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matrix {gmp}

Matrix manipulation with gmp
Package: 
gmp
Version: 
0.5-5

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.

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

Unset:
Just play with large numbers
Set with a vector of size 1:
Example: matrix.bigz(1:6,nrow=2,ncol=3,mod=7) This means you work in Z/nZ, for the whole matrix. It is the only case where the %*% and solve functions will work in Z/nZ.
Set with a vector smaller than data:
Example: matrix.bigz(1:6,nrow=2,ncol=3,mod=1:5). Then, the modulus is repeated to the end of data. This can be used to define a matrix with a different modulus at each row.
Set with same size as data:
Modulus is defined for each cell

Values

A matrix of class bigz or bigq

See Also

Solving linear algebra system solve.bigz; matrix

Examples

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}

Author(s)

Antoine Lucas

Documentation reproduced from package gmp, version 0.5-5. License: GPL