How many floating point operations are required for the function "pinv"?

i want to find pinv of complex correlation matrix of NXN how many addition ,multiplication are required of the number of floating Counts or flops?

[James Tursa]

What do you intend to do with this information? Would timing with tic & toc be more meaningful to you?

[Vanita Pawar]

Thank you for your reply. I want to know the actual computational count required for pinv() command.

Answer 1

[Steven Lord]

Read this Cleve's Corner article, particularly the last three paragraphs.

[Vanita Pawar]

Thank you so much Steven. U answered my question.

Answer 2

[Walter Roberson]

Is the question about pinv() as implemented by Mathworks, or is the question about how efficiently a Moore-Penrose Pseudo-Inverse could be done in theory? If you are talking about algorithmic complexity rather than about implementation then see http://cs.stackexchange.com/questions/24060/complexity-of-finding-the-pseudoinverse-matrix

[Vanita Pawar]

Thank you for your answer.

Yes, pinv() as implemented by Mathworks. I want to know the actual computational count required for pinv() command.

[Walter Roberson]

It is not possible to measure that on any modern processor. It has been fundamentally unmeasurable since the introduction of the MIPS R8000 in 1994, which introduced conditional movements and out-of-order execution; the 1996 introduction of the MIPS R10000 chip especially made it really impossible.

For example on modern Intel architectures you need to worry about how to count operations coded as Multiply And Add instructions, or coded as HADDPD (Packed Double-Floating Point Horizontal Add).

The closest you can get is a Cycle Counter. But that is pretty unreliable; see https://software.intel.com/en-us/node/561442