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gmp

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,...)

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

Value

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

is.matrixZQ(): TRUE or FALSE.

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

Author(s)

Antoine Lucas

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}

gmp

Multiple Precision Arithmetic

v0.6-2

GPL (>= 2)

Authors

Antoine Lucas, Immanuel Scholz, Rainer Boehme <rb-gmp@reflex-studio.de>, Sylvain Jasson <Sylvain.Jasson@inrae.fr>, Martin Maechler <maechler@stat.math.ethz.ch>

Initial release

2021-01-07