Mixing
Efficiently creating a tensor of diagonal matrices
1
Assume a map from scalars to matrices of a fixed dimension.
How would one efficiently create a vectorized version of this map?
More specifically assume there is a constant vector lamb with n entries.
Given a scalar t I'm interested in the diagonal matrix given by
np.diag(np.exp(lamb*t))
using numpy.
This will be an n times n matrix.
Now given a matrix T of size m_1 times m_2 I would like to calculate the tensor D of shape (m_1,m_2,n,n) given for 0 <= i < m_1, 0 <= j < m_2 by
D[i,j,:,:] = np.diag(np.exp(lamb*T[i,j]))
How would one efficiently get this tensor?
python-3.x numpy vectorization
asked Nov 19 '18 at 16:20
user447457
62
add a comment |
1
Assume a map from scalars to matrices of a fixed dimension.
How would one efficiently create a vectorized version of this map?
More specifically assume there is a constant vector lamb with n entries.
Given a scalar t I'm interested in the diagonal matrix given by
np.diag(np.exp(lamb*t))
using numpy.
This will be an n times n matrix.
Now given a matrix T of size m_1 times m_2 I would like to calculate the tensor D of shape (m_1,m_2,n,n) given for 0 <= i < m_1, 0 <= j < m_2 by
D[i,j,:,:] = np.diag(np.exp(lamb*T[i,j]))
How would one efficiently get this tensor?
python-3.x numpy vectorization
asked Nov 19 '18 at 16:20
user447457
62
Could you add minimal representative sample data? What doestlook like?
– Divakar
Nov 19 '18 at 16:21
There aren't any restrictions for the scalar t and for the matrix T as well. Or what to you mean by "minimal representative sample"?
– user447457
Nov 19 '18 at 16:30
Well first offlambda*tdoesn't seem like a valid syntax withtas scalar. Secondly, with minimal representative sample, I meant some sample data fortand a valid code (loopy code even) that could work on it.
– Divakar
Nov 19 '18 at 17:02
Oh, I'm sorry. The word lambda is reserved in python. Locally I called the variable lamb instead of lambda which is of type ndarray. Thus multiplication by a scalar is defined as entrywise multiplication with t. The answer given by Paul Panzer produces the output I'm interested in.
– user447457
Nov 19 '18 at 17:35
We are lazy. We don't like to make up test cases. And we don't like the potential ambiguity of word problems. Good answers include working examples. Good questions should as well.
– hpaulj
Nov 19 '18 at 17:36
add a comment |
1
1
1
Assume a map from scalars to matrices of a fixed dimension.
How would one efficiently create a vectorized version of this map?
More specifically assume there is a constant vector lamb with n entries.
Given a scalar t I'm interested in the diagonal matrix given by
np.diag(np.exp(lamb*t))
using numpy.
This will be an n times n matrix.
Now given a matrix T of size m_1 times m_2 I would like to calculate the tensor D of shape (m_1,m_2,n,n) given for 0 <= i < m_1, 0 <= j < m_2 by
D[i,j,:,:] = np.diag(np.exp(lamb*T[i,j]))
How would one efficiently get this tensor?
python-3.x numpy vectorization
asked Nov 19 '18 at 16:20
user447457
62
Assume a map from scalars to matrices of a fixed dimension.
How would one efficiently create a vectorized version of this map?
More specifically assume there is a constant vector lamb with n entries.
Given a scalar t I'm interested in the diagonal matrix given by
np.diag(np.exp(lamb*t))
using numpy.
This will be an n times n matrix.
Now given a matrix T of size m_1 times m_2 I would like to calculate the tensor D of shape (m_1,m_2,n,n) given for 0 <= i < m_1, 0 <= j < m_2 by
D[i,j,:,:] = np.diag(np.exp(lamb*T[i,j]))
How would one efficiently get this tensor?
python-3.x numpy vectorization
python-3.x numpy vectorization
asked Nov 19 '18 at 16:20
user447457
62
asked Nov 19 '18 at 16:20
user447457
62
edited Nov 19 '18 at 17:40
asked Nov 19 '18 at 16:20
user447457
62
asked Nov 19 '18 at 16:20
user447457
62
asked Nov 19 '18 at 16:20
user447457
62
62
Could you add minimal representative sample data? What doestlook like?
– Divakar
Nov 19 '18 at 16:21
There aren't any restrictions for the scalar t and for the matrix T as well. Or what to you mean by "minimal representative sample"?
– user447457
Nov 19 '18 at 16:30
Well first offlambda*tdoesn't seem like a valid syntax withtas scalar. Secondly, with minimal representative sample, I meant some sample data fortand a valid code (loopy code even) that could work on it.
– Divakar
Nov 19 '18 at 17:02
Oh, I'm sorry. The word lambda is reserved in python. Locally I called the variable lamb instead of lambda which is of type ndarray. Thus multiplication by a scalar is defined as entrywise multiplication with t. The answer given by Paul Panzer produces the output I'm interested in.
– user447457
Nov 19 '18 at 17:35
We are lazy. We don't like to make up test cases. And we don't like the potential ambiguity of word problems. Good answers include working examples. Good questions should as well.
– hpaulj
Nov 19 '18 at 17:36
add a comment |
Could you add minimal representative sample data? What doestlook like?
– Divakar
Nov 19 '18 at 16:21
There aren't any restrictions for the scalar t and for the matrix T as well. Or what to you mean by "minimal representative sample"?
– user447457
Nov 19 '18 at 16:30
Well first offlambda*tdoesn't seem like a valid syntax withtas scalar. Secondly, with minimal representative sample, I meant some sample data fortand a valid code (loopy code even) that could work on it.
– Divakar
Nov 19 '18 at 17:02
Oh, I'm sorry. The word lambda is reserved in python. Locally I called the variable lamb instead of lambda which is of type ndarray. Thus multiplication by a scalar is defined as entrywise multiplication with t. The answer given by Paul Panzer produces the output I'm interested in.
– user447457
Nov 19 '18 at 17:35
We are lazy. We don't like to make up test cases. And we don't like the potential ambiguity of word problems. Good answers include working examples. Good questions should as well.
– hpaulj
Nov 19 '18 at 17:36
Could you add minimal representative sample data? What does
t look like?– Divakar
Nov 19 '18 at 16:21
Could you add minimal representative sample data? What does
t look like?– Divakar
Nov 19 '18 at 16:21
There aren't any restrictions for the scalar t and for the matrix T as well. Or what to you mean by "minimal representative sample"?
– user447457
Nov 19 '18 at 16:30
There aren't any restrictions for the scalar t and for the matrix T as well. Or what to you mean by "minimal representative sample"?
– user447457
Nov 19 '18 at 16:30
Well first off
lambda*t doesn't seem like a valid syntax with t as scalar. Secondly, with minimal representative sample, I meant some sample data for tand a valid code (loopy code even) that could work on it.– Divakar
Nov 19 '18 at 17:02
Well first off
lambda*t doesn't seem like a valid syntax with t as scalar. Secondly, with minimal representative sample, I meant some sample data for tand a valid code (loopy code even) that could work on it.– Divakar
Nov 19 '18 at 17:02
Oh, I'm sorry. The word lambda is reserved in python. Locally I called the variable lamb instead of lambda which is of type ndarray. Thus multiplication by a scalar is defined as entrywise multiplication with t. The answer given by Paul Panzer produces the output I'm interested in.
– user447457
Nov 19 '18 at 17:35
Oh, I'm sorry. The word lambda is reserved in python. Locally I called the variable lamb instead of lambda which is of type ndarray. Thus multiplication by a scalar is defined as entrywise multiplication with t. The answer given by Paul Panzer produces the output I'm interested in.
– user447457
Nov 19 '18 at 17:35
We are lazy. We don't like to make up test cases. And we don't like the potential ambiguity of word problems. Good answers include working examples. Good questions should as well.
– hpaulj
Nov 19 '18 at 17:36
We are lazy. We don't like to make up test cases. And we don't like the potential ambiguity of word problems. Good answers include working examples. Good questions should as well.
– hpaulj
Nov 19 '18 at 17:36
add a comment |
1 Answer
1
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One comparatively straight-forward way would be using einsum.
Example:
>>> T = np.array([[1,2,3], [4,6,7]])
>>> lam = np.array([1,2,5])
>>> D = np.zeros((*T.shape, n, n))
>>> np.einsum('ijkk->ijk', D)[...] = np.exp(np.multiply.outer(T, lam))
>>> D
array([[[[2.71828183e+00, 0.00000000e+00, 0.00000000e+00],
[0.00000000e+00, 7.38905610e+00, 0.00000000e+00],
[0.00000000e+00, 0.00000000e+00, 1.48413159e+02]],
[[7.38905610e+00, 0.00000000e+00, 0.00000000e+00],
[0.00000000e+00, 5.45981500e+01, 0.00000000e+00],
[0.00000000e+00, 0.00000000e+00, 2.20264658e+04]],
[[2.00855369e+01, 0.00000000e+00, 0.00000000e+00],
[0.00000000e+00, 4.03428793e+02, 0.00000000e+00],
[0.00000000e+00, 0.00000000e+00, 3.26901737e+06]]],
[[[5.45981500e+01, 0.00000000e+00, 0.00000000e+00],
[0.00000000e+00, 2.98095799e+03, 0.00000000e+00],
[0.00000000e+00, 0.00000000e+00, 4.85165195e+08]],
[[4.03428793e+02, 0.00000000e+00, 0.00000000e+00],
[0.00000000e+00, 1.62754791e+05, 0.00000000e+00],
[0.00000000e+00, 0.00000000e+00, 1.06864746e+13]],
[[1.09663316e+03, 0.00000000e+00, 0.00000000e+00],
[0.00000000e+00, 1.20260428e+06, 0.00000000e+00],
[0.00000000e+00, 0.00000000e+00, 1.58601345e+15]]]])
You can speed this up a little bit using the out keyword to avoid one copy:
np.exp(np.multiply.outer(T, lam), out=np.einsum('ijkk->ijk', D))
answered Nov 19 '18 at 17:27
Paul Panzer
29.9k21240
Thank you! Something like this was exactly what I was looking for.
– user447457
Nov 19 '18 at 20:06
add a comment |
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One comparatively straight-forward way would be using einsum.
Example:
>>> T = np.array([[1,2,3], [4,6,7]])
>>> lam = np.array([1,2,5])
>>> D = np.zeros((*T.shape, n, n))
>>> np.einsum('ijkk->ijk', D)[...] = np.exp(np.multiply.outer(T, lam))
>>> D
array([[[[2.71828183e+00, 0.00000000e+00, 0.00000000e+00],
[0.00000000e+00, 7.38905610e+00, 0.00000000e+00],
[0.00000000e+00, 0.00000000e+00, 1.48413159e+02]],
[[7.38905610e+00, 0.00000000e+00, 0.00000000e+00],
[0.00000000e+00, 5.45981500e+01, 0.00000000e+00],
[0.00000000e+00, 0.00000000e+00, 2.20264658e+04]],
[[2.00855369e+01, 0.00000000e+00, 0.00000000e+00],
[0.00000000e+00, 4.03428793e+02, 0.00000000e+00],
[0.00000000e+00, 0.00000000e+00, 3.26901737e+06]]],
[[[5.45981500e+01, 0.00000000e+00, 0.00000000e+00],
[0.00000000e+00, 2.98095799e+03, 0.00000000e+00],
[0.00000000e+00, 0.00000000e+00, 4.85165195e+08]],
[[4.03428793e+02, 0.00000000e+00, 0.00000000e+00],
[0.00000000e+00, 1.62754791e+05, 0.00000000e+00],
[0.00000000e+00, 0.00000000e+00, 1.06864746e+13]],
[[1.09663316e+03, 0.00000000e+00, 0.00000000e+00],
[0.00000000e+00, 1.20260428e+06, 0.00000000e+00],
[0.00000000e+00, 0.00000000e+00, 1.58601345e+15]]]])
You can speed this up a little bit using the out keyword to avoid one copy:
np.exp(np.multiply.outer(T, lam), out=np.einsum('ijkk->ijk', D))
answered Nov 19 '18 at 17:27
Paul Panzer
29.9k21240
Thank you! Something like this was exactly what I was looking for.
– user447457
Nov 19 '18 at 20:06
add a comment |
0
One comparatively straight-forward way would be using einsum.
Example:
>>> T = np.array([[1,2,3], [4,6,7]])
>>> lam = np.array([1,2,5])
>>> D = np.zeros((*T.shape, n, n))
>>> np.einsum('ijkk->ijk', D)[...] = np.exp(np.multiply.outer(T, lam))
>>> D
array([[[[2.71828183e+00, 0.00000000e+00, 0.00000000e+00],
[0.00000000e+00, 7.38905610e+00, 0.00000000e+00],
[0.00000000e+00, 0.00000000e+00, 1.48413159e+02]],
[[7.38905610e+00, 0.00000000e+00, 0.00000000e+00],
[0.00000000e+00, 5.45981500e+01, 0.00000000e+00],
[0.00000000e+00, 0.00000000e+00, 2.20264658e+04]],
[[2.00855369e+01, 0.00000000e+00, 0.00000000e+00],
[0.00000000e+00, 4.03428793e+02, 0.00000000e+00],
[0.00000000e+00, 0.00000000e+00, 3.26901737e+06]]],
[[[5.45981500e+01, 0.00000000e+00, 0.00000000e+00],
[0.00000000e+00, 2.98095799e+03, 0.00000000e+00],
[0.00000000e+00, 0.00000000e+00, 4.85165195e+08]],
[[4.03428793e+02, 0.00000000e+00, 0.00000000e+00],
[0.00000000e+00, 1.62754791e+05, 0.00000000e+00],
[0.00000000e+00, 0.00000000e+00, 1.06864746e+13]],
[[1.09663316e+03, 0.00000000e+00, 0.00000000e+00],
[0.00000000e+00, 1.20260428e+06, 0.00000000e+00],
[0.00000000e+00, 0.00000000e+00, 1.58601345e+15]]]])
You can speed this up a little bit using the out keyword to avoid one copy:
np.exp(np.multiply.outer(T, lam), out=np.einsum('ijkk->ijk', D))
answered Nov 19 '18 at 17:27
Paul Panzer
29.9k21240
Thank you! Something like this was exactly what I was looking for.
– user447457
Nov 19 '18 at 20:06
add a comment |
0
0
0
One comparatively straight-forward way would be using einsum.
Example:
>>> T = np.array([[1,2,3], [4,6,7]])
>>> lam = np.array([1,2,5])
>>> D = np.zeros((*T.shape, n, n))
>>> np.einsum('ijkk->ijk', D)[...] = np.exp(np.multiply.outer(T, lam))
>>> D
array([[[[2.71828183e+00, 0.00000000e+00, 0.00000000e+00],
[0.00000000e+00, 7.38905610e+00, 0.00000000e+00],
[0.00000000e+00, 0.00000000e+00, 1.48413159e+02]],
[[7.38905610e+00, 0.00000000e+00, 0.00000000e+00],
[0.00000000e+00, 5.45981500e+01, 0.00000000e+00],
[0.00000000e+00, 0.00000000e+00, 2.20264658e+04]],
[[2.00855369e+01, 0.00000000e+00, 0.00000000e+00],
[0.00000000e+00, 4.03428793e+02, 0.00000000e+00],
[0.00000000e+00, 0.00000000e+00, 3.26901737e+06]]],
[[[5.45981500e+01, 0.00000000e+00, 0.00000000e+00],
[0.00000000e+00, 2.98095799e+03, 0.00000000e+00],
[0.00000000e+00, 0.00000000e+00, 4.85165195e+08]],
[[4.03428793e+02, 0.00000000e+00, 0.00000000e+00],
[0.00000000e+00, 1.62754791e+05, 0.00000000e+00],
[0.00000000e+00, 0.00000000e+00, 1.06864746e+13]],
[[1.09663316e+03, 0.00000000e+00, 0.00000000e+00],
[0.00000000e+00, 1.20260428e+06, 0.00000000e+00],
[0.00000000e+00, 0.00000000e+00, 1.58601345e+15]]]])
You can speed this up a little bit using the out keyword to avoid one copy:
np.exp(np.multiply.outer(T, lam), out=np.einsum('ijkk->ijk', D))
answered Nov 19 '18 at 17:27
Paul Panzer
29.9k21240
One comparatively straight-forward way would be using einsum.
Example:
>>> T = np.array([[1,2,3], [4,6,7]])
>>> lam = np.array([1,2,5])
>>> D = np.zeros((*T.shape, n, n))
>>> np.einsum('ijkk->ijk', D)[...] = np.exp(np.multiply.outer(T, lam))
>>> D
array([[[[2.71828183e+00, 0.00000000e+00, 0.00000000e+00],
[0.00000000e+00, 7.38905610e+00, 0.00000000e+00],
[0.00000000e+00, 0.00000000e+00, 1.48413159e+02]],
[[7.38905610e+00, 0.00000000e+00, 0.00000000e+00],
[0.00000000e+00, 5.45981500e+01, 0.00000000e+00],
[0.00000000e+00, 0.00000000e+00, 2.20264658e+04]],
[[2.00855369e+01, 0.00000000e+00, 0.00000000e+00],
[0.00000000e+00, 4.03428793e+02, 0.00000000e+00],
[0.00000000e+00, 0.00000000e+00, 3.26901737e+06]]],
[[[5.45981500e+01, 0.00000000e+00, 0.00000000e+00],
[0.00000000e+00, 2.98095799e+03, 0.00000000e+00],
[0.00000000e+00, 0.00000000e+00, 4.85165195e+08]],
[[4.03428793e+02, 0.00000000e+00, 0.00000000e+00],
[0.00000000e+00, 1.62754791e+05, 0.00000000e+00],
[0.00000000e+00, 0.00000000e+00, 1.06864746e+13]],
[[1.09663316e+03, 0.00000000e+00, 0.00000000e+00],
[0.00000000e+00, 1.20260428e+06, 0.00000000e+00],
[0.00000000e+00, 0.00000000e+00, 1.58601345e+15]]]])
You can speed this up a little bit using the out keyword to avoid one copy:
np.exp(np.multiply.outer(T, lam), out=np.einsum('ijkk->ijk', D))
answered Nov 19 '18 at 17:27
Paul Panzer
29.9k21240
edited Nov 19 '18 at 18:04
answered Nov 19 '18 at 17:27
Paul Panzer
29.9k21240
answered Nov 19 '18 at 17:27
Paul Panzer
29.9k21240
answered Nov 19 '18 at 17:27
Paul Panzer
29.9k21240
29.9k21240
Thank you! Something like this was exactly what I was looking for.
– user447457
Nov 19 '18 at 20:06
add a comment |
Thank you! Something like this was exactly what I was looking for.
– user447457
Nov 19 '18 at 20:06
Thank you! Something like this was exactly what I was looking for.
– user447457
Nov 19 '18 at 20:06
Thank you! Something like this was exactly what I was looking for.
– user447457
Nov 19 '18 at 20:06
add a comment |
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Could you add minimal representative sample data? What does
tlook like?– Divakar
Nov 19 '18 at 16:21
There aren't any restrictions for the scalar t and for the matrix T as well. Or what to you mean by "minimal representative sample"?
– user447457
Nov 19 '18 at 16:30
Well first off
lambda*tdoesn't seem like a valid syntax withtas scalar. Secondly, with minimal representative sample, I meant some sample data fortand a valid code (loopy code even) that could work on it.– Divakar
Nov 19 '18 at 17:02
Oh, I'm sorry. The word lambda is reserved in python. Locally I called the variable lamb instead of lambda which is of type ndarray. Thus multiplication by a scalar is defined as entrywise multiplication with t. The answer given by Paul Panzer produces the output I'm interested in.
– user447457
Nov 19 '18 at 17:35
We are lazy. We don't like to make up test cases. And we don't like the potential ambiguity of word problems. Good answers include working examples. Good questions should as well.
– hpaulj
Nov 19 '18 at 17:36