Re: [eigen] How to subtract a diagonal matrix from a matrix in one expre

On Thu, Jan 12, 2017 at 4:50 PM, Christoph Hertzberg <chtz@xxxxxxxxxxxxxxxxxxxxxxxx> 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.

Depends a lot on the compiler, with clang 3.9 -O3:

M2 = M - Matrix2d(v.asDiagonal());

movsd (%rdx), %xmm0

movsd 8(%rdx), %xmm1

pslldq $8, %xmm1

movapd (%rsi), %xmm2

subpd %xmm0, %xmm2

movapd %xmm2, (%rdi)

movapd 16(%rsi), %xmm0

subpd %xmm1, %xmm0

movapd %xmm0, 16(%rdi)

M2 = M; M2.diagonal()-=v;

movapd (%rsi), %xmm0

movapd %xmm0, (%rdi)

movapd 16(%rsi), %xmm1

movapd %xmm1, 16(%rdi)

subsd (%rdx), %xmm0

movsd %xmm0, (%rdi)

shufpd $1, %xmm1, %xmm1

subsd 8(%rdx), %xmm1

movsd %xmm1, 24(%rdi)

Yes, clang is pretty good at understanding intrinsics and re-vectorizing them.

gael

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

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Dr. Alexander Voigt
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--
Dipl. Inf., Dipl. Math. Christoph Hertzberg

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