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diff --git a/src/algebra/matstor.spad.pamphlet b/src/algebra/matstor.spad.pamphlet new file mode 100644 index 00000000..f34f9e29 --- /dev/null +++ b/src/algebra/matstor.spad.pamphlet @@ -0,0 +1,246 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/algebra matstor.spad} +\author{Clifton J. Williamson} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\section{package MATSTOR StorageEfficientMatrixOperations} +<<package MATSTOR StorageEfficientMatrixOperations>>= +)abbrev package MATSTOR StorageEfficientMatrixOperations +++ Author: Clifton J. Williamson +++ Date Created: 18 July 1990 +++ Date Last Updated: 18 July 1990 +++ Basic Operations: +++ Related Domains: Matrix(R) +++ Also See: +++ AMS Classifications: +++ Keywords: matrix, linear algebra +++ Examples: +++ References: +++ Description: +++ This package provides standard arithmetic operations on matrices. +++ The functions in this package store the results of computations +++ in existing matrices, rather than creating new matrices. This +++ package works only for matrices of type Matrix and uses the +++ internal representation of this type. +StorageEfficientMatrixOperations(R): Exports == Implementation where + R : Ring + M ==> Matrix R + NNI ==> NonNegativeInteger + ARR ==> PrimitiveArray R + REP ==> PrimitiveArray PrimitiveArray R + + Exports ==> with + copy_! : (M,M) -> M + ++ \spad{copy!(c,a)} copies the matrix \spad{a} into the matrix c. + ++ Error: if \spad{a} and c do not have the same + ++ dimensions. + plus_! : (M,M,M) -> M + ++ \spad{plus!(c,a,b)} computes the matrix sum \spad{a + b} and stores the + ++ result in the matrix c. + ++ Error: if \spad{a}, b, and c do not have the same dimensions. + minus_! : (M,M) -> M + ++ \spad{minus!(c,a)} computes \spad{-a} and stores the result in the + ++ matrix c. + ++ Error: if a and c do not have the same dimensions. + minus_! : (M,M,M) -> M + ++ \spad{!minus!(c,a,b)} computes the matrix difference \spad{a - b} + ++ and stores the result in the matrix c. + ++ Error: if \spad{a}, b, and c do not have the same dimensions. + leftScalarTimes_! : (M,R,M) -> M + ++ \spad{leftScalarTimes!(c,r,a)} computes the scalar product + ++ \spad{r * a} and stores the result in the matrix c. + ++ Error: if \spad{a} and c do not have the same dimensions. + rightScalarTimes_! : (M,M,R) -> M + ++ \spad{rightScalarTimes!(c,a,r)} computes the scalar product + ++ \spad{a * r} and stores the result in the matrix c. + ++ Error: if \spad{a} and c do not have the same dimensions. + times_! : (M,M,M) -> M + ++ \spad{times!(c,a,b)} computes the matrix product \spad{a * b} + ++ and stores the result in the matrix c. + ++ Error: if \spad{a}, b, and c do not have + ++ compatible dimensions. + power_! : (M,M,M,M,NNI) -> M + ++ \spad{power!(a,b,c,m,n)} computes m ** n and stores the result in + ++ \spad{a}. The matrices b and c are used to store intermediate results. + ++ Error: if \spad{a}, b, c, and m are not square + ++ and of the same dimensions. + "**" : (M,NNI) -> M + ++ \spad{x ** n} computes the n-th power + ++ of a square matrix. The power n is assumed greater than 1. + + Implementation ==> add + + rep : M -> REP + rep m == m pretend REP + + copy_!(c,a) == + m := nrows a; n := ncols a + not((nrows c) = m and (ncols c) = n) => + error "copy!: matrices of incompatible dimensions" + aa := rep a; cc := rep c + for i in 0..(m-1) repeat + aRow := qelt(aa,i); cRow := qelt(cc,i) + for j in 0..(n-1) repeat + qsetelt_!(cRow,j,qelt(aRow,j)) + c + + plus_!(c,a,b) == + m := nrows a; n := ncols a + not((nrows b) = m and (ncols b) = n) => + error "plus!: matrices of incompatible dimensions" + not((nrows c) = m and (ncols c) = n) => + error "plus!: matrices of incompatible dimensions" + aa := rep a; bb := rep b; cc := rep c + for i in 0..(m-1) repeat + aRow := qelt(aa,i); bRow := qelt(bb,i); cRow := qelt(cc,i) + for j in 0..(n-1) repeat + qsetelt_!(cRow,j,qelt(aRow,j) + qelt(bRow,j)) + c + + minus_!(c,a) == + m := nrows a; n := ncols a + not((nrows c) = m and (ncols c) = n) => + error "minus!: matrices of incompatible dimensions" + aa := rep a; cc := rep c + for i in 0..(m-1) repeat + aRow := qelt(aa,i); cRow := qelt(cc,i) + for j in 0..(n-1) repeat + qsetelt_!(cRow,j,-qelt(aRow,j)) + c + + minus_!(c,a,b) == + m := nrows a; n := ncols a + not((nrows b) = m and (ncols b) = n) => + error "minus!: matrices of incompatible dimensions" + not((nrows c) = m and (ncols c) = n) => + error "minus!: matrices of incompatible dimensions" + aa := rep a; bb := rep b; cc := rep c + for i in 0..(m-1) repeat + aRow := qelt(aa,i); bRow := qelt(bb,i); cRow := qelt(cc,i) + for j in 0..(n-1) repeat + qsetelt_!(cRow,j,qelt(aRow,j) - qelt(bRow,j)) + c + + leftScalarTimes_!(c,r,a) == + m := nrows a; n := ncols a + not((nrows c) = m and (ncols c) = n) => + error "leftScalarTimes!: matrices of incompatible dimensions" + aa := rep a; cc := rep c + for i in 0..(m-1) repeat + aRow := qelt(aa,i); cRow := qelt(cc,i) + for j in 0..(n-1) repeat + qsetelt_!(cRow,j,r * qelt(aRow,j)) + c + + rightScalarTimes_!(c,a,r) == + m := nrows a; n := ncols a + not((nrows c) = m and (ncols c) = n) => + error "rightScalarTimes!: matrices of incompatible dimensions" + aa := rep a; cc := rep c + for i in 0..(m-1) repeat + aRow := qelt(aa,i); cRow := qelt(cc,i) + for j in 0..(n-1) repeat + qsetelt_!(cRow,j,qelt(aRow,j) * r) + c + + copyCol_!: (ARR,REP,Integer,Integer) -> ARR + copyCol_!(bCol,bb,j,n1) == + for i in 0..n1 repeat qsetelt_!(bCol,i,qelt(qelt(bb,i),j)) + + times_!(c,a,b) == + m := nrows a; n := ncols a; p := ncols b + not((nrows b) = n and (nrows c) = m and (ncols c) = p) => + error "times!: matrices of incompatible dimensions" + aa := rep a; bb := rep b; cc := rep c + bCol : ARR := new(n,0) + m1 := (m :: Integer) - 1; n1 := (n :: Integer) - 1 + for j in 0..(p-1) repeat + copyCol_!(bCol,bb,j,n1) + for i in 0..m1 repeat + aRow := qelt(aa,i); cRow := qelt(cc,i) + sum : R := 0 + for k in 0..n1 repeat + sum := sum + qelt(aRow,k) * qelt(bCol,k) + qsetelt_!(cRow,j,sum) + c + + power_!(a,b,c,m,p) == + mm := nrows a; nn := ncols a + not(mm = nn) => + error "power!: matrix must be square" + not((nrows b) = mm and (ncols b) = nn) => + error "power!: matrices of incompatible dimensions" + not((nrows c) = mm and (ncols c) = nn) => + error "power!: matrices of incompatible dimensions" + not((nrows m) = mm and (ncols m) = nn) => + error "power!: matrices of incompatible dimensions" + flag := false + copy_!(b,m) + repeat + if odd? p then + flag => + times_!(c,b,a) + copy_!(a,c) + flag := true + copy_!(a,b) +-- one? p => return a + (p = 1) => return a + p := p quo 2 + times_!(c,b,b) + copy_!(b,c) + + m ** n == + not square? m => error "**: matrix must be square" + a := copy m; b := copy m; c := copy m + power_!(a,b,c,m,n) + +@ +\section{License} +<<license>>= +--Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd. +--All rights reserved. +-- +--Redistribution and use in source and binary forms, with or without +--modification, are permitted provided that the following conditions are +--met: +-- +-- - Redistributions of source code must retain the above copyright +-- notice, this list of conditions and the following disclaimer. +-- +-- - Redistributions in binary form must reproduce the above copyright +-- notice, this list of conditions and the following disclaimer in +-- the documentation and/or other materials provided with the +-- distribution. +-- +-- - Neither the name of The Numerical ALgorithms Group Ltd. nor the +-- names of its contributors may be used to endorse or promote products +-- derived from this software without specific prior written permission. +-- +--THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS +--IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED +--TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A +--PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER +--OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, +--EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, +--PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR +--PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF +--LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING +--NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS +--SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. +@ +<<*>>= +<<license>> + +<<package MATSTOR StorageEfficientMatrixOperations>> +@ +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} |