Calculator of matrix products

Claim 2

A calculator for developing a product Bw, where B is a sparse matrix and w is a vector, comprising: means for entering signals representative of matrix B and vector w into said calculator; memory means responsive to said means for entering for storing matrix B in sets of columns where one set comprises columns with at least two of non-zero valued entries in each column, said sets being stored with row references to said entries of non-zero values; means for dividing each of said sets into subgroups of columns characterized by each column in each of said subgroups having a non-zero value in a common row; means, responsive to said means for dividing, for deleting from said memory means duplicate instances of said common row references, to form a reduced stored list of row references; means, responsive to said reduced stored list, for developing a product signal equal to ##EQU16## where each b i is a column in matrix B and each w i is an element of said vector w; and means for delivering said product signal out of said calculator.

Claim 3

The apparatus of claim 1 wherein said memory means comprises means for storing said B matrix in a list that groups said columns of said B matrix into sets, where one set represents columns that include a single entry of non-zero value and stores row references of said non-zero valued columns; another set represnets columns that contain two non-zero values of equal sign, and stores row references of said equal signed columns; and still another set represents columns that contain two non-zero values of opposite sign, and stores row references of said opposite signed columns;

Claim 4

Apparatus for developing a matrix product AD 2 A T w, where A is a matrix comprising columns a i , D is a diagonal matrix, and w is a vector, comprising: first means having a storage for storing said A matrix in a list that groups said columns of said A matrix into sets, where one set represents columns that include a single entry of non-zero value and stores row references of said non-zero valued columns; another set represents columns that contain two non-zero values of equal sign, and stores row references of said equal signed columns; and still another set represents columns that contain two non-zero values of opposite sign, and stores row references of said opposite signed columns; second means for dividing each of said sets into subgroups of columns characterized by each column in each of said subgroups having a non-zero value in a common row; third means responsive to said first means for deleting from storage duplicate instances of said common row references, to form a reduced stored list of row references; and fourth means, responsive to said reduced stored list, for evaluating ##EQU17## where d i is the element in the i th row of said D matrix.

Claim 5

Apparatus for developing a matrix product AD 2 A T w, where A is a matrix comprising columns a i , D is a diagonal matrix, and w is a vector, comprising: first means having a storage for storing said A matrix in a list that groups said columns of said A matrix into sets, where one set represents columns that include a single entry of non-zero value and stores row references of said non-zero valued columns; another set represents columns that contain two non-zero values of equal sign, and stores row references of said equal signed columns; and still another set represents columns that contain two non-zero values of opposite sign, and stores row references of said opposite signed columns; second means for dividing each of said sets into subgroups of columns characterized by each column in each of said subgroups having a non-zero value in a common row; third means responsive to said first means for deleting from storage duplicate instances of said common row references, to form a reduced stored list of row references; and fourth means, responsive to said reduced stored list, for evaluating ##EQU17## where d i is the element in the i th row of said D matrix.

Claim 6

The apparatus of claim 3 wherein said fourth means evaluates ##EQU18## with apparatus comprising: means for developing a dot product of each column in said A matrix, a i , with vector w to yield a scalar a i T w, where i is a summation index; means for multiplying said scalar with the diagonal entry in row i of said D matrix, d i , squared; means for developing a vector signal d i 2 (a i T w)a i ; and means for accumulating the vector signals developed by said means for developing a vector signal to produce a resultant vector from the sum ##EQU19##