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digitalmars.D - Einstein summation

reply =?iso-8859-1?q?Knud_S=F8rensen?= <knud NetRunner.all-technology.com> writes:
Hi

I am new to D. 

But I think is is very promising.

While it have better support for arrays than c/c++;

There is sill space for improvements.

I will suggests build in support for Einstein summation!

That is automatic summation over the same indexes. 
 
index[3] i,j,k; // 3 dimensional indexes.

double[3] v,v1,v2;

double[3][3] m;

// dot product

p=v[k]*v[k];

// Vector & Matrix multiplication.

v2[i]=m[i][k]*v1[k];

// transposing a matrix is also easy 
// just switch the indexes.

v2[i]=m[k][i]*v1[k];

// trace of matrix

tr = m[i][i];

// quadratic forms

q=v[i]*m[i][k]*v[k];


// cross product.

v[i]=P(i,j,k)*v1[j]*v2[k];

// P(i,j,k) is the permutation tensor  

etc.
see 
http://mathworld.wolfram.com/EinsteinSummation.html


Because this notation don't dictate a specials order of execution
it should be possible for the compiler to parallelize this code 
for MMX,FPGA's and GPU's.
May 02 2004
parent reply resistor AT nospam DOT mac DOT com <resistor_member pathlink.com> writes:
I'm not sure how desirable it would be to have such specialized syntax in the
core language, but you'll 
be glad to know that with D's operator overloading it should be fairly simple to
write classes to work 
exactly like that.

Owen

In article <pan.2004.05.02.21.20.02.48217 NetRunner.all-technology.com>,
=?iso-8859-1?q?
Knud_S=F8rensen?= says...
Hi

I am new to D. 

But I think is is very promising.

While it have better support for arrays than c/c++;

There is sill space for improvements.

I will suggests build in support for Einstein summation!

That is automatic summation over the same indexes. 
 
index[3] i,j,k; // 3 dimensional indexes.

double[3] v,v1,v2;

double[3][3] m;

// dot product

p=v[k]*v[k];

// Vector & Matrix multiplication.

v2[i]=m[i][k]*v1[k];

// transposing a matrix is also easy 
// just switch the indexes.

v2[i]=m[k][i]*v1[k];

// trace of matrix

tr = m[i][i];

// quadratic forms

q=v[i]*m[i][k]*v[k];


// cross product.

v[i]=P(i,j,k)*v1[j]*v2[k];

// P(i,j,k) is the permutation tensor  

etc.
see 
http://mathworld.wolfram.com/EinsteinSummation.html


Because this notation don't dictate a specials order of execution
it should be possible for the compiler to parallelize this code 
for MMX,FPGA's and GPU's.

May 02 2004
parent reply School <itsnotvalid-news yahoo.com.hk> writes:
resistor AT nospam DOT mac DOT com :

 I'm not sure how desirable it would be to have such specialized syntax in the
 core language, but you'll 
 be glad to know that with D's operator overloading it should be fairly simple
to
 write classes to work 
 exactly like that.
 
 Owen
 
 In article <pan.2004.05.02.21.20.02.48217 NetRunner.all-technology.com>,
 =?iso-8859-1?q?
 Knud_S=F8rensen?= says...
 
Hi

I am new to D. 

But I think is is very promising.

While it have better support for arrays than c/c++;

There is sill space for improvements.

I will suggests build in support for Einstein summation!

That is automatic summation over the same indexes. 

index[3] i,j,k; // 3 dimensional indexes.

double[3] v,v1,v2;

double[3][3] m;

// dot product

p=v[k]*v[k];

// Vector & Matrix multiplication.

v2[i]=m[i][k]*v1[k];

// transposing a matrix is also easy 
// just switch the indexes.

v2[i]=m[k][i]*v1[k];

// trace of matrix

tr = m[i][i];

// quadratic forms

q=v[i]*m[i][k]*v[k];


// cross product.

v[i]=P(i,j,k)*v1[j]*v2[k];

// P(i,j,k) is the permutation tensor  

etc.
see 
http://mathworld.wolfram.com/EinsteinSummation.html


Because this notation don't dictate a specials order of execution
it should be possible for the compiler to parallelize this code 
for MMX,FPGA's and GPU's.


designed to meet maths problems but meets any kind of problems. If you are interested in making a library for that, we are happy to download it and use it :-D.
May 03 2004
parent =?iso-8859-1?q?Knud_S=F8rensen?= <knud NetRunner.all-technology.com> writes:
On Mon, 03 May 2004 21:44:11 +0800, School wrote:
 resistor AT nospam DOT mac DOT com:
 
 I'm not sure how desirable it would be to have such specialized syntax in the
 core language, but you'll 
 be glad to know that with D's operator overloading it should be fairly simple
to
 write classes to work 
 exactly like that.
 
 Owen


The Einstein summation is not a specialization but a generalization of vector, matrix and tensor operations. Which is more used in programing than complex numbers, and thus d got all ready. How it is possible to tell the compiler how it should optimize on overloaded operators ????


designed to meet maths problems but meets any kind of problems. If you are interested in making a library for that, we are happy to download it and use it :-D.

No, but D is a programing language like FORTRAN. And FORTRAN is still a preferred language to use for scientific calculations. The reason is that FORTRAN have build in support for operations on arrays, and this make it possible for the FORTRAN compiler to make better use of the hardware. I think that making Einstein summation available in D will make it easier to specify complex calculations and make it better suited to replace FORTRAN in scientific computing. You might take a look at http://www.ii.uib.no/~krister/EinSum/ I don't think that D need the upper/lower notation he use. Knud
May 04 2004