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
See Also
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}