matrix: Matrix manipulation with gmp

Description

Overload of all standard tools useful for matrix manipulation adapted to large numbers.

Usage

## S3 method for class 'bigz':
matrix(data = NA, nrow = 1, ncol = 1, byrow = FALSE, dimnames = NULL, mod = NA,...)
## S3 method for class 'bigz':
\%*\%(x, y)
## S3 method for class 'bigq':
\%*\%(x, y)
## S3 method for class 'bigq':
crossprod(x, y=NULL)
## S3 method for class 'bigz':
tcrossprod(x, y=NULL)
## ..... etc

Arguments

data

an optional data vector

nrow

the desired number of rows

ncol

the desired number of columns

byrow

logical. If FALSE (the default), the matrix is filled by columns, otherwise the matrix is filled by rows.

dimnames

not implemented for "bigz" or "bigq" matrices.

mod

optional modulus (when data is "bigz").

...

Not used

x,y

numeric, bigz, or bigq matrices or vectors.

Value

A matrix of class bigz or bigq

Details

Extract function is the same use for vector or matrix. Then, x[i] return same value as x[i,].

Special features concerning the "bigz" class: the modulus can be [object Object],[object Object],[object Object],[object Object]

Examples

Run this code

V <- as.bigz(v <- 3:7)
crossprod(V)# scalar product
(C <- t(V))
stopifnot(dim(C) == dim(t(v)), C == v,
          dim(t(C)) == c(length(v), 1),
          crossprod(V) == sum(V * V),
         tcrossprod(V) == outer(v,v),
          identical(C, t(t(C))) )

## a matrix
x <- diag(1:4)
## invert this matrix
(xI <- solve(x))

## matrix in Z/7Z
y <- as.bigz(x,7)
## invert this matrix (result is *different* from solve(x)):
(yI <- solve(y))
stopifnot(yI %*% y == diag(4),
          y %*% yI == diag(4))

## matrix in Q
z  <- as.bigq(x)
## invert this matrix (result is the same as solve(x))
(zI <- solve(z))

stopifnot(abs(zI - xI) <= 1e-13,
          z %*% zI == diag(4),
          identical(crossprod(zI), zI %*% t(zI))
         )

A <- matrix(2^as.bigz(1:12), 3,4)
for(a in list(A, as.bigq(A, 16), factorialZ(20), as.bigq(2:9, 3:4))) {
  a.a <- crossprod(a)
  aa. <- tcrossprod(a)
  stopifnot(identical(a.a, crossprod(a,a)),
 	    identical(a.a, t(a) %*% a)
            ,
            identical(aa., tcrossprod(a,a)),
	    identical(aa., a %*% t(a))
 	   )
}# {for}