63 lines
1.8 KiB
Factor
Executable File
63 lines
1.8 KiB
Factor
Executable File
! Copyright (C) 2005, 2009 Slava Pestov.
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! See http://factorcode.org/license.txt for BSD license.
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USING: arrays kernel math math.order math.vectors
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sequences sequences.private accessors columns ;
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IN: math.matrices
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! Matrices
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: zero-matrix ( m n -- matrix )
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[ nip 0 <array> ] curry map ;
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: identity-matrix ( n -- matrix )
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#! Make a nxn identity matrix.
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dup [ [ = 1 0 ? ] with map ] curry map ;
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! Matrix operations
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: mneg ( m -- m ) [ vneg ] map ;
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: n*m ( n m -- m ) [ n*v ] with map ;
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: m*n ( m n -- m ) [ v*n ] curry map ;
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: n/m ( n m -- m ) [ n/v ] with map ;
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: m/n ( m n -- m ) [ v/n ] curry map ;
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: m+ ( m m -- m ) [ v+ ] 2map ;
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: m- ( m m -- m ) [ v- ] 2map ;
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: m* ( m m -- m ) [ v* ] 2map ;
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: m/ ( m m -- m ) [ v/ ] 2map ;
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: v.m ( v m -- v ) flip [ v. ] with map ;
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: m.v ( m v -- v ) [ v. ] curry map ;
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: m. ( m m -- m ) flip [ swap m.v ] curry map ;
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: mmin ( m -- n ) [ 1/0. ] dip [ [ min ] each ] each ;
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: mmax ( m -- n ) [ -1/0. ] dip [ [ max ] each ] each ;
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: mnorm ( m -- n ) dup mmax abs m/n ;
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<PRIVATE
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: x ( seq -- elt ) first ; inline
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: y ( seq -- elt ) second ; inline
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: z ( seq -- elt ) third ; inline
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: i ( seq1 seq2 -- n ) [ [ y ] [ z ] bi* * ] [ [ z ] [ y ] bi* * ] 2bi - ;
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: j ( seq1 seq2 -- n ) [ [ z ] [ x ] bi* * ] [ [ x ] [ z ] bi* * ] 2bi - ;
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: k ( seq1 seq2 -- n ) [ [ y ] [ x ] bi* * ] [ [ x ] [ y ] bi* * ] 2bi - ;
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PRIVATE>
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: cross ( vec1 vec2 -- vec3 ) [ i ] [ j ] [ k ] 2tri 3array ;
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: proj ( v u -- w )
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[ [ v. ] [ norm-sq ] bi / ] keep n*v ;
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: (gram-schmidt) ( v seq -- newseq )
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[ dupd proj v- ] each ;
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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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: cross-zip ( seq1 seq2 -- seq1xseq2 )
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[ [ 2array ] with map ] curry map ; |