Prime 3.1 Column vs Row operator performance difference?

[StuartBruff]

In the thread Re: Similar to vector matrix product, but different… the poster put the return value from a program inside the loop, which you don't normally see.

Out of idle curiosity, I wondered if it had any effect on Mathcad's performance by doing this rather than placing the return value outside of the loop.   I also wondered what effect using the Prime row operator would make and doing without the vectorized multiplication.  What I found rather surprised me, in that the row operator method was considerably faster than the original column method.   I looked at doing array expansion by replicating a column-wise to conform with b and then doing Hademard (element-by-element) multiplication.   I also tried transposing b, multiplying each "column" by its corresponding vector element and then transposing the result.  This is what I found (on an i7 with 8 GiB RAM running Windows 10).

I was surprised to see that the row operator method was so quick.  I wonder if the internal order of array storage is row-wise rather than column-wise (which I'd kind of expect given that Mathcad deals with column vectors)?  I also did the same test (minus the row operator) in Mathcad M15 M040 and got the following result ... considerably slower in all cases and not much to choose between them.

Stuart

[StuartBruff]

StuartBruff wrote:

In the thread Re: Similar to vector matrix product, but different… the poster put the return value from a program inside the loop, which you don't normally see.

Out of idle curiosity, I wondered if it had any effect on Mathcad's performance by doing this rather than placing the return value outside of the loop.   I also wondered what effect using the Prime row operator would make and doing without the vectorized multiplication.  What I found rather surprised me, in that the row operator method was considerably faster than the original column method.   I looked at doing array expansion by replicating a column-wise to conform with b and then doing Hademard (element-by-element) multiplication.   I also tried transposing b, multiplying each "column" by its corresponding vector element and then transposing the result.  This is what I found (on an i7 with 8 GiB RAM running Windows 10).

I was surprised to see that the row operator method was so quick.  I wonder if the internal order of array storage is row-wise rather than column-wise (which I'd kind of expect given that Mathcad deals with column vectors)?  I also did the same test (minus the row operator) in Mathcad M15 M040 and got the following result ... considerably slower in all cases and not much to choose between them.

Mystery solved and its' not really a mystery.   The array storage does indeed appear to be columnwise.  However, it takes time to extend an existing array and this is what's happening as the for loops iterate through the columns.  At each iteration, a new column is added to A and Mathcad spends time doing this.

However, when operating on rows, Mathcad Prime appears to be more efficient at creating the necessary memory (even though (for a square array) the same number of elements are added).  I don't know why this should be.

A standard Mathcad method of improving execution time when creating large arrays is to predefine the array; this means that Mathcad merely has to replace elements of the array rather than extend it, and this is a quicker operation.   The easy way to check this is to reverse the order of iterating across the columns.  As can be seen, this results in a significant reduction in execution time for the column operations.

Mathcad 15: (r = reverse column indexing version)

Prime 3.1

Stuart

[tslewis]

Thanks for this. I have also investigated your worksheet further and you can get much improved performance almost identical to iterating backwards form end of column to start by intially assigning the size of the array prior to filling it in. I tested your example and I get almost identical speed. This gives massive speed increase. This seems to be consistent with what others have reported and what is documented in the official mathcad prime help - it recommends not to allow mathcad to dynamically resize arrays and instead size them statically. This has massive impact on memory usage.

[MarcoEvangelosB]

I confirm. For a large array you can have good performances by allocating first the storage an then processing.

You can do that in programming block. You just need to set a value for the last member of the vector (or matrix) (usually I set this to zero).

This is true for Mathcad 14 (and 15 I guess).

Now I'm finally moving to Prime! It took years to have a version working with Italian keyboards (not supported properly up to 3.1). But now it seems to work and I've just downloaded the trial. 🙂

[tslewis]

Has anybody checked the speed when using the matrix function where a function can be used to define the elements of a matrix, where the arguments of the matrix function include setting the size of the array? I like this way of assigning an areay than assigning elements through a for loop - it’s much cleaner and more concise

[tslewis]

Has anybody checked the speed when using the matrix function where a function can be used to define the elements of a matrix, where the arguments of the matrix function include setting the size of the array? I like this way of assigning an areay than assigning elements through a for loop - it’s much cleaner and more concise