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Shibin_B

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07-05-2013
12:47 PM

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MKL Library Capability

We need to calculate

• Matrix Inverse

• Matrix Multiplication

• Matrix solving

Input matrix dimensions will be in the order of 10^8

We would like to know will MKL library be able to handle such inputs and calculations.

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15 Replies

SKost

Valued Contributor II

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07-05-2013
05:12 PM

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Alexander_K_Intel2

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07-06-2013
02:37 AM

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Hi Shibin,

Its look like your matrices is sparse. In case of positive answer multiplication of such matrices can be implemented via MKL SparseBlas functionality. Inverse can be implemented as solution of system with many rhs by setting instead rhs unit matrix. The typical solver of system with sparse matrix is MKL Pardiso solver - solver based on multifrontal approach. Moreover currently we investigate possibility of expanding it on clusters with distributed memory. So, on the first slight we can satisfy your requirements but it will be better if you send us test matrices to propose best way of solving it

Shibin_B

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07-06-2013
03:21 AM

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You are right our matrix is sparse.

And I am already aware that MKL Pardiso solver can solve sparse matrices efficiently.

But my concern is about the range of inputs MKL pardiso solver can handle and performance .

If you can quote something like this then it will be very much useful.

"We have solved matrix of dimensions xxx with MKL solver with xx cores and xx threads with in x time."

TimP

Black Belt

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07-06-2013
04:06 AM

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A report on performance of MKL with Florida State sparse matrices:

mecej4

Black Belt

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07-07-2013
03:52 AM

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Shibin B wrote:

If you can quote something like this then it will be very much useful.

"We have solved matrix of dimensions xxx with MKL solver with xx cores and xx threads with in x time."

I doubt that. Here is a counterexample: I could create a tridiagonal matrix (such a matrix may arise from the discretization of a problem with a single spatial dimension), and report the results that you specified, but those results would be next to useless if your problem involved two or three spatial dimensions. If one tries hard enough, one may succeed in finding a simple answer to a complex question, but the simple answer is quite likely to be wrong.

SKost

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07-07-2013
10:12 AM

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Zhang_Z_Intel

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07-07-2013
10:24 PM

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Shibin B wrote:

"We have solved matrix of dimensions xxx with MKL solver with xx cores and xx threads with in x time."

Shibin,

Look at the MKL PARDISO performance charts published on the MKL product page: http://software.intel.com/sites/default/files/Intel-MKL_Pardiso_900.png. This may answer your questions. For details (dimensions, sparsity, pattern, etc.) about the matrices used in the charts, see "The Univ. of Florida Sparse Matrix Collection" (http://www.cise.ufl.edu/research/sparse/matrices/index.html).

TimP

Black Belt

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07-08-2013
04:34 AM

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Sergey Kostrov wrote:

>>A report on performance of MKL with Florida State sparse matrices:

>>

>>http://arxiv.org/abs/1302.1078I'm not sure that the article is about MKL ( there is just one reference of the abbreviation MKL ) and it looks like the authors used some in-house implemented algorithms to test performance of Intel Xeon Phi coprocessor rather than MKL. Here is a quote:

...

The SpMV kernel isimplemented in C++ using OpenMPand processes the rows in parallel.

...

and when testing they compare performance of codes compiled with /O1 and /O3 command line options.

The paper is cryptic on the subject, but they tested both C++ OpenMP source code implementation and MKL, choosing the better of the two for quotation. Intel C++ compiler did quite well and exceeded the performance of the MKL which was available when the work was begun on both host and MIC. I'm not certain whether the final version of the paper is available on line.

OpenMP work balancing is done in the source code version by dynamic or guided schedule. Internal to MKL it is done apparently by estimating the work of each loop and dividing the work among threads. KMP_AFFINITY setting is important.

Sorry for mis-identifying Univ. of Florida.

SKost

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07-08-2013
05:29 AM

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Gennady_F_Intel

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07-08-2013
08:22 AM

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Shibin_B

Beginner

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07-08-2013
08:26 AM

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Hi Gennady,

Can you please explain how it differs from the pardiso solver in MKL?

Gennady_F_Intel

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07-09-2013
05:14 AM

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Gennady_F_Intel

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07-18-2013
12:06 AM

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Shibin, are there any interest in evaluation of this package?

Shibin_B

Beginner

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07-18-2013
12:26 AM

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I did some evaluation of MKL library. I was able to solve sparse matrices of dimension - 2.5 x 10^7 with in 12 Minutes.

System Spec - intel i7 quad core, 12 GB ram,

Mr Fedorov,

We decided to use MKL library. But my project is stalled till September. So license will be purchased only then. It will be better if you can provide me the details about licensing in the mean time.

Gennady_F_Intel

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07-18-2013
12:49 AM

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that's perfect if you was able to solve 2.5 x 10^7 case. MPI version will allow to solve much larger cases.

regard to license: I have asked my teammate to help you with this information.

For more complete information about compiler optimizations, see our Optimization Notice.