acb-class: Arbitrary Precision Floating-Point Complex Numbers with Error Bounds

Description

Class acb extends virtual class flint. It represents vectors of complex numbers with error bounds on the real and imaginary parts. Elements are specified by two pairs of mixed format floating-point numbers: an arb real part and an arb imaginary part, each specified by an arf midpoint and a mag radius.

Usage

## The class generator function:
.acb(...)
## Mode 1: initialize with zeros
## .acb(length = 0L)
##
## Mode 2: initialize with vector
## .acb(length = length(x), x)
##
## Mode 3: initialize by parts
## .acb(length = max0(length(real), length(imag)), real, imag)
##
## where max0 <- function(m, n) if (min(m, n)) max(m, n) else 0L

Value

The class generator function returns new("acb", ...).

Arguments

...: arguments passed to methods for initialize.

Slots

.xData, names: inherited from virtual class flint.

Methods

Due to constraints imposed by generic functions, methods typically do not provide a formal argument prec allowing for a precision to be indicated in the function call. Such methods use the current default precision set by flintPrec.

!: signature(x = "acb"):
equivalent to (but faster than) x == 0.
+: signature(e1 = "acb", e2 = "missing"):
returns a copy of the argument.
-: signature(e1 = "acb", e2 = "missing"):
returns the negation of the argument.
Complex: signature(z = "acb"):
mathematical functions of one argument; see S4groupGeneric.
Math: signature(x = "acb"):
mathematical functions of one argument; see S4groupGeneric. Member functions floor, ceiling, trunc, cummin, cummax are not implemented.
Math2: signature(x = "acb"):
decimal rounding according to a second argument digits; see S4groupGeneric. There are just two member member functions: round, signif.
Ops: signature(e1 = "ANY", e2 = "acb"):
signature(e1 = "acb", e2 = "ANY"):
binary arithmetic, comparison, and logical operators; see S4groupGeneric. The “other” operand must be atomic or inherit from virtual class flint. The operands are recycled and promoted as necessary.
Summary: signature(x = "acb"):
univariate summary statistics; see S4groupGeneric. The return value is a logical vector of length 1 (any, all) or an acb vector of length 1 or 2 (sum, prod). Member functions min, max, range are not implemented.
anyNA: signature(x = "acb"):
returns TRUE if any element of x has real or imaginary part with midpoint NaN, FALSE otherwise.
as.vector: signature(x = "acb"):
returns as.vector(y, mode), where y is a complex vector containing the result of converting the midpoints of the real and imaginary parts of x to the range of double, rounding if the value is not exactly representable in double precision. The rounding mode is to the nearest representable number (with precedence to even significands in case of ties), unless a midpoint exceeds .Machine[["double.xmax"]] in absolute value, in which case -Inf or Inf is introduced with a warning. Coercion to types "character", "symbol" (synonym "name"), "pairlist", "list", and "expression", which are not “number-like”, is handled specially.
coerce: signature(from = "ANY", to = "acb"):
returns .acb(x = from). An error is signaled if the class or type of from is not supported by the method for initialize.
format: signature(x = "acb"):
returns a character vector suitable for printing, using string format "(m +/- r)+(m +/- r)i" and scientific format for each m and r. Optional arguments control the output; see format-methods.
initialize: signature(.Object = "acb", length = "numeric"):
returns .Object after setting its .xData slot. The new slot value is an external pointer to an array of the corresponding C type, which is newly allocated and initialized entirely with zeros (zero midpoint, zero radius in the real and imaginary parts). .Object is not copied, so all references are affected.
initialize: signature(.Object = "acb", length = "numeric", x = "atomic|flint"):
as above, except that the new slot value points to an array initialized with values from x.
initialize: signature(.Object = "acb", length = "numeric", real = "atomic|flint", imag = "atomic|flint"):
as above, except that the new slot value points to an array whose real and imaginary parts are initialized separately with values from real and imag, which are coerced to class arb and recycled as necessary.
is.finite: signature(x = "acb"):
returns a logical vector indicating which elements of x do not have real or imaginary part with midpoint NaN, -Inf, or Inf or radius Inf.
is.infinite: signature(x = "acb"):
returns a logical vector indicating which elements of x have real or imaginary part with midpoint -Inf or Inf or radius Inf.
is.na, is.nan: signature(x = "acb"):
returns a logical vector indicating which elements of x have real or imaginary part with midpoint NaN.
is.unsorted: signature(x = "acb"):
signals an error indicating that <= is not a total order on the range of arb; see xtfrm below.
log: signature(x = "acb"):
returns the logarithm of the argument. The natural logarithm is computed by default (when optional argument base is unset).
mean: signature(x = "acb"):
returns the arithmetic mean.
xtfrm: signature(x = "acb"):
signals an error indicating that <= is not a total order on the range of arb: a <= b || b <= a is is not TRUE for all finite a and b of class arb. Thus, direct sorting of acb, which is based on arb, is not supported. Users wanting to order the midpoints of the real and imaginary parts should operate on Mid(Real(x)) and Mid(Imag(x)).

References

The FLINT documentation of the underlying C type: https://flintlib.org/doc/acb.html

Johansson, F. (2017). Arb: efficient arbitrary-precision midpoint-radius interval arithmetic. IEEE Transactions on Computers, 66(8), 1281-1292. tools:::Rd_expr_doi("10.1109/TC.2017.2690633")

Examples

Run this code

showClass("acb")
showMethods(classes = "acb")

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