Browse Prior Art Database

Transposition Algorithm

IP.com Disclosure Number: IPCOM000042606D
Original Publication Date: 1984-Jun-01
Included in the Prior Art Database: 2005-Feb-04

Publishing Venue

IBM

Related People

Authors:
Wagner, EG [+details]

Abstract

Given an nxm matrix A, it is common practice to store it in nm consecutive memory locations, A[i,j] being stored in the ((i-1)*m)+j location. In effect, this is storing the matrix as a vector VA, where VA[((i-1)* m+j] = A[i,j]. Using the same vector representation, we can represent the matrix T (the transpose of A) by a vector VT where VT[((i-1)*n)+j] = T(i,j) = A(j,i). Using this vector notation, we can describe our purpose here as that of transforming VA, step-by-step, into VT. Some Notation: Given integers p and q, let div(p,q) denote the integer part of p/q and rem(p,q) denote the remainder of p/q (i.e., rem(p,q) = p-q*div(p,q) ). It is easily seen that, for any k, i