Arbitrary Precision Floating-Point Complex Numbers with Error Bounds
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. class
## 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
...: arguments passed to methods for initialize.The class generator function returns new("acb", ...).
.xData, names: inherited from virtual class flint.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 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))`.
Virtual class flint. Generic functions Real and Imag and their replacement forms for getting and setting real and imaginary parts.
The FLINT documentation of the underlying
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")
showClass("acb") showMethods(classes = "acb")