import Miranda 2.066 from upstream

1 files changed, 70 insertions, 0 deletions

diff --git a/miralib/ex/matrix.m b/miralib/ex/matrix.m
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+||very simple matrix package (DT)
+||note that to include this in one of your own scripts, you can say
+||	%include <ex/matrix>
+
+%export matrix idmat matadd matsub matmult scalmult mkrow mkcol det
+        adjoint inv
+
+matrix == [[num]]
+
+idmat :: num->matrix ||identity matrix of given size
+idmat n = [[delta i j|j<-[1..n]]|i<-[1..n]]
+          where
+	  delta i j = 1, if i=j
+		    = 0, otherwise
+
+matadd :: matrix->matrix->matrix
+matadd x y = map2 vadd x y
+             where
+	     vadd x y = map2 (+) x y
+
+matsub :: matrix->matrix->matrix
+matsub x y = map2 vsub x y
+             where
+	     vsub = map2 (-)
+
+matmult :: matrix->matrix->matrix
+matmult x y = outer inner x (transpose y)  ||*
+inner x y = sum (map2 (*) x y)
+outer f x y = [[f a b|b<-y]|a<-x]
+
+||*note that transpose is already defined in the standard environment
+
+scalmult :: num->matrix->matrix ||multiply a matrix by a scalar
+scalmult n x = map (map (*n)) x
+
+mkrow :: [num]->matrix ||make vector into matrix with a single row
+mkrow x = [x]
+
+mkcol :: [num]->matrix ||make vector into matrix with a single column
+mkcol x = map (:[]) x
+
+det :: matrix->num ||determinant, of square matrix
+det [[a]] = a
+det xs = sum [xs!0!i*cofactor 0 i xs|i<-index xs], if #xs=#xs!0
+       = error "det of nonsquare matrix", otherwise
+cofactor i j xs = (-1)^(i+j) * det (minor i j xs)
+minor i j xs = [omit j x | x<-omit i xs]
+omit i x = take i x ++ drop (i+1) x
+
+adjoint :: matrix->matrix ||adjoint, of square matrix
+adjoint xs = transpose[[cofactor i j xs | j<-index xs] | i <- index xs]
+
+inv :: matrix->matrix ||inverse, of non-singular square matrix
+inv xs = transpose[[cofactor i j xs/h | j<-index xs] | i <- index xs]
+	 where
+	 h = det xs
+||The above is a literal transcription of the mathematical definition of
+||matrix  inverse.   A  less  naive version of the package would rewrite
+||this to use Gaussian elimination.
+
+||a few test matrices (these are not exported from the script, but  will
+||be in scope if this is your current script)
+a = [[1,2],[3,4]]
+b = [[1,1,1],[1,2,3],[2,4,8]]
+c = [[0,1,2,3],[1,2,3,4],[2,3,4,0],[3,4,0,1]]
+i2 = idmat 2
+i3 = idmat 3
+i4 = idmat 4
+
+test = matmult b (inv b)