# matrix {gmp}

Matrix manipulation with gmp
Package:
gmp
Version:
0.5-11

### 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,...)

is.matrixZQ(x))

## 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

The extract function ("[") is the same use for vector or matrix. Hence, x[i] returns the same values as x[i,]. This is not considered a feature and may be changed in the future (with warnings).

All matrix multiplications should work as with numeric matrices.

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

matrix(): A matrix of class "bigz" or "bigq".

is.matrixZQ(): TRUE or FALSE.

dim(), ncol(), etc: integer or NULL, as for simple matrices.

Solving a linear 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))),
is.matrixZQ(C), !is.matrixZQ(V), !is.matrixZQ(5)
)

## 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 0.5-11. License: GPL