# matrix

0th

Percentile

##### Matrix manipulation with gmp

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

Keywords
arith
##### 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.
##### 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

##### Value

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

##### Aliases
• matrix
• matrix.default
• matrix.bigz
• matrix.bigq
• is.matrixZQ
• as.matrix.bigz
• as.matrix.bigq
• as.vector.bigq
• as.vector.bigz
• %*%
• %*%.default
• %*%.bigq
• %*%.bigz
• crossprod
• crossprod.default
• crossprod.bigq
• crossprod.bigz
• tcrossprod
• tcrossprod.default
• tcrossprod.bigq
• tcrossprod.bigz
• ncol.bigq
• ncol.bigz
• nrow.bigq
• nrow.bigz
• cbind.bigz
• cbind.bigq
• rbind.bigz
• rbind.bigq
• t.bigq
• t.bigz
• dim.bigq
• dim<-.bigq
• dim.bigz
• dim<-.bigz
##### 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}

Documentation reproduced from package gmp, version 0.5-13, License: GPL

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