mpfrMatrix: Classes "mpfrMatrix" and "mpfrArray"

Description

The classes "mpfrMatrix" and "mpfrArray" are, analogously to the base matrix and array functions and classes simply “numbers” of class mpfr with an additional Dim and Dimnames slot.

Arguments

Objects from the Class

Objects should typically be created by mpfrArray(), but can also be created by new("mpfrMatrix", ...) or new("mpfrArray", ...), or also by t(x), dim(x) <- dd, or mpfr2array(x, dim=dd) where x is a an mpfr “number vector”.

A (slightly more flexible) alternative to dim(x) <- dd is mpfr2array(x, dd, dimnames).

Slots

.Data:: as for the mpfr class, a "list" of mpfr1 numbers.
Dim:: of class "integer", specifying the array dimension.
Dimnames:: of class "list" and the same length as Dim, each list component either NULL or a character vector of length Dim[j].

Extends

Class "mpfrMatrix" extends "mpfrArray", directly.

Class "mpfrArray" extends class "mpfr", by class "mpfrArray", distance 2; class "list", by class "mpfrArray", distance 3; class "vector", by class "mpfrArray", distance 4.

Methods

Arith: signature(e1 = "mpfr", e2 = "mpfrArray"): ...
Arith: signature(e1 = "numeric", e2 = "mpfrArray"): ...
Arith: signature(e1 = "mpfrArray", e2 = "mpfrArray"): ...
Arith: signature(e1 = "mpfrArray", e2 = "mpfr"): ...
Arith: signature(e1 = "mpfrArray", e2 = "numeric"): ...
as.vector: signature(x = "mpfrArray", mode = "missing"): drops the dimension ‘attribute’, i.e., transforms x into a simple mpfr vector. This is an inverse of t(.) or dim(.) <- * on such a vector.
atan2: signature(y = "ANY", x = "mpfrArray"): ...
atan2: signature(y = "mpfrArray", x = "mpfrArray"): ...
atan2: signature(y = "mpfrArray", x = "ANY"): ...
[<-: signature(x = "mpfrArray", i = "ANY", j = "ANY", value = "ANY"): ...
[: signature(x = "mpfrArray", i = "ANY", j = "ANY", drop = "ANY"): ...
[: signature(x = "mpfrArray", i = "ANY", j = "missing", drop = "missing"): "mpfrArray"s can be subset (“indexed”) as regular R arrays.
%*%: signature(x = "mpfr", y = "mpfrMatrix"): Compute the matrix/vector product \(x y\) when the dimensions (dim) of x and y match. If x is not a matrix, it is treated as a 1-row or 1-column matrix (aka “row vector” or “column vector”) depending on which one makes sense, see the documentation of the base function %*%.
%*%: signature(x = "mpfr", y = "Mnumber"): method definition for cases with one mpfr and any “number-like” argument are to use MPFR arithmetic as well.
%*%: signature(x = "mpfrMatrix", y = "mpfrMatrix"),
%*%: signature(x = "mpfrMatrix", y = "mpfr"), etc. Further method definitions with identical semantic.
crossprod: signature(x = "mpfr", y = "missing"): Computes \(x'x\), i.e., t(x) %*% x, typically more efficiently.
crossprod: signature(x = "mpfr", y = "mpfrMatrix"): Computes \(x'y\), i.e., t(x) %*% y, typically more efficiently.
crossprod: signature(x = "mpfrMatrix", y = "mpfrMatrix"): ...
crossprod: signature(x = "mpfrMatrix", y = "mpfr"): ...
tcrossprod: signature(x = "mpfr", y = "missing"): Computes \(xx'\), i.e., x %*% t(x), typically more efficiently.
tcrossprod: signature(x = "mpfrMatrix", y = "mpfrMatrix"): Computes \(xy'\), i.e., x %*% t(y), typically more efficiently.
tcrossprod: signature(x = "mpfrMatrix", y = "mpfr"): ...
tcrossprod: signature(x = "mpfr", y = "mpfrMatrix"): ...
coerce: signature(from = "mpfrArray", to = "array"): coerces from to a numeric array of the same dimension.
coerce: signature(from = "mpfrArray", to = "vector"): as for standard arrays, this “drops” the dim (and dimnames), i.e., returns an mpfr vector.
Compare: signature(e1 = "mpfr", e2 = "mpfrArray"): ...
Compare: signature(e1 = "numeric", e2 = "mpfrArray"): ...
Compare: signature(e1 = "mpfrArray", e2 = "mpfr"): ...
Compare: signature(e1 = "mpfrArray", e2 = "numeric"): ...
dim: signature(x = "mpfrArray"): ...
dimnames<-: signature(x = "mpfrArray"): ...
dimnames: signature(x = "mpfrArray"): ...
show: signature(object = "mpfrArray"): ...
sign: signature(x = "mpfrArray"): ...
norm: signature(x = "mpfrMatrix", type = "character"): computes the matrix norm of x, see norm or the one in package Matrix.
t: signature(x = "mpfrMatrix"): tranpose the mpfrMatrix.
aperm: signature(a = "mpfrArray"): aperm(a, perm) is a generalization of t(.) to permute the dimensions of an mpfrArray; it has the same semantics as the standard aperm() method for simple R arrays.

Author

Martin Maechler

Examples

Run this code

showClass("mpfrMatrix")

validObject(mm <- new("mpfrMatrix"))
validObject(aa <- new("mpfrArray"))

v6 <- mpfr(1:6, 128)
m6 <- new("mpfrMatrix", v6, Dim = c(2L, 3L))
validObject(m6)
m6
which(m6 == 3, arr.ind = TRUE) # |-->  (1, 2)
## Coercion back to "vector": Both of these work:
stopifnot(identical(as(m6, "mpfr"), v6),
	  identical(as.vector(m6), v6)) # < but this is a "coincidence"

S2 <- m6[,-3] # 2 x 2
S3 <- rbind(m6, c(1:2,10)) ; s3 <- asNumeric(S3)
det(S2)
str(determinant(S2))
det(S3)
stopifnot(all.equal(det(S2), det(asNumeric(S2)), tol=1e-15),
	  all.equal(det(S3), det(s3), tol=1e-15))

## 2-column matrix indexing and replacement:
(sS <- S3[i2 <- cbind(1:2, 2:3)])
stopifnot(identical(asNumeric(sS), s3[i2]))
C3 <- S3; c3 <- s3
C3[i2] <- 10:11
c3[i2] <- 10:11
stopifnot(identical(asNumeric(C3), c3))

AA <- new("mpfrArray", as.vector(cbind(S3, -S3)), Dim=c(3L,3:2))
stopifnot(identical(AA[,,1] , S3), identical(AA[,,2] , -S3))
aa <- asNumeric(AA)

i3 <- cbind(3:1, 1:3, c(2L, 1:2))
ii3 <- Rmpfr:::.mat2ind(i3, dim(AA), dimnames(AA))
stopifnot(aa[i3] == new("mpfr", getD(AA)[ii3]))
stopifnot(identical(aa[i3], asNumeric(AA[i3])))
CA <- AA; ca <- aa
ca[i3] <- ca[i3] ^ 3
CA[i3] <- CA[i3] ^ 3

## scale():
S2. <- scale(S2)
stopifnot(all.equal(abs(as.vector(S2.)), rep(sqrt(1/mpfr(2, 128)), 4),
		    tol = 1e-30))

## norm() :
norm(S2)
stopifnot(identical(norm(S2), norm(S2, "1")),
          norm(S2, "I") == 6,
          norm(S2, "M") == 4,
          abs(norm(S2, "F") - 5.477225575051661) < 1e-15)

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