corrected inverse_exact

[shahsaurabh0605]

NMatrix#inverse_exact was not correctly implemented in math.cpp. I solved this problem. Please review this and suggest if there is anything more to add.

[shahsaurabh0605]

Can you be more specific on how it could be more efficient?

[translunar]

@shahsaurabh0605 Sure. It seems like you're declaring a lot of temporary variables when you could just be writing directly. They may be optimized out for some dtypes, but I'm not sure if that's the case for others.

[shahsaurabh0605]

@MohawkJohn See the thing is inverse_exact won't give correct outputs if those temporary variables are not declared. Just using the array, removing temporary variables won't work.

[translunar]

I don't see why that should be the case. For example, you do this:

DType i1= A[2*lda+2];
DType i2 = i1;
B[1]      = (- A[1]     * i2 + A[2]     * h2) / det;
DType i3=i2;
B[ldb]    = (- d1   * i2 + f2 * g1)   / det; // B = -di + fg
B[ldb+1]  = (  a1     * i3 - c2     * g2)   / det; // E = ai - cg

You're creating a lot of unnecessary copies of i1. Why?

[shahsaurabh0605]

@MohawkJohn you were correct. I have to use the local variables only once. Made the required changes in the code.

[translunar]

I'm looking at this and still don't see why you need temporary variables at all.

[shahsaurabh0605]

Actually why do we need a different array B at all! What if the result is computed itself in array A and the output shown. This could save a lot of space and will be more efficient. I have made the code ready which is using just array A to return the result.

[translunar]

You need B because the operation is destructive.