Dear all
how to make multiple element by element and result as matrix? (Function As(DB,n,i)
Thank you
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Here is an attempt from what I understood so far.
Vectorization as suggested by Terry sure is the clue, but its not so straightforward as you may think because we don't want to vectorize the elements of DB or n but just the elements of the results of the function n.s1() and A.sDB().
Here is one possible way to do it:
Additional remark: Its not necessary to vectorize the call A.sDB(DB) because the function uses DB^2 and squaring a vector is not defined in mathematics. So Prime automatically applies vectorization.
But in my opinion its good habit to apply the vectorization explicitly yourself in cases like this - just to be on the safe side in case you later change the function A.sDB.
Here is an attempt from what I understood so far.
Vectorization as suggested by Terry sure is the clue, but its not so straightforward as you may think because we don't want to vectorize the elements of DB or n but just the elements of the results of the function n.s1() and A.sDB().
Here is one possible way to do it:
Additional remark: Its not necessary to vectorize the call A.sDB(DB) because the function uses DB^2 and squaring a vector is not defined in mathematics. So Prime automatically applies vectorization.
But in my opinion its good habit to apply the vectorization explicitly yourself in cases like this - just to be on the safe side in case you later change the function A.sDB.
As I'm in a cat-skinning mood, here's another approach that uses functions to achieve the desired outcome.
Element-by-element multiplication is conventionally referred to as Hadamard (or Schur) multiplication. The attached worksheet implements it as the function hadamard and applies it to your problem. The worksheet also includes the map, zeros, ones and seq functions.
Here are the hadamard and map functions,
And here are the zeros, ones and seq functions.
Stuart
Nice, Stuart,
However there's no need to define the _one() and _zero() functions, see below:
Caution: With the 'min' function, you have to set the label of it to 'function'. Prime doesn't understand simple things...
Luc
@LucMeekes wrote:
Nice, Stuart,
However there's no need to define the _one() and _zero() functions, see below:
Caution: With the 'min' function, you have to set the label of it to 'function'. Prime doesn't understand simple things...
Luc
Hi, Luc.
Yes, I've been bitten a few times by forgetting that Prime treats min a bit differently.
The reason I use zero and one is simply to avoid having to do further operations on larger matrices ... I grew up in an era when milliseconds counted and it paid to be familiar with the number of clock cycles the processor took to perform an operation!
The real nuisance is not being able to use partial application in Prime. What I'd have done (and did do) in M15 would be to write a function like matseq(m,i,j) := i + m * j and then define a function matint(m,n) := matrix(m,n,matseq(m)) to generate a matrix of successive integers, increasing in normal Mathcad order.
Unfortunately, I can't think of a neat way of doing this in Prime Express (it would be straightforward in Prime Premium, of course, by defining a local function matrix(m,n,l(i,j)<-matseq(m,i,j)). The best I've been able to come up with is a double-matrix addition function, and a recursive replicator-adder. On the other hand, they both seem to execute as quickly as the matrix function alone, with the edge going to the recursive function for large matrices.
Anyway, enough rambling, here's a plot of the times for the two approaches to generating an all-ones matrix:
Stuart
