Extensions of the matrix interpreter (June-August 1999)
The code of many matrix operations has been optimized.
Certain functions are 2-5 times faster than earlier.
MAT QR OF A TO Q,R
makes the QR decomposition by the Householder transformations.
MAT B=SUB(A,Srow,Scol) selects a submatrix of A with rows indicated by
vector Srow and columns indicated by Scol.
MAT C=SELECT(A,k) selects those rows of A where the element in the k'th
column is not 0.
MAT #MAXDET(C,dim,S)
finds the principal dim*dim submatrix with the maximal determinant from
a symmetric matrix C. Indices of rows (and columns) belonging to that
submatrix are saved as a column vector S.
This operation can be applied, for example for determination of
the basis of the column space of a matrix and for selection of
the most representative subset of columns of a matrix.
The algorithms and potential applications are explained in
S. Mustonen: Matrix computations in Survo
(www.helsinki.fi/survo/matrix99.html).
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