topic Re: cross product function in Intel® oneAPI Math Kernel Library

cross product function

kooka — Fri, 08 May 2009 03:52:25 GMT

is the first time I try to use MKL, im confused and kind of frustrated because I am searching a cross product and ROTATION MATRIX subrutine and cant find it, i will thank if someone can tell me what MKL function can help me.

Regards!

Re: cross product function

crispybits — Sun, 10 May 2009 02:39:00 GMT

I don't see cross product either, it might be because it's only defined for 3 dimensions, while most MKL functions are for more general n-dimensions.

You might look at the wikipedia page for cross product, under "Conversion to Matrix Multiplication". You can store one vector as a 3x3 matrix then do a matrix-vector multiply using one of the BLAS level 2 functions in MKL.

For rotation matrices, can't you just construct them yourself then use MKL to apply them?

If you're after speed, I'd look to see if graphics cards can do these things in hardware.

Quoting - kooka

Re: cross product function

Gennady_F_Intel — Sun, 10 May 2009 18:27:12 GMT

Quoting - kooka

kooka,
I am just interested what are the typical sizes of vectors and matrices you are working with?
--Gennady

Re: cross product function

jay_oswald — Mon, 11 May 2009 20:52:26 GMT

Quoting - kooka

If you are using C++, I wrote this code to construct a rotation matrix that makes a right-handed rotation about a normal vector.

Regards,

Jay

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#include
#include

typedef float Real;

// computes a 3x3 rotation matrix
void compute_R_3x3(Real *v, Real a, Real *R);

// test program
int main()
{
// v is a normal vector that is the axis of rotation
Real v[3] = {0.0, 0.0, 1.0};
// a is the angle (in radians) that you rotate about v (right-handed)
Real a = (45.0/180.0)*acos(-1.0);
// 3x3 matrix (column-major) - pre-initialized for debug purposes
Real R[] = {99.9, 99.9, 99.9, 99.9, 99.9, 99.9, 99.9, 99.9, 99.9};
// call the rotation matrix function
compute_R_3x3(v, a, R);
// output the matrix to console
for (int i=0; i<3; i++) std::cout<<<'t'< return 0;
}

// computes a 3x3 rotation matrix
void compute_R_3x3(Real *v, Real a, Real *R)
{
const Real eijk[2] = {-1.0, 1.0}; // permutation value
const Real COSa=cos(a), SINa=sin(a);
for (int i=0; i<3; i++){
const double cv = (1.0 - COSa) * v;
R = cv*v[0];
R[i+3] = cv*v[1];
R[i+6] = cv*v[2];
R[4*i] += COSa;
int j = (i&1)+(i!=2); // computes cyclic permutation of i
R[i+3*j] -= SINa*v[3-i-j]*eijk[i-j+3*(j>i)-1];
j = (j&1)+(j!=2); // compute(i-j+3*(j>i))-1s cyclic permutation of j
R[i+3*j] -= SINa*v[3-i-j]*eijk[i-j+3*(j>i)-1];
}
}
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Re: cross product function

kooka — Mon, 11 May 2009 21:20:24 GMT

Quoting - Gennady Fedorov (Intel)

kooka,
I am just interested what are the typical sizes of vectors and matrices you are working with?
--Gennady

3 size vector and 3 by 3 matrices

Re: cross product function

kooka — Mon, 11 May 2009 21:23:49 GMT

Quoting - kallog

thanks, i think it will help

Re: cross product function

Gennady_F_Intel — Mon, 18 May 2009 04:51:30 GMT

kooka,
this is very inefficient to use MKL for such small inputs because of MKL mainly oriented on the task size much bigger then 3x3 you are using.
I'd recommend you to use another library - Intel^{Integrated Performance Primitives (Intel IPP), aka IPP.}

Please refer to the ippmman.pdf ( Small matrix ) manual and you can find there all needed routines.

The main advantage of IPP's small matrix functionality - these functions is highly optimized for the inputs you needed.
--Gennady