Numpy and Scipy: Using Sparse Matrices to Speed up Calculations (part 1)

In response to a comment on the videos dealing with Monte Carlo models of stocks market movement, and how to calculate the probability of making 50% of max profit on an options trade, I want to revisit some of the concepts presented in those videos. In particular the concept of linear systems which can be represented by matrix equations where the coefficient matrix is sparse. I will go through the calculations used in these videos and show, step-by-step, how the matrices involved are generated. This will be part one of three where we show how sparse matrices and linear algebra are used to speed up calculations. Part two will deal with solving a partial differential equation. Part three will return to to the matrices used in the Monte Carlo calculation.
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[@0mon0zz]

Good vid! But what about solving a system of non-linear equations that have large sparse matrices?

[@AJ-et3vf]

Thank you so much for this. Very useful.

[@RajeshSingh-hx2sc]

But at 8:43, Ainv is not really an identity matrix, right? (since, its non diagonal elements are not zeros) Or Am I missing something?

[@fai212]

Yes they are, all of them have a value very very very close to zero which means 0. I think the reason is because of the computer.

[@kpmooney]

There are always rounding errors involved. The off-diagonals are essentially zero within machine precision.

[@hardikkharel3519]

can we do it in any ide without juypter notebook?

[@kpmooney]

Yes, of course. Copy and paste the code into an editor.

[@adamfit9158]

What about sparse matrix + sparse matrix

[@kpmooney]

Yes, you can do that.