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# Algorithm to Generate Structures of Real Symmetric Matrices

IP.com Disclosure Number: IPCOM000074024D
Original Publication Date: 1971-Mar-01
Included in the Prior Art Database: 2005-Feb-23
Document File: 2 page(s) / 13K

IBM

## Related People

Reynolds, SW: AUTHOR

## Abstract

An algorithm is presented for the generation of structures of real symmetric matrices. The algorithm is particularly adaptable to array-oriented languages such as APL and an APL implementation is given. The principal advantage of this algorithm is that it permits the generation of such structures by entering but one-half of the data required by the structure.

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Algorithm to Generate Structures of Real Symmetric Matrices

An algorithm is presented for the generation of structures of real symmetric matrices. The algorithm is particularly adaptable to array-oriented languages such as APL and an APL implementation is given. The principal advantage of this algorithm is that it permits the generation of such structures by entering but one-half of the data required by the structure.

In dealing with various engineering problems it is frequently required to enter into a computer real symmetric matrices, i.e., matrices over the real number field and which are symmetrical about the principal diagonal.

The algorithm to be presented provides a method for generating such structures and is suited for array-oriented languages such as APL. For convenience and simplicity only a structure whose elements are entered as the catenation, in row major order, of the elements of the matrices occurring in the upper triangles will be considered although the method is readily and easily adaptable to element entry as the catenation of upper triangles in column major order. Here it should be observed that, due to the symmetry, entering the upper triangles in row major order is the same as entering the lower triangles in column major order. Similarly, entering the upper triangles in column major order is the same as entering the lower triangles in row major order.

Let A denote a vector representing the number of structures of real symmetric matrices desired. Let B denote a vector consisting of the catenation of elements of the upper triangles of the real symmetric matrices in row major order. The algorithm, which works in either 0 or 1 origin indexing, is described as follows: 1) The row or column dimension of the matrices which are to occur in the structure is given by the last component of A. Form the outer product of the vector of integers (from 1 to the dimension) with itself and with respect to the standard scalar dya...