| Re: [eigen] How to subtract a diagonal matrix from a matrix in one expression? |
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Hi Adrien and Gael,
many thanks for checking the compiler output!
> Generally, one should not store the result of an Eigen operation
> inside an `auto` variable, unless you really want the
> _expression_-tree and you are sure that it only references
> sub-expressions which are valid as long as the _expression_ tree is
> used.
You are of course right. But I think one would be safe if one would
write
auto M2 = (M - Matrix2d(v.asDiagonal())).eval();
right?
Best regards
Alex
On 01/12/2017 04:50 PM, Christoph Hertzberg wrote:
> On 2017-01-11 17:51, Adrien Escande wrote:
>> Dear Alexander,
>>
>> if you are using fixed size matrices, I don't see any problem with having
>> temporary objects as they don't induce any memory allocation.
>> The following one-liner ther work:
>> const Matrix2d M2 = M - Matrix2d(v.asDiagonal());
>> and I guess the compiler can be quite smart to avoid any overhead.
>
> Yes, especially for small fixed sized expressions, this is often the
> case. Unfortunately, it is slightly sub-optimal here. I was trying this:
> void foo(Matrix2d& M2, const Matrix2d& M, const Vector2d& v) {
> M2 = M - Matrix2d(v.asDiagonal());
> }
>
> I'm getting something like this when compiling it with -O2:
> pxor %xmm0, %xmm0
> movaps %xmm0, (%rsp)
> movaps %xmm0, 16(%rsp)
> movsd (%rdx), %xmm0
> movsd %xmm0, (%rsp)
> movsd 8(%rdx), %xmm0
> movsd %xmm0, 24(%rsp)
> movapd (%rsi), %xmm0
> subpd (%rsp), %xmm0
> movaps %xmm0, (%rdi)
> movapd 16(%rsi), %xmm0
> subpd 16(%rsp), %xmm0
> movaps %xmm0, 16(%rdi)
>
> That means there is an actual temporary allocated (on the stack).
>
> In this case, I'm getting slightly better code when compiling with
> -DEIGEN_DONT_VECTORIZE here:
> movsd (%rsi), %xmm0
> movsd 8(%rdx), %xmm1
> subsd (%rdx), %xmm0
> movsd %xmm0, (%rdi)
> movsd 8(%rsi), %xmm0
> movsd %xmm0, 8(%rdi)
> movsd 16(%rsi), %xmm0
> movsd %xmm0, 16(%rdi)
> movsd 24(%rsi), %xmm0
> subsd %xmm1, %xmm0
> movsd %xmm0, 24(%rdi)
>
> I'm pretty sure, if M and v were known at compile time this would
> entirely be evaluated at compile time.
>
> Btw: Notice that x-0.0 can be simplified to x, whereas x+0.0 cannot,
> because (-0.0+0.0) == +0.0. (For any other x, including NaNs or inf, the
> result is x.)
>
> If one changes the _expression_ to:
> M2 = M; M2.diagonal()-=v;
> I'm getting this:
> movapd (%rsi), %xmm0
> movaps %xmm0, (%rdi)
> movapd 16(%rsi), %xmm0
> movaps %xmm0, 16(%rdi)
> movsd (%rdi), %xmm0
> subsd (%rdx), %xmm0
> movsd %xmm0, (%rdi)
> movsd 24(%rdi), %xmm0
> subsd 8(%rdx), %xmm0
> movsd %xmm0, 24(%rdi)
>
>> A a side remarks, be very mindful of the auto keyword with Eigen
>> expressions.
>> If you do
>> const auto M2 = M - Matrix2d(v.asDiagonal());
>> M2 will be a CwiseBinaryOp, not a Matrix2d, meaning that you subtraction
>> will be recomputed each time you are using M2.
>
> Actually, it is much worse in this case:
> Matrix2d(v.asDiagonal()) will be a temporary, which gets destructed
> after the assignment to M2. But the CwiseBinaryOp stored in M2 only
> holds a const reference to this temporary, therefore the _expression_
> actually becomes invalid/undefined behavior (it still sometimes works,
> because sometimes compilers delay the actual destruction of temporaries).
> Generally, one should not store the result of an Eigen operation inside
> an `auto` variable, unless you really want the _expression_-tree and you
> are sure that it only references sub-expressions which are valid as long
> as the _expression_ tree is used.
>
>
> Cheers,
> Christoph
>
>
>>
>> Best regards,
>> Adrien
>>
>> On Thu, Jan 12, 2017 at 12:44 AM, Alexander Voigt <
>> alexander..voigt@xxxxxxxxxxx-aachen.de > wrote:
>>
>>> Dear Eigen developers,
>>>
>>> is there a way to subtract a diagonal matrix (which has been constructed
>>> from a vector v using v.asDiagonal()) from a square matrix in one
>>> _expression_? (I'm asking for one _expression_, because I'd like to make
>>> the result const and avoid a temporary.)
>>>
>>> Example:
>>>
>>> =====================================================
>>> include <Eigen/Core>
>>> using namespace Eigen;
>>>
>>> int main() {
>>> Matrix<double,2,2> M;
>>> Matrix<double,2,1> v;
>>>
>>> const auto M2 = M - v.asDiagonal(); // does not compile
>>> }
>>> =====================================================
>>>
>>> The marked line yields a compiler error with g++ 4.9.2.
>>> I know that it is possible to write instead:
>>>
>>> =====================================================
>>> Matrix<double,2,2> M2(M);
>>> M2 -= v.asDiagonal(); // works
>>> =====================================================
>>>
>>> However, this latter approach has the disadvantage that M2 cannot be
>>> made const, which I'd like to achieve. An approach that works with one
>>> _expression_ would be
>>>
>>> =====================================================
>>> const Matrix<double,2,2> M2 = [&M,&v]{
>>> Matrix<double,2,2> tmp(M);
>>> tmp -= v.asDiagonal();
>>> return tmp;
>>> }();
>>> =====================================================
>>>
>>> but this has the disadvantage that it is more complicated and needs a
>>> temporary object.
>>>
>>> Many thanks and best regards,
>>> Alex
>>>
>>> --
>>> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
>>> Dr. Alexander Voigt
>>> Institute for Theoretical Particle Physics and Cosmology
>>> RWTH Aachen
>>> Sommerfeldstr. 14
>>> 52074 Aachen
>>> Room: 28A408
>>> Phone: +49 (0)241 80 27049
>>> Fax : +49 (0)241 80 22187
>>> E-Mail: alexander.voigt@xxxxxxxxxxx-aachen.de
>>> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
>>>
>>>
>>>
>>
>
--
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Dr. Alexander Voigt
Institute for Theoretical Particle Physics and Cosmology
RWTH Aachen
Sommerfeldstr. 14
52074 Aachen
Room: 28A408
Phone: +49 (0)241 80 27049
Fax : +49 (0)241 80 22187
E-Mail: alexander.voigt@xxxxxxxxxxx-aachen.de
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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