unimodular

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Unimodular matrices

Systematically generates unimodular matrices; numerical verfication of a function's unimodularness

Keywords
array
Usage
unimodular(n)
unimodularity(n,o, FUN, ...)
Arguments
n

Maximum size of entries of matrices

o

Two element vector

FUN

Function whose unimodularity is to be checked

...

Further arguments passed to FUN

Details

Here, a ‘unimodular’ matrix is of size \(2\times 2\), with integer entries and a determinant of unity.

Value

Function unimodular() returns an array a of dimension c(2,2,u) (where u is a complicated function of n). Thus 3-slices of a (that is, a[,,i]) are unimodular.

Function unimodularity() returns the result of applying FUN() to the unimodular transformations of o. The function returns a vector of length dim(unimodular(n))[3]; if FUN() is unimodular and roundoff is neglected, all elements of the vector should be identical.

Note

In function as.primitive(), a ‘unimodular’ may have determinant minus one.

See Also

as.primitive

Aliases
  • unimodular
  • unimodularity
Examples
# NOT RUN {
unimodular(3)

o <- c(1,1i)
plot(abs(unimodularity(3,o,FUN=g2.fun,maxiter=100)-g2.fun(o)))


# }
Documentation reproduced from package elliptic, version 1.4-0, License: GPL-2

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