111 lines
2.7 KiB
Factor
111 lines
2.7 KiB
Factor
! Copyright (C) 2006, 2007 Slava Pestov.
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! See http://factorcode.org/license.txt for BSD license.
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IN: matrices
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USING: kernel math namespaces parser sequences ;
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SYMBOL: matrix
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: with-matrix ( matrix quot -- )
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[ swap matrix set call matrix get ] with-scope ; inline
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: nth-row ( row# -- seq ) matrix get nth ;
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: change-row ( row# quot -- | quot: seq -- seq )
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matrix get swap change-nth ; inline
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: exchange-rows ( row# row# -- ) matrix get exchange ;
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: rows ( -- n ) matrix get length ;
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: cols ( -- n ) 0 nth-row length ;
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: first-col ( row# -- n )
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#! First non-zero column
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0 swap nth-row [ zero? not ] skip ;
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: clear-scale ( col# pivot-row i-row -- n )
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>r over r> nth dup zero? [
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3drop 0
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] [
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>r nth dup zero? [
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r> 2drop 0
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] [
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r> swap / neg
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] if
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] if ;
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: (clear-col) ( col# pivot-row i -- )
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[ [ clear-scale ] 2keep >r n*v r> v+ ] change-row ;
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: rows-from ( row# -- slice )
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rows dup <slice> ;
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: clear-col ( col# row# rows -- )
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>r nth-row r> [ >r 2dup r> (clear-col) ] each 2drop ;
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: do-row ( exchange-with row# -- )
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[ exchange-rows ] keep
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[ first-col ] keep
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dup 1+ rows-from clear-col ;
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: find-row ( row# quot -- i elt )
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>r rows-from r> find ; inline
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: pivot-row ( col# row# -- n )
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[ dupd nth-row nth zero? not ] find-row 2nip ;
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: (echelon) ( col# row# -- )
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over cols < over rows < and [
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2dup pivot-row [ over do-row 1+ ] when*
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>r 1+ r> (echelon)
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] [
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2drop
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] if ;
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: echelon ( matrix -- matrix' )
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[ 0 0 (echelon) ] with-matrix ;
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: nonzero-rows [ [ zero? ] all? not ] subset ;
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: null/rank ( matrix -- null rank )
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echelon dup length swap nonzero-rows length [ - ] keep ;
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: leading ( seq -- n ) [ zero? not ] find drop ;
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: reduced ( matrix' -- matrix'' )
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[
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rows <reversed> [
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dup nth-row leading
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dup 0 >= [ swap dup clear-col ] [ 2drop ] if
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] each
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] with-matrix ;
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: basis-vector ( row col# -- )
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>r clone r>
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[ swap nth neg recip ] 2keep
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[ 0 swap rot set-nth ] 2keep
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>r n*v r>
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matrix get set-nth ;
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: nullspace ( matrix -- seq )
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echelon reduced dup empty? [
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dup first length identity-matrix [
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[
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dup leading
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dup 0 >= [ basis-vector ] [ 2drop ] if
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] each
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] with-matrix flip nonzero-rows
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] unless ;
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: proj ( v u -- w )
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[ [ v. ] keep norm-sq / ] keep n*v ;
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: (gram-schmidt) ( v seq -- newseq )
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dupd [ proj v- ] each-with ;
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: gram-schmidt ( seq -- orthogonal )
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V{ } clone [ over (gram-schmidt) over push ] reduce ;
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: norm-gram-schmidt ( seq -- orthonormal )
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gram-schmidt [ normalize ] map ;
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