**Synopsis**-
Compute the absolute value of a number

**Usage**-
`y = abs(x)`

**Description**-
The

`abs`

function returns the absolute value of an arithmetic type. If its argument is a complex number (`Complex_Type`

), then it returns the modulus. If the argument is an array, a new array will be created whose elements are obtained from the original array by using the`abs`

function. **See Also**

**Synopsis**-
Compute the arc-cosine of a number

**Usage**-
`y = acos (x)`

**Description**-
The

`acos`

function computes the arc-cosine of a number and returns the result. If its argument is an array, the`acos`

function will be applied to each element and the result returned as an array. **See Also**

**Synopsis**-
Compute the inverse cosh of a number

**Usage**-
`y = acosh (x)`

**Description**-
The

`acosh`

function computes the inverse hyperbolic cosine of a number and returns the result. If its argument is an array, the`acosh`

function will be applied to each element and the result returned as an array. **See Also**

**Synopsis**-
Compute the arc-sine of a number

**Usage**-
`y = asin (x)`

**Description**-
The

`asin`

function computes the arc-sine of a number and returns the result. If its argument is an array, the`asin`

function will be applied to each element and the result returned as an array. **See Also**

**Synopsis**-
Compute the inverse-sinh of a number

**Usage**-
`y = asinh (x)`

**Description**-
The

`asinh`

function computes the inverse hyperbolic sine of a number and returns the result. If its argument is an array, the`asinh`

function will be applied to each element and the result returned as an array. **See Also**

**Synopsis**-
Compute the arc-tangent of a number

**Usage**-
`y = atan (x)`

**Description**-
The

`atan`

function computes the arc-tangent of a number and returns the result. If its argument is an array, the`atan`

function will be applied to each element and the result returned as an array. **See Also**

**Synopsis**-
Compute the arc-tangent of the ratio of two variables

**Usage**-
`z = atan2 (y, x)`

**Description**-
The

`atan2`

function computes the arc-tangent of the ratio`y/x`

and returns the result as a value that has the proper sign for the quadrant where the point (x,y) is located. The returned value`z`

will satisfy (-PI < z <= PI). If either of the arguments is an array, an array of the corresponding values will be returned. **See Also**

**Synopsis**-
Compute the inverse-tanh of a number

**Usage**-
`y = atanh (x)`

**Description**-
The

`atanh`

function computes the inverse hyperbolic tangent of a number and returns the result. If its argument is an array, the`atanh`

function will be applied to each element and the result returned as an array. **See Also**

**Synopsis**-
Round x up to the nearest integral value

**Usage**-
`y = ceil (x)`

**Description**-
This function rounds its numeric argument up to the nearest integral value. If the argument is an array, the corresponding array will be returned.

**See Also**

**Synopsis**-
Compute the complex conjugate of a number

**Usage**-
`z1 = Conj (z)`

**Description**-
The

`Conj`

function returns the complex conjugate of a number. If its argument is an array, the`Conj`

function will be applied to each element and the result returned as an array. **See Also**

**Synopsis**-
Compute the cosine of a number

**Usage**-
`y = cos (x)`

**Description**-
The

`cos`

function computes the cosine of a number and returns the result. If its argument is an array, the`cos`

function will be applied to each element and the result returned as an array. **See Also**

**Synopsis**-
Compute the hyperbolic cosine of a number

**Usage**-
`y = cosh (x)`

**Description**-
The

`cosh`

function computes the hyperbolic cosine of a number and returns the result. If its argument is an array, the`cosh`

function will be applied to each element and the result returned as an array. **See Also**

**Synopsis**-
Compute the absolute difference of two values

**Usage**-
`y = _diff (x, y)`

**Description**-
The

`_diff`

function returns a floating point number equal to the absolute value of the difference of its two arguments. If either argument is an array, an array of the corresponding values will be returned. **See Also**

**Synopsis**-
Compute the exponential of a number

**Usage**-
`y = exp (x)`

**Description**-
The

`exp`

function computes the exponential of a number and returns the result. If its argument is an array, the`exp`

function will be applied to each element and the result returned as an array. **See Also**

**Synopsis**-
Compute exp(x)-1

**Usage**-
`y = expm1(x)`

**Description**-
The

`expm1`

function computes`exp(x)-1`

and returns the result. If its argument is an array, the`expm1`

function will be applied to each element and the results returned as an array.This function should be called whenever

`x`

is close to 0 to avoid the numerical error that would arise in a naive computation of`exp(x)-1`

. **See Also**

**Synopsis**-
Test the approximate equality of two numbers

**Usage**-
`Char_Type feqs (a, b [,reldiff [,absdiff]])`

**Description**-
This function compares two floating point numbers

`a`

and`b`

, and returns a non-zero value if they are equal to within a specified tolerance; otherwise 0 will be returned. If either is an array, a corresponding boolean array will be returned.The tolerances are specified as relative and absolute differences via the optional third and fourth arguments. If no optional arguments are present, the tolerances default to

`reldiff=0.01`

and`absdiff=1e-6`

. If only the relative difference has been specified, the absolute difference (`absdiff`

) will be taken to be 0.0.For the case when

`|b|>=|a|`

,`a`

and`b`

are considered to be equal to within the specified tolerances if either`|b-a|<=absdiff`

or`|b-a|/|b|<=reldiff`

is true. **See Also**

**Synopsis**-
Compare two numbers using specified tolerances.

**Usage**-
`Char_Type fgteqs (a, b [,reldiff [,absdiff]])`

**Description**-
This function is functionally equivalent to:

See the documentation of(a >= b) or feqs(a,b,...)

`feqs`

for more information. **See Also**

**Synopsis**-
Round x down to the nearest integer

**Usage**-
`y = floor (x)`

**Description**-
This function rounds its numeric argument down to the nearest integral value. If the argument is an array, the corresponding array will be returned.

**See Also**

**Synopsis**-
Compare two numbers using specified tolerances.

**Usage**-
`Char_Type flteqs (a, b [,reldiff [,absdiff]])`

**Description**-
This function is functionally equivalent to:

See the documentation of(a <= b) or feqs(a,b,...)

`feqs`

for more information. **See Also**

**Synopsis**-
Test the approximate inequality of two numbers

**Usage**-
`Char_Type fneqs (a, b [,reldiff [,absdiff]])`

**Description**-
This function is functionally equivalent to:

See the documentation ofnot fneqs(a,b,...)

`feqs`

for more information. **See Also**

**Synopsis**-
Get the format for printing floating point values.

**Usage**-
`String_Type get_float_format ()`

**Description**-
The

`get_float_format`

retrieves the format string used for printing single and double precision floating point numbers. See the documentation for the`set_float_format`

function for more information about the format. **See Also**

**Synopsis**-
Compute sqrt(x1^2+x2^2+...+xN^2)

**Usage**-
`r = hypot (x1 [,x2,..,xN])`

**Description**-
If given two or more arguments,

`x1,...,xN`

, the`hypot`

function computes the quantity`sqrt(x1^2+...+xN^2)`

using an algorithm that tries to avoid arithmetic overflow. If any of the arguments is an array, an array of the corresponding values will be returned.If given a single array argument

`x`

, the`hypot`

function computes`sqrt(sumsq(x))`

, where`sumsq(x)`

computes the sum of the squares of the elements of`x`

. **Example**-
A vector in Euclidean 3 dimensional space may be represented by an array of three values representing the components of the vector in some orthogonal cartesian coordinate system. Then the length of the vector may be computed using the

`hypot`

function, e.g.,

The dot-product or scalar-product between two such vectorsA = [2,3,4]; len_A = hypot (A);

`A`

and`B`

may be computed using the`sum(A*B)`

. It is well known that this is also equal to the product of the lengths of the two vectors and the cosine of the angle between them. Hence, the angle between the vectors`A`

and`B`

may be computed using

Here,ahat = A/hypot(A); bhat = B/hypot(B); theta = acos(\sum(ahat*bhat));

`ahat`

and`bhat`

are the unit vectors associated with the vectors`A`

and`B`

, respectively. Unfortunately, the above method for computing the angle between the vectors is numerically unstable when`A`

and`B`

are nearly parallel. An alternative method is to use:ahat = A/hypot(A); bhat = B/hypot(B); ab = sum(ahat*bhat); theta = atan2 (hypot(bhat - ab*ahat), ab);

**See Also**

**Synopsis**-
Compute the imaginary part of a number

**Usage**-
`i = Imag (z)`

**Description**-
The

`Imag`

function returns the imaginary part of a number. If its argument is an array, the`Imag`

function will be applied to each element and the result returned as an array. **See Also**

**Synopsis**-
Test for infinity

**Usage**-
`y = isinf (x)`

**Description**-
This function returns 1 if x corresponds to an IEEE infinity, or 0 otherwise. If the argument is an array, an array of the corresponding values will be returned.

**See Also**

**Synopsis**-
isnan

**Usage**-
`y = isnan (x)`

**Description**-
This function returns 1 if x corresponds to an IEEE NaN (Not a Number), or 0 otherwise. If the argument is an array, an array of the corresponding values will be returned.

**See Also**

**Synopsis**-
Test if a number is less than 0

**Usage**-
`Char_Type _isneg(x)`

**Description**-
This function returns 1 if a number is less than 0, and zero otherwise. If the argument is an array, then the corresponding array of boolean (

`Char_Type`

) values will be returned. **See Also**

**Synopsis**-
Test if a number is greater than or equal to 0

**Usage**-
`Char_Type _isnonneg(x)`

**Description**-
This function returns 1 if a number is greater than or equal to 0, and zero otherwise. If the argument is an array, then the corresponding array of boolean (

`Char_Type`

) values will be returned. **See Also**

**Synopsis**-
Test if a number is greater than 0

**Usage**-
`Char_Type _ispos(x)`

**Description**-
This function returns 1 if a number is greater than 0, and zero otherwise. If the argument is an array, then the corresponding array of boolean (

`Char_Type`

) values will be returned. **See Also**

**Synopsis**-
Compute the logarithm of a number

**Usage**-
`y = log (x)`

**Description**-
The

`log`

function computes the natural logarithm of a number and returns the result. If its argument is an array, the`log`

function will be applied to each element and the result returned as an array. **See Also**

**Synopsis**-
Compute the base-10 logarithm of a number

**Usage**-
`y = log10 (x)`

**Description**-
The

`log10`

function computes the base-10 logarithm of a number and returns the result. If its argument is an array, the`log10`

function will be applied to each element and the result returned as an array. **See Also**

**Synopsis**-
Compute the logarithm of 1 plus a number

**Usage**-
`y = log1p (x)`

**Description**-
The

`log1p`

function computes the natural logarithm of 1.0 plus`x`

returns the result. If its argument is an array, the`log1p`

function will be applied to each element and the results returned as an array.This function should be used instead of

`log(1+x)`

to avoid numerical errors whenever`x`

is close to 0. **See Also**

**Synopsis**-
Compute the maximum of two or more numeric values

**Usage**-
`z = _max (x1,...,xN)`

**Description**-
The

`_max`

function returns a floating point number equal to the maximum value of its arguments. If any of the argiments are arrays (of equal length), an array of the corresponding values will be returned. **Notes**-
This function returns a floating point result even when the arguments are integers.

**See Also**

**Synopsis**-
Compute the minimum of two or more numeric values

**Usage**-
`z = _min (x1,...,xN)`

**Description**-
The

`_min`

function returns a floating point number equal to the minimum value of its arguments. If any of the argiments are arrays (of equal length), an array of the corresponding values will be returned. **Notes**-
This function returns a floating point result even when the arguments are integers.

**See Also**

**Synopsis**-
Multiply a number by 2

**Usage**-
`y = mul2(x)`

**Description**-
The

`mul2`

function multiplies an arithmetic type by two and returns the result. If its argument is an array, a new array will be created whose elements are obtained from the original array by using the`mul2`

function. **See Also**

**Synopsis**-
Round to the nearest integer

**Usage**-
`i = nint(x)`

**Description**-
The

`nint`

rounds its argument to the nearest integer and returns the result. If its argument is an array, a new array will be created whose elements are obtained from the original array elements by using the`nint`

function. **See Also**

**Synopsis**-
Evaluate a polynomial

**Usage**-
`Double_Type polynom([a0,a1,...aN], x [,use_factorial])`

**Description**-
The

`polynom`

function returns the value of the polynomial expression

where the coefficients are given by an array of valuesa0 + a1*x + a2*x^2 + ... + aN*x^N

`[a0,...,aN]`

. If`x`

is an array, the function will return a corresponding array. If the value of the optional`use_factorial`

parameter is non-zero, then each term in the sum will be normalized by the corresponding factorial, i.e.,a0/0! + a1*x/1! + a2*x^2/2! + ... + aN*x^N/N!

**Notes**-
Prior to version 2.2, this function had a different calling syntax and and was less useful.

The

`polynom`

function does not yet support complex-valued coefficients.For the case of a scalar value of

`x`

and a small degree polynomial, it is more efficient to use an explicit expression. **See Also**

**Synopsis**-
Compute the real part of a number

**Usage**-
`r = Real (z)`

**Description**-
The

`Real`

function returns the real part of a number. If its argument is an array, the`Real`

function will be applied to each element and the result returned as an array. **See Also**

**Synopsis**-
Round to the nearest integral value

**Usage**-
`y = round (x)`

**Description**-
This function rounds its argument to the nearest integral value and returns it as a floating point result. If the argument is an array, an array of the corresponding values will be returned.

**See Also**

**Synopsis**-
Set the format for printing floating point values.

**Usage**-
`set_float_format (String_Type fmt)`

**Description**-
The

`set_float_format`

function is used to set the floating point format to be used when floating point numbers are printed. The routines that use this are the traceback routines and the`string`

function, any anything based upon the`string`

function. The default value is`"%S"`

, which causes the number to be displayed with enough significant digits such that`x==atof(string(x))`

. **Example**-
set_float_format ("%S"); % default s = string (PI); % --> s = "3.141592653589793" set_float_format ("%16.10f"); s = string (PI); % --> s = "3.1415926536" set_float_format ("%10.6e"); s = string (PI); % --> s = "3.141593e+00"

**See Also**

**Synopsis**-
Compute the sign of a number

**Usage**-
`y = sign(x)`

**Description**-
The

`sign`

function returns the sign of an arithmetic type. If its argument is a complex number (`Complex_Type`

), the`sign`

will be applied to the imaginary part of the number. If the argument is an array, a new array will be created whose elements are obtained from the original array by using the`sign`

function.When applied to a real number or an integer, the

`sign`

function returns`-1`

,`0`

, or`+1`

according to whether the number is less than zero, equal to zero, or greater than zero, respectively. **See Also**

**Synopsis**-
Compute the sine of a number

**Usage**-
`y = sin (x)`

**Description**-
The

`sin`

function computes the sine of a number and returns the result. If its argument is an array, the`sin`

function will be applied to each element and the result returned as an array. **See Also**

**Synopsis**-
Compute the sine and cosine of a number

**Usage**-
`(s, c) = sincos (x)`

**Description**-
The

`sincos`

function computes the sine and cosine of a number and returns the result. If its argument is an array, the`sincos`

function will be applied to each element and the result returned as an array. **See Also**

**Synopsis**-
Compute the hyperbolic sine of a number

**Usage**-
`y = sinh (x)`

**Description**-
The

`sinh`

function computes the hyperbolic sine of a number and returns the result. If its argument is an array, the`sinh`

function will be applied to each element and the result returned as an array. **See Also**

**Synopsis**-
Compute the square of a number

**Usage**-
`y = sqr(x)`

**Description**-
The

`sqr`

function returns the square of an arithmetic type. If its argument is a complex number (`Complex_Type`

), then it returns the square of the modulus. If the argument is an array, a new array will be created whose elements are obtained from the original array by using the`sqr`

function. **Notes**-
For real scalar numbers, using

`x*x`

instead of`sqr(x)`

will result in faster executing code. However, if`x`

is an array, then`sqr(x)`

will execute faster. **See Also**

**Synopsis**-
Compute the square root of a number

**Usage**-
`y = sqrt (x)`

**Description**-
The

`sqrt`

function computes the square root of a number and returns the result. If its argument is an array, the`sqrt`

function will be applied to each element and the result returned as an array. **See Also**

**Synopsis**-
Compute the tangent of a number

**Usage**-
`y = tan (x)`

**Description**-
The

`tan`

function computes the tangent of a number and returns the result. If its argument is an array, the`tan`

function will be applied to each element and the result returned as an array. **See Also**

**Synopsis**-
Compute the hyperbolic tangent of a number

**Usage**-
`y = tanh (x)`

**Description**-
The

`tanh`

function computes the hyperbolic tangent of a number and returns the result. If its argument is an array, the`tanh`

function will be applied to each element and the result returned as an array. **See Also**

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