=[g[1].subs(x:x1, y:y1) for (x1,y1) in zip(X,Y)]

plt.quiver(X,Y,U,V, linewidth=1)
plt.title("vector field")
plt.show()

What i'm wondering about is why the sympy "subs" function is not working in this code. Its just returns the expression without inserting a value of X and Y to evaluate to a numerical value, instead its just returning the sympy object without any subsitution.

python matplotlib sympy

share|improve this question

asked Mar 25 at 0:23

DiscreteMathDiscreteMath

84

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  stackoverflow.com/questions/36013063/…
  
  – DiscreteMath
  Mar 25 at 1:17
  

  
  
  
  

add a comment | 

I wrote some code to use sympy to find the gradient of a function f(x,y) = x*y**2, and then to plot the vector field from the gradient. See Below:

%matplotlib inline
import matplotlib.pyplot as plt
import sympy as sp
import numpy as np

sp.init_printing()
x,y = sp.symbols('x y')

def gradient(f):
 return (f.diff(x), f.diff(y))

f = x*y**2
g = gradient(f)
g

X,Y = np.meshgrid(np.linspace(-3,3,15), np.linspace(-3,3,15))

U=[g[0].subs(x:x1, y:y1) for (x1,y1) in zip(X,Y)]
V=[g[1].subs(x:x1, y:y1) for (x1,y1) in zip(X,Y)]

plt.quiver(X,Y,U,V, linewidth=1)
plt.title("vector field")
plt.show()

What i'm wondering about is why the sympy "subs" function is not working in this code. Its just returns the expression without inserting a value of X and Y to evaluate to a numerical value, instead its just returning the sympy object without any subsitution.

python matplotlib sympy

share|improve this question

asked Mar 25 at 0:23

DiscreteMathDiscreteMath

84

%matplotlib inline
import matplotlib.pyplot as plt
import sympy as sp
import numpy as np

sp.init_printing()
x,y = sp.symbols('x y')

def gradient(f):
 return (f.diff(x), f.diff(y))

f = x*y**2
g = gradient(f)
g

X,Y = np.meshgrid(np.linspace(-3,3,15), np.linspace(-3,3,15))

U=[g[0].subs(x:x1, y:y1) for (x1,y1) in zip(X,Y)]
V=[g[1].subs(x:x1, y:y1) for (x1,y1) in zip(X,Y)]

plt.quiver(X,Y,U,V, linewidth=1)
plt.title("vector field")
plt.show()

share|improve this question

asked Mar 25 at 0:23

DiscreteMathDiscreteMath

84

share|improve this question

asked Mar 25 at 0:23

DiscreteMathDiscreteMath

84

asked Mar 25 at 0:23

DiscreteMathDiscreteMath

84

asked Mar 25 at 0:23

DiscreteMathDiscreteMath

84

1 Answer
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oldest

votes

0

The problem with your code is that you need to access a meshgrid as a 2-dimensional array.

Example: U[i,j] not U[i]

%matplotlib inline
import matplotlib.pyplot as plt
import sympy as sp
import numpy as np

sp.init_printing()
x,y = sp.symbols('x y')

def gradient(f):
 return (f.diff(x), f.diff(y))

f = x*y**2
g = gradient(f)
g

xrange = np.linspace(-3,3,15)
yrange = np.linspace(-3,3,15)
X,Y = np.meshgrid(xrange, yrange)

U=X
V=Y

for i in range(len(xrange)):
 for j in range(len(yrange)):
 x1 = X[i,j]
 y1 = Y[i,j]
 U[i,j] = g[0].subs(x:x1, y:y1)
 V[i,j] = g[1].subs(x:x1, y:y1)

plt.quiver(X,Y,U,V, linewidth=1)
plt.title("vector field")
plt.show()

share|improve this answer

answered Mar 25 at 1:32

Bill MooreBill Moore

2,0781323

add a comment | 

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0

The problem with your code is that you need to access a meshgrid as a 2-dimensional array.

Example: U[i,j] not U[i]

%matplotlib inline
import matplotlib.pyplot as plt
import sympy as sp
import numpy as np

sp.init_printing()
x,y = sp.symbols('x y')

def gradient(f):
 return (f.diff(x), f.diff(y))

f = x*y**2
g = gradient(f)
g

xrange = np.linspace(-3,3,15)
yrange = np.linspace(-3,3,15)
X,Y = np.meshgrid(xrange, yrange)

U=X
V=Y

for i in range(len(xrange)):
 for j in range(len(yrange)):
 x1 = X[i,j]
 y1 = Y[i,j]
 U[i,j] = g[0].subs(x:x1, y:y1)
 V[i,j] = g[1].subs(x:x1, y:y1)

plt.quiver(X,Y,U,V, linewidth=1)
plt.title("vector field")
plt.show()

share|improve this answer

answered Mar 25 at 1:32

Bill MooreBill Moore

2,0781323

add a comment | 

0

The problem with your code is that you need to access a meshgrid as a 2-dimensional array.

Example: U[i,j] not U[i]

%matplotlib inline
import matplotlib.pyplot as plt
import sympy as sp
import numpy as np

sp.init_printing()
x,y = sp.symbols('x y')

def gradient(f):
 return (f.diff(x), f.diff(y))

f = x*y**2
g = gradient(f)
g

xrange = np.linspace(-3,3,15)
yrange = np.linspace(-3,3,15)
X,Y = np.meshgrid(xrange, yrange)

U=X
V=Y

for i in range(len(xrange)):
 for j in range(len(yrange)):
 x1 = X[i,j]
 y1 = Y[i,j]
 U[i,j] = g[0].subs(x:x1, y:y1)
 V[i,j] = g[1].subs(x:x1, y:y1)

plt.quiver(X,Y,U,V, linewidth=1)
plt.title("vector field")
plt.show()

share|improve this answer

answered Mar 25 at 1:32

Bill MooreBill Moore

2,0781323

add a comment | 

The problem with your code is that you need to access a meshgrid as a 2-dimensional array.

Example: U[i,j] not U[i]

%matplotlib inline
import matplotlib.pyplot as plt
import sympy as sp
import numpy as np

sp.init_printing()
x,y = sp.symbols('x y')

def gradient(f):
 return (f.diff(x), f.diff(y))

f = x*y**2
g = gradient(f)
g

xrange = np.linspace(-3,3,15)
yrange = np.linspace(-3,3,15)
X,Y = np.meshgrid(xrange, yrange)

U=X
V=Y

for i in range(len(xrange)):
 for j in range(len(yrange)):
 x1 = X[i,j]
 y1 = Y[i,j]
 U[i,j] = g[0].subs(x:x1, y:y1)
 V[i,j] = g[1].subs(x:x1, y:y1)

plt.quiver(X,Y,U,V, linewidth=1)
plt.title("vector field")
plt.show()

share|improve this answer

answered Mar 25 at 1:32

Bill MooreBill Moore

2,0781323

%matplotlib inline
import matplotlib.pyplot as plt
import sympy as sp
import numpy as np

sp.init_printing()
x,y = sp.symbols('x y')

def gradient(f):
 return (f.diff(x), f.diff(y))

f = x*y**2
g = gradient(f)
g

xrange = np.linspace(-3,3,15)
yrange = np.linspace(-3,3,15)
X,Y = np.meshgrid(xrange, yrange)

U=X
V=Y

for i in range(len(xrange)):
 for j in range(len(yrange)):
 x1 = X[i,j]
 y1 = Y[i,j]
 U[i,j] = g[0].subs(x:x1, y:y1)
 V[i,j] = g[1].subs(x:x1, y:y1)

plt.quiver(X,Y,U,V, linewidth=1)
plt.title("vector field")
plt.show()

share|improve this answer

answered Mar 25 at 1:32

Bill MooreBill Moore

2,0781323

answered Mar 25 at 1:32

Bill MooreBill Moore

2,0781323

answered Mar 25 at 1:32

Bill MooreBill Moore

2,0781323