matrix: Matrix manipulation with gmp

Description

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

Usage

"matrix"(data = NA, nrow = 1, ncol = 1, byrow = FALSE, dimnames = NULL, mod = NA,...)
is.matrixZQ(x)
"%*%"(x, y)
"%*%"(x, y)
"crossprod"(x, y=NULL)
"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

matrix(): A matrix of class "bigz" or "bigq".is.matrixZQ(): TRUE or FALSE.dim(), ncol(), etc: integer or NULL, as for simple matrices.

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

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))),
          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}