by Mustafa Al-Janabi
- Gradient of scalar field
- Divergence and rotation of vector field
Once you have installed Go, run this command
to install the vcalc package:
go get github.com/aljanabim/vcalc
The package is used by defining a new scalar- or a vector field. Definig a field requires a mathematical expression as well as a coordinate system. The gradient is then calcualted for scalar fields by entering a point in the assigned coordinates system to the method Grad. Using the methods Div and Rot with a point in the assigned coordinate system the divergence and rotation are calculated for a vector field.
To define a new scalar field you use the function NewScalarField. You enter the expression of your scalar field and the coordinate system as arguments.
NewScalarField{EXPRESSION, COORDINATE SYSTEM}To define a new vector field you use the function NewVectorField. You enter the expression of each axis of the vector field as well as the coordinate system as inputs.
NewVectorField{EXPRESSION, EXPRESSION, EXPRESSION, COORDINATE SYSTEM}You enter an expression as a string. The expression string should follow the following pattern
"[OPR]a[FUNC](b[COORD]^c)^d"Where
| Expression parts | Possible string values |
|---|---|
| [OPR] | "", "+", "-", "*" or "/" |
| [FUNC] | "", "sin", "cos", "tan", "exp" or "sqrt" |
| [COORD] | "", "x", "y" or "z" for cartesian coordinates "", "r", "phi" or "z" for cylinder coordinates "", "r", "theta" or "phi" for spherical coordinates |
| a,b,c and d | arbitrary positive integers as strings |
Note that every part is optional and can be left empty to cover diverce mathematical expressions, however every coordinate has to be present in the expression.
For example
"72+3x^2+5cos(y^2)-3z"
is valid. While
"72+3x^2+5cos(0)-3z"
is invalid, because the y-coordinate is missing.
Note that multiplication and division are calculated first (from left to right), then addition and subtraction are calculated (from left to right) just like regular arithmetics
For example
"3z*3x/y+3x^2"
is calculated the following order:
3*z -> (3*z)*(3*x) -> (3*z*3*x)/y -> 3*x^2 -> (3*z*3*x/y) + 3*x^2
Note that within the expresion within the parenthesis of [FUNC] can only contain a single [COORD]
For example
"72+3x^2+5cos(y^2)-3z"
is valid, while
"72+3x^2+5cos(y^2+z)-3z"
is invalid.
You enter a coordinate system as a string. The string should be
- "car" for cartesian coordinates
- "cyl" for cylinder coordinates
- "sph" for spherical coordinates
To calculate gradient you use the methods Grad on a scalar field at a specific point in the 3-dimensional space.
To calculate divergence and rotation you use the methods Div and Rot on a vector field.
s := NewScalarField("3^5-7x^2-y+3cos(z^2)^2", "car")
fmt.Println(s.Grad([]float64{4, 2, 7.2}))
// Prints
// [-55.99999999994054 -1.0000000000331966 0.3215104938192326] s := NewScalarField("-3sin(2r^3)^5+phi*z^2", "cyl")
fmt.Println(s.Grad([]float64{-1, 2, 0}))
// Prints
// [25.604287369124233 -0 0] v := NewVectorField("x^2+cos(7y)", "y^2", "3z^2", "car")
fmt.Println(v.Div([]float64{-1, 2.76, 0}))
// Prints
// 3.520000000012402 v := NewVectorField("3theta*5^2-r^2",
"sqrt(theta*phi)",
"3theta*7r+2exp(3phi^2)",
"sph")
fmt.Println(v.Rot([]float64{-11, 3.14, 2}))
// Prints
// [303.38803709633146 -2.207322328156872e+07 1.0414537246060633] - func NewVectorField(e1,e2,e3, c string) vectorField
- func (v vectorField) Div(c []float64) float64
- func (v vectorField) Rot(c []float64) []float64
type scalarField {
// contains the expression, point, coordinate system and precision
}
func NewScalarField(e, c string) scalarField
New creates a new scalar field with given expression and coordinate system
func (s scalarField) Grad(c []float64) []float64
Grad calculates gradient of scalar field at given coordinates
type vectorField {
// contains the expression of each coordiante, point, coordinate system and precision
}
func NewVectorField(e1,e2,e3, c string) vectorField
New creates a new scalar field with given expression and coordinate system
func (v vectorField) Div(c []float64) float64
Div calculates divergence of vector field at given coordinates
func (v vectorField) Rot(c []float64) []float64
Rot calculates rotation/curl of vector field at given coordinates
- The package has yet to support "pi" and floats in the expression.
- Package has no complete expression check
- Package needs to include Laplacian and vector laplacian
Mustafa Al-Janabi