Vecrtorized evluation of function defined by matrix over grid
I'm looking to plot the value of a function defined by a matrix over a grid of values.
Let S be an invertable 2x2 matrix and let x be a 2-dimensional vector. How can vectorize the evaluation of x@S@x over a two dimensional grid?
Here is how I currently do it. It works, but takes a beat to perform the computation since the grid is so fine.
#Initialize Matrix
S = np.zeros(shape = (2,2))
while np.linalg.matrix_rank(S)<S.shape[1]:
S = np.random.randint(-5,5+1, size = (2,2))
X,Y = [j.ravel() for j in np.meshgrid(np.linspace(-2,2,1001),np.linspace(-2,2,1001))]
Z = np.zeros_like(X)
for i,v in enumerate(zip(X,Y)):
v = np.array(v)
Z[i] = v@S@v
n = int(np.sqrt(X.size))
Z = Z.reshape(n,n)
X = X.reshape(n,n)
Y = Y.reshape(n,n)
plt.contour(X,Y,Z)
python numpy
asked Dec 27 '18 at 20:08
Demetri Pananos
1,9911231
add a comment |
I'm looking to plot the value of a function defined by a matrix over a grid of values.
Let S be an invertable 2x2 matrix and let x be a 2-dimensional vector. How can vectorize the evaluation of x@S@x over a two dimensional grid?
Here is how I currently do it. It works, but takes a beat to perform the computation since the grid is so fine.
#Initialize Matrix
S = np.zeros(shape = (2,2))
while np.linalg.matrix_rank(S)<S.shape[1]:
S = np.random.randint(-5,5+1, size = (2,2))
X,Y = [j.ravel() for j in np.meshgrid(np.linspace(-2,2,1001),np.linspace(-2,2,1001))]
Z = np.zeros_like(X)
for i,v in enumerate(zip(X,Y)):
v = np.array(v)
Z[i] = v@S@v
n = int(np.sqrt(X.size))
Z = Z.reshape(n,n)
X = X.reshape(n,n)
Y = Y.reshape(n,n)
plt.contour(X,Y,Z)
python numpy
asked Dec 27 '18 at 20:08
Demetri Pananos
1,9911231
add a comment |
I'm looking to plot the value of a function defined by a matrix over a grid of values.
Let S be an invertable 2x2 matrix and let x be a 2-dimensional vector. How can vectorize the evaluation of x@S@x over a two dimensional grid?
Here is how I currently do it. It works, but takes a beat to perform the computation since the grid is so fine.
#Initialize Matrix
S = np.zeros(shape = (2,2))
while np.linalg.matrix_rank(S)<S.shape[1]:
S = np.random.randint(-5,5+1, size = (2,2))
X,Y = [j.ravel() for j in np.meshgrid(np.linspace(-2,2,1001),np.linspace(-2,2,1001))]
Z = np.zeros_like(X)
for i,v in enumerate(zip(X,Y)):
v = np.array(v)
Z[i] = v@S@v
n = int(np.sqrt(X.size))
Z = Z.reshape(n,n)
X = X.reshape(n,n)
Y = Y.reshape(n,n)
plt.contour(X,Y,Z)
python numpy
asked Dec 27 '18 at 20:08
Demetri Pananos
1,9911231
I'm looking to plot the value of a function defined by a matrix over a grid of values.
Let S be an invertable 2x2 matrix and let x be a 2-dimensional vector. How can vectorize the evaluation of x@S@x over a two dimensional grid?
Here is how I currently do it. It works, but takes a beat to perform the computation since the grid is so fine.
#Initialize Matrix
S = np.zeros(shape = (2,2))
while np.linalg.matrix_rank(S)<S.shape[1]:
S = np.random.randint(-5,5+1, size = (2,2))
X,Y = [j.ravel() for j in np.meshgrid(np.linspace(-2,2,1001),np.linspace(-2,2,1001))]
Z = np.zeros_like(X)
for i,v in enumerate(zip(X,Y)):
v = np.array(v)
Z[i] = v@S@v
n = int(np.sqrt(X.size))
Z = Z.reshape(n,n)
X = X.reshape(n,n)
Y = Y.reshape(n,n)
plt.contour(X,Y,Z)
python numpy
python numpy
asked Dec 27 '18 at 20:08
Demetri Pananos
1,9911231
asked Dec 27 '18 at 20:08
Demetri Pananos
1,9911231
asked Dec 27 '18 at 20:08
Demetri Pananos
1,9911231
asked Dec 27 '18 at 20:08
Demetri Pananos
1,9911231
asked Dec 27 '18 at 20:08
Demetri Pananos
1,9911231
1,9911231
add a comment |
add a comment |
1 Answer
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Simplest would be with stacking those X,Y into a 2-column 2D array and then using np.einsum to replace the loopy matrix-multiplications -
p = np.column_stack((X,Y)) # or np.stack((X,Y)).T
Zout = np.einsum('ij,jk,ik->i',p,S,p,optimize=True)
answered Dec 27 '18 at 20:34
Divakar
154k1483172
add a comment |
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1 Answer
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1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
Simplest would be with stacking those X,Y into a 2-column 2D array and then using np.einsum to replace the loopy matrix-multiplications -
p = np.column_stack((X,Y)) # or np.stack((X,Y)).T
Zout = np.einsum('ij,jk,ik->i',p,S,p,optimize=True)
answered Dec 27 '18 at 20:34
Divakar
154k1483172
add a comment |
Simplest would be with stacking those X,Y into a 2-column 2D array and then using np.einsum to replace the loopy matrix-multiplications -
p = np.column_stack((X,Y)) # or np.stack((X,Y)).T
Zout = np.einsum('ij,jk,ik->i',p,S,p,optimize=True)
answered Dec 27 '18 at 20:34
Divakar
154k1483172
add a comment |
Simplest would be with stacking those X,Y into a 2-column 2D array and then using np.einsum to replace the loopy matrix-multiplications -
p = np.column_stack((X,Y)) # or np.stack((X,Y)).T
Zout = np.einsum('ij,jk,ik->i',p,S,p,optimize=True)
answered Dec 27 '18 at 20:34
Divakar
154k1483172
Simplest would be with stacking those X,Y into a 2-column 2D array and then using np.einsum to replace the loopy matrix-multiplications -
p = np.column_stack((X,Y)) # or np.stack((X,Y)).T
Zout = np.einsum('ij,jk,ik->i',p,S,p,optimize=True)
answered Dec 27 '18 at 20:34
Divakar
154k1483172
edited Dec 27 '18 at 20:42
answered Dec 27 '18 at 20:34
Divakar
154k1483172
answered Dec 27 '18 at 20:34
Divakar
154k1483172
answered Dec 27 '18 at 20:34
Divakar
154k1483172
154k1483172
add a comment |
add a comment |
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