Functions
Introduction
The available functions are:
- arithmetic operators
- usual mathematical functions admitted by Fortran
- functions for treatment of complex quantities
- functions for treatment of vector quantities
- other specific functions (Modulo, Valid, Trapez, …)
Operators
The arithmetic operators are described in the table below.
| Operator | Description |
|---|---|
| + | add two values |
| subtract two values | |
| * | multiply two values |
| / | divide two values |
| ** or ^ | raise the left operand to the power specified by the right hand operand |
Mathematical functions
The usual mathematical functions are gathered in the tables below.
| Square function and absolute value | |
|---|---|
| Sqrt(x) | Square root of the expression x |
| Abs(x) | Absolute value of the expression x |
| Logarithm and exponential functions | |
|---|---|
| Exp(x) | Exponential function of the expression x |
| Log(x) | Natural logarithm of the expression x |
| Log10(x) | Common logarithm of the expression x |
| Other functions | |
|---|---|
| Int(x) | Integral part of the expression x |
| Modulo(x,x1) | Remainder of the division of x by x1 |
| Min(x1,x2) | Minimum of the expressions x1 and x2 |
| Max(x1,x2) | Maximum of the expressions x1 and x2 |
| Sign(x) |
Sign of the expression x: Sign(x)=+1 if x>0; = -1 if x<0; = 0 if x=0 |
Trigonometry
The usual trigonometric functions are gathered in the tables below.
| Trigonometric functions | |
|---|---|
| Sin(x) | Sine of the angle x expressed in radians |
| Cos(x) | Cosine of the angle x expressed in radians |
| Tan(x) | Tangent of the angle x expressed in radians |
| Asin(x) | Arcsine in radians of the expression x; x ∈ [-1,1] |
| Acos(x) | Arccosine in radians of the expression x; x ∈ [-1,1] |
| Atan2(x,y) | Arctangent in radians of the expression (x/y) |
| Sind(x) | Sine of the angle x expressed in degrees |
| Cosd(x) | Cosine of the angle x expressed in degrees |
| Tand(x) | Tangent of the angle x expressed in degrees |
| Asind(x) | Arcsine in degrees of the expression x; x ∈ [-1,1] |
| Acosd(x) | Arccosine in degrees of the expression x; x ∈ [-1,1] |
| Atan2d(x,y) | Arctangent in degrees of the expression (x/y) |
| Sinh(x) | Hyperbolic sine of the expression x |
| Cosh(x) | Hyperbolic cosine of the expression x |
| Tanh(x) | Hyperbolic tangent of the expression x |
| Asinh(x) | Arcsine hyperbolic of the expression x; x ∈ [-1, ∝[ |
| Acosh(x) | Arccosine hyperbolic of the expression x; x ∈]-∝ , ∝[ |
| Atan2h (x,y) | Arctangent hyperbolic of the expression (x/y); x ∈ [-1,1] |
Treatment of complex quantities
The functions for treatment of the complex quantities are gathered in the table below.
| Functions for treatment of the complex quantities | |
|---|---|
| ModC(z) | Complex modulus of the complex expression z |
| Arg(z) | Argument (in radians) of the complex expression z |
| Inst(z,t) | Value at the instant t (in degrees) of the complex expression z |
| Real(z) | Real part of the complex expression z |
| Imag(z) | Imaginary part of the complex expression z |
| Conj(z) | Conjugate of the complex expression z |
| Cmplx(x,y) |
Complex expression built starting from the real expressions x and y |
Vector treatment
The functions for treatment of the vectors are gathered in the table below.
| Functions for vector treatment | |
|---|---|
| ModV(v) | Vector modulus of the vector expression v |
| Comp(i,v) | Component i of the vector expression v |
| PVec(v1,v2) | Vector product of 2 real vector expressions |
| Vec2(x,y) | 2D vector built starting from the real expressions x and y |
| Vec3(x,y,z) | 3D vector built starting from the real expressions x, y and z |
| Mod(x) | General modulus of the expression x: Mod(x)=ModV(ModC(x)) |
Modification of the coordinate system
The modification of a coordinate system is obtained with the functions in the table below.
| CLCS(r,i) |
Component i of coordinates in the local coordinate system r (i=1, 2 or 3) |
| VLCS(r,v) | Vector v in the local coordinate system r |
Other functions
The other functions (or specific functions) are gathered in the table below.
| Other functions | ||
|---|---|---|
| Valid(x,x1,x2) |
if x1 ≤ x<x2: else: |
Valid(x,x1,x2)= 1 Valid(x,x1,x2)= 0 |
| Trapez(x,x1,x2,x3) |
if x1 ≤ x ≤ x1+x2: if x<0 or x>x1+x2+x3: |
Trapez(x,x1,x2,x3)= 1 Trapez(x,x1,x2,x3)= 0 |
| Trapezper(x,x1,x2,x3,x4,x5,x6,x7) |
Periodic trapezoidal function see § Trapezper function |
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