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Unless otherwise noted, all of the functions described in this chapter
will work for real and complex scalar or matrix arguments.
The following functions are available for working with complex numbers.
Each expects a single argument, and given a matrix, they work on an
element by element basis.
ceil (x)
-
Return the smallest integer not less than x. If x is
complex, return
ceil (real (x)) + ceil (imag (x)) * I
.
floor (x)
-
Return the largest integer not greater than x. If x is
complex, return
floor (real (x)) + floor (imag (x)) * I
.
fix (x)
-
Truncate x toward zero. If x is complex, return
fix (real (x)) + fix (imag (x)) * I
.
round (x)
-
Return the integer nearest to x. If x is complex, return
round (real (x)) + round (imag (x)) * I
.
sign (x)
-
Compute the signum function, which is defined as
For complex arguments,
sign
returns x ./ abs (x)
.
exp (x)
-
Compute the exponential of x. To compute the matrix exponential,
see section Linear Algebra.
gcd (x, ...
)
-
Compute the greatest common divisor of the elements of x, or the
list of all the arguments. For example,
gcd (a1, ..., ak)
is the same as
gcd ([a1, ..., ak])
An optional second return value, v
contains an integer vector such that
g = v(1) * a(k) + ... + v(k) * a(k)
lcm (x, ...
)
-
Compute the least common multiple of the elements elements of x, or
the list of all the arguments. For example,
lcm (a1, ..., ak)
is the same as
lcm ([a1, ..., ak]).
log (x)
-
Compute the natural logarithm of x. To compute the matrix logarithm,
see section Linear Algebra.
log2 (x)
-
Compute the base-2 logarithm of x.
log10 (x)
-
Compute the base-10 logarithm of x.
sqrt (x)
-
Compute the square root of x. To compute the matrix square root,
see section Linear Algebra.
max (x)
-
For a vector argument, return the maximum value. For a matrix argument,
return the maximum value from each column, as a row vector. Thus,
max (max (x))
returns the largest element of x.
For complex arguments, the magnitude of the elements are used for
comparison.
min (x)
-
Like
max
, but return the minimum value.
rem (x, y)
-
Return the remainder of
x / y
, computed using the
expression
x - y .* fix (x ./ y)
An error message is printed if the dimensions of the arguments do not
agree, or if either of the arguments is complex.
The following functions are available for working with complex
numbers. Each expects a single argument. Given a matrix they work on
an element by element basis.
abs (x)
-
Compute the magnitude of x.
angle (x)
-
arg (x)
-
Compute the argument of x.
conj (x)
-
Return the complex conjugate of x.
imag (x)
-
Return the imaginary part of x.
real (x)
-
Return the real part of x.
Octave provides the following trigonometric functions:
sin asin sinh asinh
cos acos cosh acosh
tan atan tanh atanh
sec asec sech asech
csc acsc csch acsch
cot acot coth acoth
Each of these functions expect a single argument. For matrix arguments,
they work on an element by element basis. For example, the expression
sin ([1, 2; 3, 4])
produces
ans =
0.84147 0.90930
0.14112 -0.75680
atan2 (y, x)
sum (x)
-
For a vector argument, return the sum of all the elements. For a matrix
argument, return the sum of the elements in each column, as a row
vector. The sum of an empty matrix is 0 if it has no columns, or a
vector of zeros if it has no rows (see section Empty Matrices).
prod (x)
-
For a vector argument, return the product of all the elements. For a
matrix argument, return the product of the elements in each column, as a
row vector. The product of an empty matrix is 1 if it has no columns,
or a vector of ones if it has no rows (see section Empty Matrices).
cumsum (x)
-
Return the cumulative sum of each column of x. For example,
cumsum ([1, 2; 3, 4])
produces
ans =
1 2
4 6
cumprod (x)
-
Return the cumulative product of each column of x. For example,
cumprod ([1, 2; 3, 4])
produces
ans =
1 2
3 8
sumsq (x)
-
For a vector argument, return the sum of the squares of all the
elements. For a matrix argument, return the sum of the squares of the
elements in each column, as a row vector.
beta
-
Returns the beta function,
betai (a, b, x)
-
Returns the incomplete beta function,
If x has more than one component, both a and b must be
scalars. If x is a scalar, a and b must be of
compatible dimensions.
erf
-
Computes the error function,
erfc (z)
-
Computes the complementary error function,
1 - erf (z)
.
erfinv
-
Computes the inverse of the error function.
gamma (z)
-
Computes the gamma function,
gammai (a, x)
-
Computes the incomplete gamma function,
If a is scalar, then
gammai (a, x)
is returned
for each element of x and vice versa.
If neither a nor x is scalar, the sizes of a and
x must agree, and gammai is applied element-by-element.
lgamma
-
Returns the natural logarithm of the gamma function.
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