#5974: [with patch; needs review] the generic linear_combination_of_rows and
linear_combination_of_columns functions for matrices are very stupidly
slotch
----------------------------+-----------------------------------------------
Reporter: was | Owner: was
Type: defect | Status: new
Priority: major | Milestone: sage-4.0
Component: linear algebra | Keywords:
----------------------------+-----------------------------------------------
Old description:
> Behold. By replacing about 40 confusing lines by 2 trivial lines, I get
> a *speedup* by more than a factor of 10!
>
> {{{
> BEFORE:
> sage: A = random_matrix(QQ,50)
> sage: v = [1..50]
> sage: timeit('A.linear_combination_of_rows(v)')
> 125 loops, best of 3: 5.48 ms per loop
>
> AFTER:
> sage: A = random_matrix(QQ,50)
> sage: v = [1..50]
> sage: timeit('A.linear_combination_of_rows(v)')
> 625 loops, best of 3: 503 µs per loop
>
> }}}
New description:
Behold. By replacing about 40 confusing lines by 2 trivial lines, I get a
*speedup* by more than a factor of 10!
{{{
BEFORE:
sage: A = random_matrix(QQ,50)
sage: v = [1..50]
sage: timeit('A.linear_combination_of_rows(v)')
125 loops, best of 3: 5.48 ms per loop
AFTER:
sage: A = random_matrix(QQ,50)
sage: v = [1..50]
sage: timeit('A.linear_combination_of_rows(v)')
625 loops, best of 3: 503 µs per loop
}}}
We also uncover several bugs in matrix multiply, which this patch also
fixes.
--
Comment(by was):
I ran a fulldoctest cycle with this patch applied and found yet another
serious bug in matrix multiplication (not caused by this patch, but
uncovered by it). E.g., in vanilla released 3.4.1, some multiplies of
cyclotomic matrices just go boom!
{{{
wst...@sage:~$ sage
----------------------------------------------------------------------
| Sage Version 3.4.1, Release Date: 2009-04-21 |
| Type notebook() for the GUI, and license() for information. |
----------------------------------------------------------------------
sage: K.<zeta6>=CyclotomicField(6); matrix(K,1,2) * matrix(K,2,[0, 1, 0,
-2*zeta6, 0, 0, 1, -2*zeta6 + 1])
---------------------------------------------------------------------------
IndexError Traceback (most recent call
last)
/scratch/wstein/sage/temp/sage.math.washington.edu/15110/_scratch_wstein_sage_init_sage_0.py
in <module>()
/home/wstein/sage/local/lib/python2.5/site-
packages/sage/structure/element.so in
sage.structure.element.Matrix.__mul__ (sage/structure/element.c:11263)()
/home/wstein/sage/local/lib/python2.5/site-
packages/sage/structure/coerce.so in
sage.structure.coerce.CoercionModel_cache_maps.bin_op
(sage/structure/coerce.c:5396)()
/home/wstein/sage/local/lib/python2.5/site-packages/sage/matrix/action.so
in sage.matrix.action.MatrixMatrixAction._call_
(sage/matrix/action.c:2485)()
/home/wstein/sage/local/lib/python2.5/site-
packages/sage/matrix/matrix_cyclo_dense.so in
sage.matrix.matrix_cyclo_dense.Matrix_cyclo_dense._matrix_times_matrix_
(sage/matrix/matrix_cyclo_dense.cpp:5674)()
/home/wstein/sage/local/lib/python2.5/site-
packages/sage/matrix/matrix_integer_dense.so in
sage.matrix.matrix_integer_dense._lift_crt
(sage/matrix/matrix_integer_dense.c:32188)()
IndexError: list index out of range
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5974#comment:2>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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