MATINV Fast inversion of arrays of small matrices. MATINV is a low-level function called by POLYSMOOTH. Let MAT be an array of K different M x M matrices A1,A2,...,AK. INV=MATINV(MAT) then returns an array of N inverse matrices. If MAT has dimensions K1 x K2 x .... M x M, then MATINV returns an array of the same size containing the inverses of the M x M matrices. For example, MAT could be 10 x 10 x 4 x 4, in which case the inverses of one hundred 4 x 4 matrices are found. MAT can have any dimensionality so long as the matrices to be inverted occupy the last two dimensions. The last dimension is interpreted as "columns" and the second to last as "rows." Note that MATINV only works matrices with M=2 through M=6. ____________________________________________________________ Algorithms MATINV can use either of two different algorithms. This is specified with INV=MATINV(MAT,STR). MATINV(MAT,'direct') uses algebraic expressions for 2 x 2 and 3 x 3 matrix inverses together with Boltz's block diagonal recursion formula. For details, see the following links http://mathworld.wolfram.com/MatrixInverse.html http://en.wikipedia.org/wiki/Invertible_matrix. MATINV(MAT,'loop') uses Matlab's INV function together with a straightforward loop. The direct algorithm, which is the default, can be much faster when MAT is large and the dimension to be inverted is small. ____________________________________________________________ See also MATMULT. 'matinv --t' runs some tests. Usage: inv=matinv(mat); __________________________________________________________________ This is part of JLAB --- type 'help jlab' for more information (C) 2008--2015 J.M. Lilly --- type 'help jlab_license' for details