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Barry Warsaw 2000-11-27 05:41:46 +00:00
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pep-0211.txt
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@ -20,7 +20,7 @@ Introduction
definitive historical record.
Proposal
Summary
Add a single new infix binary operator '@' ("across"), and
corresponding special methods "__across__()", "__racross__()", and
@ -141,38 +141,12 @@ Proposal
A new operator '@' (pronounced "across") will be added to Python,
along with special methods "__across__()", "__racross__()", and
"__iacross__()", with the usual semantics.
NumPy will overload "@" to perform mathematical multiplication of
arrays where shapes permit, and to throw an exception otherwise.
Its implementation of "@" will treat built-in sequence types as if
they were column vectors. This takes care of the cases MM and MV.
An attribute "T" will be added to the NumPy array type, such that
"m.T" is:
(a) the transpose of "m" for a 2-dimensional array
(b) the 1xN matrix transpose of "m" if "m" is a 1-dimensional
array; or
(c) a runtime error for an array with rank >= 3.
This attribute will alias the memory of the base object. NumPy's
"transpose()" function will be extended to turn built-in sequence
types into row vectors. This takes care of the VM, VD, and VO
cases. We propose an attribute because:
(a) the resulting notation is similar to the 'superscript T' (at
least, as similar as ASCII allows), and
(b) it signals that the transposition aliases the original object.
"__iacross__()", with the usual semantics. (We recommend using
"@", rather than the times-like "><", because of the ease with
which the latter could be mis-typed as inequality "<>".)
No new operators will be defined to mean "solve a set of linear
equations", or "invert a matrix". Instead, NumPy will define a
value "inv", which will be recognized by the exponentiation
operator, such that "A ** inv" is the inverse of "A". This is
similar in spirit to NumPy's existing "newaxis" value.
equations", or "invert a matrix".
(Optional) When applied to sequences, the "@" operator will return
a tuple of tuples containing the cross-product of their elements
@ -293,7 +267,8 @@ Related Proposals
0225 : Elementwise/Objectwise Operators
A (much) larger proposal that addresses the same subject.
A larger proposal that addresses the same subject, but
which proposes many more additions to the language.
Acknowledgments
@ -313,19 +288,37 @@ References
[7] http://www.python.org/pipermail/python-list/2000-August/112529.html
Appendix: Other Operations
Appendix: NumPy
NumPy will overload "@" to perform mathematical multiplication of
arrays where shapes permit, and to throw an exception otherwise.
Its implementation of "@" will treat built-in sequence types as if
they were column vectors. This takes care of the cases MM and MV.
We considered syntactic support for three other operations:
An attribute "T" will be added to the NumPy array type, such that
"m.T" is:
T
(a) transposition: A => A[j, i] for A[i, j]
(a) the transpose of "m" for a 2-dimensional array
-1
(b) inverse: A => A' such that A' * A = I (the identity matrix)
(b) the 1xN matrix transpose of "m" if "m" is a 1-dimensional
array; or
(c) solution: A/b => x such that A * x = b
A\b => x such that x * A = b
(c) a runtime error for an array with rank >= 3.
This attribute will alias the memory of the base object. NumPy's
"transpose()" function will be extended to turn built-in sequence
types into row vectors. This takes care of the VM, VD, and VO
cases. We propose an attribute because:
(a) the resulting notation is similar to the 'superscript T' (at
least, as similar as ASCII allows), and
(b) it signals that the transposition aliases the original object.
NumPy will define a value "inv", which will be recognized by the
exponentiation operator, such that "A ** inv" is the inverse of
"A". This is similar in spirit to NumPy's existing "newaxis"
value.