octave: Mathematical Constants
17.9 Mathematical Constants
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-- : e
-- : e (N)
-- : e (N, M)
-- : e (N, M, K, ...)
-- : e (..., CLASS)
Return a scalar, matrix, or N-dimensional array whose elements are
all equal to the base of natural logarithms.
The constant ‘e’ satisfies the equation ‘log’ (e) = 1.
When called with no arguments, return a scalar with the value e.
When called with a single argument, return a square matrix with the
dimension specified.
When called with more than one scalar argument the first two
arguments are taken as the number of rows and columns and any
further arguments specify additional matrix dimensions.
The optional argument CLASS specifies the return type and may be
either "double" or "single".
See also: 
log XREFlog, exp XREFexp, pi XREFpi,
I XREFI.
-- : pi
-- : pi (N)
-- : pi (N, M)
-- : pi (N, M, K, ...)
-- : pi (..., CLASS)
Return a scalar, matrix, or N-dimensional array whose elements are
all equal to the ratio of the circumference of a circle to its
diameter.
Internally, ‘pi’ is computed as ‘4.0 * atan (1.0)’.
When called with no arguments, return a scalar with the value of
pi.
When called with a single argument, return a square matrix with the
dimension specified.
When called with more than one scalar argument the first two
arguments are taken as the number of rows and columns and any
further arguments specify additional matrix dimensions.
The optional argument CLASS specifies the return type and may be
either "double" or "single".
See also: e XREFe, I XREFI.
-- : I
-- : I (N)
-- : I (N, M)
-- : I (N, M, K, ...)
-- : I (..., CLASS)
Return a scalar, matrix, or N-dimensional array whose elements are
all equal to the pure imaginary unit, defined as ‘sqrt (-1)’.
I, and its equivalents i, j, and J, are functions so any of the
names may be reused for other purposes (such as i for a counter
variable).
When called with no arguments, return a scalar with the value i.
When called with a single argument, return a square matrix with the
dimension specified.
When called with more than one scalar argument the first two
arguments are taken as the number of rows and columns and any
further arguments specify additional matrix dimensions.
The optional argument CLASS specifies the return type and may be
either "double" or "single".
See also: e XREFe, pi XREFpi, log XREFlog,
exp XREFexp.
-- : Inf
-- : Inf (N)
-- : Inf (N, M)
-- : Inf (N, M, K, ...)
-- : Inf (..., CLASS)
Return a scalar, matrix or N-dimensional array whose elements are
all equal to the IEEE representation for positive infinity.
Infinity is produced when results are too large to be represented
using the IEEE floating point format for numbers. Two common
examples which produce infinity are division by zero and overflow.
[ 1/0 e^800 ]
⇒ Inf Inf
When called with no arguments, return a scalar with the value
‘Inf’.
When called with a single argument, return a square matrix with the
dimension specified.
When called with more than one scalar argument the first two
arguments are taken as the number of rows and columns and any
further arguments specify additional matrix dimensions.
The optional argument CLASS specifies the return type and may be
either "double" or "single".
See also: isinf XREFisinf, NaN XREFNaN.
-- : NaN
-- : NaN (N)
-- : NaN (N, M)
-- : NaN (N, M, K, ...)
-- : NaN (..., CLASS)
Return a scalar, matrix, or N-dimensional array whose elements are
all equal to the IEEE symbol NaN (Not a Number).
NaN is the result of operations which do not produce a well defined
numerical result. Common operations which produce a NaN are
arithmetic with infinity (Inf - Inf), zero divided by zero (0/0),
and any operation involving another NaN value (5 + NaN).
Note that NaN always compares not equal to NaN (NaN != NaN). This
behavior is specified by the IEEE standard for floating point
arithmetic. To find NaN values, use the ‘isnan’ function.
When called with no arguments, return a scalar with the value
‘NaN’.
When called with a single argument, return a square matrix with the
dimension specified.
When called with more than one scalar argument the first two
arguments are taken as the number of rows and columns and any
further arguments specify additional matrix dimensions.
The optional argument CLASS specifies the return type and may be
either "double" or "single".
See also: isnan XREFisnan, Inf XREFInf.
-- : eps
-- : eps (X)
-- : eps (N, M)
-- : eps (N, M, K, ...)
-- : eps (..., CLASS)
Return a scalar, matrix or N-dimensional array whose elements are
all eps, the machine precision.
More precisely, ‘eps’ is the relative spacing between any two
adjacent numbers in the machine’s floating point system. This
number is obviously system dependent. On machines that support
IEEE floating point arithmetic, ‘eps’ is approximately 2.2204e-16
for double precision and 1.1921e-07 for single precision.
When called with no arguments, return a scalar with the value ‘eps
(1.0)’.
Given a single argument X, return the distance between X and the
next largest value.
When called with more than one argument the first two arguments are
taken as the number of rows and columns and any further arguments
specify additional matrix dimensions. The optional argument CLASS
specifies the return type and may be either "double" or "single".
See also: realmax XREFrealmax, realmin XREFrealmin,
intmax XREFintmax, flintmax XREFflintmax.
-- : realmax
-- : realmax (N)
-- : realmax (N, M)
-- : realmax (N, M, K, ...)
-- : realmax (..., CLASS)
Return a scalar, matrix, or N-dimensional array whose elements are
all equal to the largest floating point number that is
representable.
The actual value is system dependent. On machines that support
IEEE floating point arithmetic, ‘realmax’ is approximately
1.7977e+308 for double precision and 3.4028e+38 for single
precision.
When called with no arguments, return a scalar with the value
‘realmax ("double")’.
When called with a single argument, return a square matrix with the
dimension specified.
When called with more than one scalar argument the first two
arguments are taken as the number of rows and columns and any
further arguments specify additional matrix dimensions.
The optional argument CLASS specifies the return type and may be
either "double" or "single".
See also: realmin XREFrealmin, intmax XREFintmax,
flintmax XREFflintmax, eps XREFeps.
-- : realmin
-- : realmin (N)
-- : realmin (N, M)
-- : realmin (N, M, K, ...)
-- : realmin (..., CLASS)
Return a scalar, matrix, or N-dimensional array whose elements are
all equal to the smallest normalized floating point number that is
representable.
The actual value is system dependent. On machines that support
IEEE floating point arithmetic, ‘realmin’ is approximately
2.2251e-308 for double precision and 1.1755e-38 for single
precision.
When called with no arguments, return a scalar with the value
‘realmin ("double")’.
When called with a single argument, return a square matrix with the
dimension specified.
When called with more than one scalar argument the first two
arguments are taken as the number of rows and columns and any
further arguments specify additional matrix dimensions.
The optional argument CLASS specifies the return type and may be
either "double" or "single".
See also: realmax XREFrealmax, intmin XREFintmin,
eps XREFeps.
Info Catalog
octave: Coordinate Transformations
octave: Arithmetic