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## 10.1abs

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.

## 10.2acos

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.

## 10.3acosh

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.

## 10.4asin

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.

## 10.5asinh

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.

## 10.6atan

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.

## 10.7atan2

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.

## 10.8atanh

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.

## 10.9ceil

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.

## 10.10Conj

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.

## 10.11cos

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.

## 10.12cosh

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.

## 10.13_diff

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.

## 10.14exp

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.

## 10.15expm1

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.

## 10.16feqs

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.

## 10.17fgteqs

Synopsis

Compare two numbers using specified tolerances.

Usage

Char_Type fgteqs (a, b [,reldiff [,absdiff]])

Description

This function is functionally equivalent to:

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

## 10.18floor

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.

## 10.19flteqs

Synopsis

Compare two numbers using specified tolerances.

Usage

Char_Type flteqs (a, b [,reldiff [,absdiff]])

Description

This function is functionally equivalent to:

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

## 10.20fneqs

Synopsis

Test the approximate inequality of two numbers

Usage

Char_Type fneqs (a, b [,reldiff [,absdiff]])

Description

This function is functionally equivalent to:

 not fneqs(a,b,...) 
See the documentation of feqs for more information.

## 10.21get_float_format

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.

## 10.22hypot

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.,

 A = [2,3,4]; len_A = hypot (A); 
The dot-product or scalar-product between two such vectors 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
 ahat = A/hypot(A); bhat = B/hypot(B); theta = acos(\sum(ahat*bhat)); 
Here, 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); 

## 10.23Imag

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.

## 10.24isinf

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.

isnan, isnan<@@ref>_Inf_Inf

## 10.25isnan

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.

isinf, isinf<@@ref>_NaN_NaN

## 10.26_isneg

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.

## 10.27_isnonneg

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.

## 10.28_ispos

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.

## 10.29log

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.

## 10.30log10

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.

## 10.31log1p

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.

## 10.32_max

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.

## 10.33_min

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.

## 10.34mul2

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.

## 10.35nint

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.

## 10.36polynom

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

 a0 + a1*x + a2*x^2 + ... + aN*x^N 
where the coefficients are given by an array of values [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.

## 10.37Real

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.

## 10.38round

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.

## 10.39set_float_format

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" 

## 10.40sign

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.

## 10.41sin

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.

## 10.42sincos

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.

## 10.43sinh

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.

## 10.44sqr

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.

## 10.45sqrt

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.

## 10.46tan

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.

## 10.47tanh

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.