## cds.astro Class AstroMath

```java.lang.Object
cds.astro.AstroMath
```

`public class AstroMathextends java.lang.Object`

Trigonometric and a few other functions used in the astronomical context. This class includes also 3x3 matrix manipulation. Extracted from Class Coo

Field Summary
`static double` `ARCSEC`

`static double` `DEG`

`static double` `DEG2`

`static double[]` `powers`

Constructor Summary
`AstroMath()`

Method Summary
`static double` `asinc(double x)`
Function asinc(x), inverse function of sinc
`static double` `asind(double x)`
sin-1 (inverse function of sine), gives argument in degrees
`static double` ```atan2d(double y, double x)```
get the polar angle from 2-D cartesian coordinates
`static double` `atand(double x)`
tan-1 (inverse function of tangent), gives argument in degrees
`static double` `atanh(double x)`
tanh-1 (inverse function of tanh)
`static double` `cosd(double x)`
Cosine when argument in degrees
`static double` `cosh(double x)`
Hyperbolic cosine cosh = (exp(x) + exp(-x))/2
`static double` `dexp(double x)`
Compute just 10x
`static double` `dexp(int n)`
Compute just 10n
`static double` ```ell1(double a, double b)```
Computation of complete elliptic integral of first kind.
`static double` `log(double x)`
Compute the log base 10
`static double[][]` ```m3p(double[][] A, double[][] B)```
3-Matrices Products
`static double[][]` `m3t(double[][] A)`
Transposed of a Matrix
`static double` `sinc(double x)`
Function sinc(x) = sin(x)/x
`static double` `sind(double x)`
Sine when argument in degrees
`static double` `tand(double x)`
Tangent when argument in degrees
`static double` `tanh(double x)`
Hyperbolic tangent = (exp(x)-exp(-x))/(exp(x)+exp(-x))

Methods inherited from class java.lang.Object
`clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

Field Detail

### powers

`public static final double[] powers`

### DEG

`public static final double DEG`
See Also:
Constant Field Values

### DEG2

`public static final double DEG2`
See Also:
Constant Field Values

### ARCSEC

`public static final double ARCSEC`
See Also:
Constant Field Values
Constructor Detail

### AstroMath

`public AstroMath()`
Method Detail

### cosd

`public static final double cosd(double x)`
Cosine when argument in degrees

Parameters:
`x` - angle in degrees
Returns:
the cosine

### sind

`public static final double sind(double x)`
Sine when argument in degrees

Parameters:
`x` - angle in degrees
Returns:
the sine

### tand

`public static final double tand(double x)`
Tangent when argument in degrees

Parameters:
`x` - angle in degrees
Returns:
the tan

### asind

`public static final double asind(double x)`
sin-1 (inverse function of sine), gives argument in degrees

Parameters:
`x` - argument
Returns:
y value such that sin(y) = x

### atand

`public static final double atand(double x)`
tan-1 (inverse function of tangent), gives argument in degrees

Parameters:
`x` - argument
Returns:
angle in degrees

### atan2d

```public static final double atan2d(double y,
double x)```
get the polar angle from 2-D cartesian coordinates

Parameters:
`y` - cartesian y coordinate
`x` - cartesian x coordinate
Returns:
polar angle in degrees

### cosh

`public static final double cosh(double x)`
Hyperbolic cosine cosh = (exp(x) + exp(-x))/2

Parameters:
`x` - argument
Returns:
corresponding hyperbolic cosine (>= 1)

### tanh

`public static final double tanh(double x)`
Hyperbolic tangent = (exp(x)-exp(-x))/(exp(x)+exp(-x))

Parameters:
`x` - argument
Returns:
corresponding hyperbolic tangent (in range ]-1, 1[)

### atanh

`public static final double atanh(double x)`
tanh-1 (inverse function of tanh)

Parameters:
`x` - argument, in range ]-1, 1[ (NaN returned otherwise)
Returns:
corresponding hyperbolic inverse tangent

### sinc

`public static final double sinc(double x)`
Function sinc(x) = sin(x)/x

Parameters:
`x` - argument (radians)
Returns:
corresponding value

### asinc

`public static final double asinc(double x)`
Function asinc(x), inverse function of sinc

Parameters:
`x` - argument
Returns:
y such that sinc(y) = x

### dexp

`public static final double dexp(int n)`
Compute just 10n

Parameters:
`n` - Power to which to compute the value
Returns:
10n

### dexp

`public static final double dexp(double x)`
Compute just 10x

Parameters:
`x` - Power to which to compute the value
Returns:
10x

### log

`public static final double log(double x)`
Compute the log base 10

Parameters:
`x` - Number (positive)
Returns:
log10(x)

### ell1

```public static final double ell1(double a,
double b)```
Computation of complete elliptic integral of first kind. E1(a,b) = Integral{0,π/2} du/sqrt(a2cos2u+b2sin2u).
Computed with arithmetico-geometrical mean M(a,b) = common limit of an+1=(an+bn)/2, bn+1=sqrt(an*bn).
The arithmetico-geometrical mean M(a,b) is given by (Gauss): 1/M(a,b) = (2/π) E1(a,b)

Parameters:
`a` - factor 'a' (must be positive, a>0)
`b` - factor 'b' (must be positive, b>0)
Returns:
value of the elliptic integral function.

### m3p

```public static final double[][] m3p(double[][] A,
double[][] B)```
3-Matrices Products

Parameters:
`A` - 3x3 matrix
`B` - 3x3 matrix
Returns:
R = A * B

### m3t

`public static final double[][] m3t(double[][] A)`
Transposed of a Matrix

Parameters:
`A` - input matric
Returns:
R = t(A)