The best free cross-platform library for a higher level Matrix, Vector and especially. SparseMatrix Operations?

Question

Our platforms:

• Windows, Linux, Mac OSX.

Free:

• LGPL compatible

Support for high-level operations:

• Eigensystems, SVD, QR, LU, reverse, pseudo-reverse (so-called Moore-Penrose reverse), ...

It supports many types of matrices, as well as good performing small matrices, for example. 3x3:

• Rare, symmetric, ... (as well as operations on them !, for example, pseudoInverse ())

And of course it should be

• EFFECTIVE
• active development in recent months

It would be nice to link LAPACK, MKL, ATLAS, etc. again.

, , - Armadillo, . Eigen3 , - ( ).

:

• newmat11, boost:: uBlas, gsl, IT ++

Answer 1

! , boost:: ublas, C = A * B C = prod (A, B), ublas, , ublas.

Answer 2

Eigen3 , . , Cholesky .

Answer 3

NewMat11 - , (Eigensystems, SVD, QR, LU, ). :

Matrix M(numRows,numCols);
M << array;

:

M.element(i,j);

:

M.t();

:

M.i();

*:

M*M

, : SVD, QR, LU ..

(Moore-Penrose) , , :

if row> col, then the pseudo-inverse (least squares solution) can be calculated as: M_PseudoInv = (M ^T M) ^-1 M ^T

if the string is <col, then the pseudo-inverse (the solution of the smallest norm) can be calculated as: M_PseudoInv = M ^T (MM ^T ) ^-1