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Merged
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Feb 3, 2011
Merged

Einsum changes #37

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abcdd9a
ENH: einsum: Disable broadcasting by default, allow spaces in subscri…
mwiebe Jan 31, 2011
cdb0a56
ENH: einsum: Add alternative einsum parameter method
mwiebe Jan 31, 2011
3b6b801
ENH: einsum: Change loop unrolling to be better for small loops
mwiebe Jan 29, 2011
909e30a
ENH: einsum: Change function selection function to use tables
mwiebe Jan 31, 2011
f8fccd8
TST: einsum: Move einsum tests to a different file
mwiebe Feb 1, 2011
31f6ff9
ENH: iter: Catch another case with fixed strides.
mwiebe Feb 1, 2011
5c5d026
ENH: einsum: Write specialized unbuffered loops for several cases
mwiebe Feb 2, 2011
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51 changes: 42 additions & 9 deletions numpy/add_newdocs.py
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Original file line number Diff line number Diff line change
Expand Up @@ -1517,6 +1517,10 @@

Evaluates the Einstein summation convention on the operands.

An alternative way to provide the subscripts and operands is as
einsum(op0, sublist0, op1, sublist1, ..., [sublistout]). The examples
below have corresponding einsum calls with the two parameter methods.

Using the Einstein summation convention, many common multi-dimensional
array operations can be represented in a simple fashion. This function
provides a way compute such summations.
Expand All @@ -1540,13 +1544,16 @@
``np.einsum('ji', a)`` takes its transpose.

The output can be controlled by specifying output subscript labels
as well. This specifies the label order, and allows summing to be
disallowed or forced when desired. The call ``np.einsum('i->', a)``
is equivalent to ``np.sum(a, axis=-1)``, and
``np.einsum('ii->i', a)`` is equivalent to ``np.diag(a)``.

It is also possible to control how broadcasting occurs using
an ellipsis. To take the trace along the first and last axes,
as well. This specifies the label order, and allows summing to
be disallowed or forced when desired. The call ``np.einsum('i->', a)``
is like ``np.sum(a, axis=-1)``, and ``np.einsum('ii->i', a)``
is like ``np.diag(a)``. The difference is that ``einsum`` does not
allow broadcasting by default.

To enable and control broadcasting, use an ellipsis. Default
NumPy-style broadcasting is done by adding an ellipsis
to the left of each term, like ``np.einsum('...ii->...i', a)``.
To take the trace along the first and last axes,
you can do ``np.einsum('i...i', a)``, or to do a matrix-matrix
product with the left-most indices instead of rightmost, you can do
``np.einsum('ij...,jk...->ik...', a, b)``.
Expand Down Expand Up @@ -1602,20 +1609,30 @@

>>> np.einsum('ii', a)
60
>>> np.einsum(a, [0,0])
60
>>> np.trace(a)
60

>>> np.einsum('ii->i', a)
array([ 0, 6, 12, 18, 24])
>>> np.einsum(a, [0,0], [0])
array([ 0, 6, 12, 18, 24])
>>> np.diag(a)
array([ 0, 6, 12, 18, 24])

>>> np.einsum('ij,j', a, b)
array([ 30, 80, 130, 180, 230])
>>> np.einsum(a, [0,1], b, [1])
array([ 30, 80, 130, 180, 230])
>>> np.dot(a, b)
array([ 30, 80, 130, 180, 230])

>>> np.einsum('ji', c)
array([[0, 3],
[1, 4],
[2, 5]])
>>> np.einsum(c, [1,0])
array([[0, 3],
[1, 4],
[2, 5]])
Expand All @@ -1624,7 +1641,10 @@
[1, 4],
[2, 5]])

>>> np.einsum(',', 3, c)
>>> np.einsum('..., ...', 3, c)
array([[ 0, 3, 6],
[ 9, 12, 15]])
>>> np.einsum(3, [Ellipsis], c, [Ellipsis])
array([[ 0, 3, 6],
[ 9, 12, 15]])
>>> np.multiply(3, c)
Expand All @@ -1633,24 +1653,37 @@

>>> np.einsum('i,i', b, b)
30
>>> np.einsum(b, [0], b, [0])
30
>>> np.inner(b,b)
30

>>> np.einsum('i,j', np.arange(2)+1, b)
array([[0, 1, 2, 3, 4],
[0, 2, 4, 6, 8]])
>>> np.einsum(np.arange(2)+1, [0], b, [1])
array([[0, 1, 2, 3, 4],
[0, 2, 4, 6, 8]])
>>> np.outer(np.arange(2)+1, b)
array([[0, 1, 2, 3, 4],
[0, 2, 4, 6, 8]])

>>> np.einsum('i...->', a)
>>> np.einsum('i...->...', a)
array([50, 55, 60, 65, 70])
>>> np.einsum(a, [0,Ellipsis], [Ellipsis])
array([50, 55, 60, 65, 70])
>>> np.sum(a, axis=0)
array([50, 55, 60, 65, 70])

>>> a = np.arange(60.).reshape(3,4,5)
>>> b = np.arange(24.).reshape(4,3,2)
>>> np.einsum('ijk,jil->kl', a, b)
array([[ 4400., 4730.],
[ 4532., 4874.],
[ 4664., 5018.],
[ 4796., 5162.],
[ 4928., 5306.]])
>>> np.einsum(a, [0,1,2], b, [1,0,3], [2,3])
array([[ 4400., 4730.],
[ 4532., 4874.],
[ 4664., 5018.],
Expand Down
22 changes: 12 additions & 10 deletions numpy/core/code_generators/numpy_api.py
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Original file line number Diff line number Diff line change
Expand Up @@ -298,17 +298,19 @@
'NpyIter_GetInnerFixedStrideArray': 262,
'NpyIter_RemoveAxis': 263,
'NpyIter_GetAxisStrideArray': 264,
'NpyIter_RequiresBuffering': 265,
'NpyIter_GetInitialDataPtrArray': 266,
#
'PyArray_CastingConverter': 265,
'PyArray_CountNonzero': 266,
'PyArray_PromoteTypes': 267,
'PyArray_MinScalarType': 268,
'PyArray_ResultType': 269,
'PyArray_CanCastArrayTo': 270,
'PyArray_CanCastTypeTo': 271,
'PyArray_EinsteinSum': 272,
'PyArray_FillWithZero': 273,
'PyArray_NewLikeArray': 274,
'PyArray_CastingConverter': 267,
'PyArray_CountNonzero': 268,
'PyArray_PromoteTypes': 269,
'PyArray_MinScalarType': 270,
'PyArray_ResultType': 271,
'PyArray_CanCastArrayTo': 272,
'PyArray_CanCastTypeTo': 273,
'PyArray_EinsteinSum': 274,
'PyArray_FillWithZero': 275,
'PyArray_NewLikeArray': 276,
}

ufunc_types_api = {
Expand Down
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