Second call for sponsorship and policy updates

[Proektsoftbg]

Hello mates!

We are currently working hard on the new and exciting features in Calcpad. My goal is to add advanced vector and matrix calculations this year, including:

• basic arithmetic with real and complex vectors and matrices;
• new "for" and "while" loops for by-element processing;
• pre-compiling of loop blocks for efficiency;
• search, sort, lookup, min, max and aggregate functions;
• data import from text files and spreadsheets;
• extracting and merging;
• effective implementation of special types - identity, diagonal, row/column, symmetric, triangular, banded, skyline and sparse matrices;
• bandwidth/skyline optimization;
• L1, L2, Euclidian, Lp, L∞ (Chebyshev) norms, trace and rank;
• condition numbers and preconditioning;
• determinant, transpose, conjugate transpose and inversion;
• eigenvalues and eigenvectors;
• decomposition: LU, QR, Cholesky, spectral, SVD, etc.;
• solution of systems of linear equations: Ax = B;
• solution of systems of nonlinear equations.

The list is not fixed and limited to the above features only. More ideas may come during work. Maybe in the future, also multivariable optimization, linear and nonlinear programming, differential equations, etc. All this, in the nice and friendly Calcpad environment, with Html, pdf and MS Word output.

This will be a major update for Calcpad which will bring it to another level. Currently, we are almost done with everything about vectors, but still a huge amount of work have to be done. So, we need your support.

The new thing is that, from now on, supporters will receive additional benefits. Please, go to our GitHub sponsorship profile and select a suitable tier for your needs:

https://github.com/sponsors/Proektsoftbg

[Grefron]

Really looking forward to this. I upgraded my sponsorship, the project truly deserves the support!

[Proektsoftbg]

I did some initial benchmarks of the new vector and matrix calculations in Calcpad: I created a vector with 10 000 000 elements and filled it with a value of 10m. Subtracting a scalar of 50 cm from the vector took about 0.345s.

In Mathcad, the same operation with only 10 000 elements (1000 times less) took 0.512s. This is actually about 1500 times slower.

The new features in Calcpad are being developed for efficiency and so far showed outstanding performance. And this is in case that the whole vectors/matrix is filled with values.

However, Calcpad implements efficient sparse data structures. If they are only partially filled, the zero elements are not stored in memory and not processed during calculations. Such kind of sparse data structures are very typical for FEM.

[Proektsoftbg]

Further to the previous post: How about sparse matrices/vectors performance in Calcpad?

I created two vectors a and b with size of 10 000 000 each. Then, I filled them with numbers at every 5th and 4th element, respectively up to index of 250 000 and 200 000. Finally, I calculated the sum and saved the results into a new vector c = a + b. The whole operation of creating, filling and summing the vectors took only 0.045 s!!!

I did the same in Mathcad, but with total of 50 000 elements for each vector. It took a bit more than 20s!!! I tried with 10 000 000 elements, but the program just froze. However, we can roughly estimate that it would take approx. 4000s.

With fully filled vectors, this operation takes about a second but still about 4000 times faster than Mathcad. The sparse vectors are more than 20 times faster than filled in Calcpad and about 90 000 faster than Mathcad. All this shows that using the appropriate data structures and algorithms can lead to high quality and efficient software.

I also recorded a short video with the benchmark process. Everything runs a bit slower due to the recorder overhead, but the relations are similar.

https://youtu.be/2fMNjglF95k