Mathematical functions on Arrays

Mathematical functions on Array. More...

Various functions

template<class T>
T prod (const Array< T > &t)
 Return the product of the Array elements.
template<class T, class F>
Array< T > & applyFunction (F *op, const Array< T > &t)
template<class T, class F>
Array< T > & applyFunction (F *op, const Array< T > &t, const Array< T > &t2)
 Applies the function op to all the elements of the array t. Returns an array of type T.
template<class T, class F>
Array< T > & applyFunction (F *op, const Array< T > &t, const Array< T > &t2, const Array< T > &t3)
 Applies the function op to all the elements of the array t. Returns an array of type T.
template<class T>
T sum (const Array< T > &t)
 Return the sum of the Array elements.
template<class T>
largest< float, T >::type mean (const Array< T > &t)
 Return the mean of the Array elements.
template<class T>
largest< float, T >::type sqmean (const Array< T > &t)
 Return the quadratic mean of the Array elements.
template<class T>
long whereMin (const Array< T > &t)
template<class T>
T min (const Array< T > &t)
 Return the min of the Array elements.
template<class T>
long whereMax (const Array< T > &t)
template<class T>
T max (const Array< T > &t)
 Return the max of the Array elements.
template<class T1, class T2>
largest< T1, T2 >::type dot (const Array< T1 > &t1, const Array< T2 > &t2)
 Return the scalar product of two vectors.
template<class T>
largest< float, T >::type norm (const Array< T > &t)
 Return the euclidian norm.
template<class T>
Array< T > & abs (const Array< T > &t)
 Return an Array containing the absolute value of each elements.
template<class T>
Array< T > & floor (const Array< T > &t)
 Return an Array containing the floor value of each elements.
template<class T>
Array< T > & ceil (const Array< T > &t)
 Return an Array containing the ceil value of each elements.

Trigonometric functions

template<class T>
Array< typename idil::largest
< float, T >::type > & 		sin (const Array< T > &t)
template<class T>
Array< typename idil::largest
< float, T >::type > & 		cos (const Array< T > &t)
template<class T>
Array< typename idil::largest
< float, T >::type > & 		tan (const Array< T > &t)
template<class T>
Array< typename idil::largest
< float, T >::type > & 		asin (const Array< T > &t)
template<class T>
Array< typename idil::largest
< float, T >::type > & 		acos (const Array< T > &t)
template<class T>
Array< typename idil::largest
< float, T >::type > & 		atan (const Array< T > &t)
template<class T>
Array< typename idil::largest
< float, T >::type > & 		sinc (const Array< T > &t)

Hyperbolic functions

template<class T>
Array< typename idil::largest
< float, T >::type > & 		sinh (const Array< T > &t)
template<class T>
Array< typename idil::largest
< float, T >::type > & 		cosh (const Array< T > &t)
template<class T>
Array< typename idil::largest
< float, T >::type > & 		tanh (const Array< T > &t)
template<class T>
Array< typename idil::largest
< float, T >::type > & 		asinh (const Array< T > &t)
template<class T>
Array< typename idil::largest
< float, T >::type > & 		acosh (const Array< T > &t)
template<class T>
Array< typename idil::largest
< float, T >::type > & 		atanh (const Array< T > &t)

Exp-Log functions

template<class T>
Array< typename idil::largest
< float, T >::type > & 		exp (const Array< T > &t)
template<class T>
Array< typename idil::largest
< float, T >::type > & 		log (const Array< T > &t)
template<class T>
Array< typename idil::largest
< float, T >::type > & 		log10 (const Array< T > &t)
template<class T>
Array< typename idil::largest
< float, T >::type > & 		sqrt (const Array< T > &t)

Curves & trajectories

template<class T>
Array< T > & curvAbscissa (Array< T > &x, Array< T > &y)
 Return the curvilinear abscissa along a trajectory defined by the points $ (x,y) $.
template<class T>
Array< T > & angle (Array< T > &x, Array< T > &y)
 Return the angle along the curve with respect to the x axis.
template<class T>
Array< T > & derivative (Array< T > &x, Array< T > &y)
 Return the derivative along the curve $ dy/dx $.

Histograms

template<class T>
Array< long > & histogram (const Array< T > &t, long nbin=-1, float mn=0, float mx=0)
 Returns the histogram of an Array.
template<class T>
Array< float > & histobins (const Array< T > &t, long nbin=-1, float mn=0, float mx=0)
 Returns the bins positions.

Functions specific to complex numbers

template<class T>
Array< complex< T > > & cplx (const Array< T > &t1, const Array< T > &t2)
 Return an complex Array where the real part is t1 and the imaginary is t2.
template<class T>
Array< complex< T > > & cplx (const Array< T > &t)
 Return an complex Array where the real part is t and the imaginary is null.
template<class T>
Array< T > & real (const Array< complex< T > > &t)
 Return an Array containing the real part of each elements.
template<class T>
Array< T > & imag (const Array< complex< T > > &t)
 Return an Array containing the imaginary part of each elements.
template<class T>
Array< typename largest< float,
T >::type > & 		mod (const Array< complex< T > > &t)
 Return an Array containing the complex modulus of each elements.
template<class T>
Array< typename largest< float,
T >::type > & 		arg (const Array< complex< T > > &t)
 Return an Array containing the argument of each elements.
template<class T>
Array< complex< T > > & conjugate (const Array< complex< T > > &t)
 Return an Array containing the complexe conjugate of each elements.
template<class T>
Array< complex< typename
largest< float, T >::type > > & 		exp_i (const Array< T > &t)
 Return an Array containing the exp_i of each elements.

Linear Algebra

template<class T>
T trace (Array< T > &A)
 Returns the trace of a square matrix.
template<class T>
double determinant (Array< T > &A)
 Returns the determinant of a square matrix The function uses the GSL LU decomposition.
template<class T, class T2>
Array< double > & matmul (Array< T > &A, Array< T2 > &B)
 Matrix multiplication.
template<class T>
Array< double > & invert (Array< T > &A)
 Returns the invert of a square matrix The function uses the GSL LU decomposition.
template<class T, class T2, class T3>
void diagonalize (Array< T > &matrix, Array< T2 > &eigenvectors, Array< T3 > &eigenvalues)
 Matrix Diagonalization.
template<class T, class T2>
Array< double > & solve (Array< T > &A, Array< T2 > &Y)
 Solve a linear system A X = Y, return X.

Random numbers using GSL

template<class T>
Array< T > & randomFlat (long n)
 Return an Array of n random values in ]0;1[. You must precise the output type. Ex: random<float>(1000).
template<class T>
Array< T > & randomExp (long n, double mu)
 Return an Array of n random on a Rayleigh distribution. You must precise the output type.
template<class T>
Array< T > & randomGaussian (long n, double mu, double sigma)
 Return an Array of n random on a Gauusian distribution. You must precise the output type.
template<class T>
Array< T > & randomRayleigh (long n, double sigma)
 Return an Array of n random on a Rayleigh distribution. You must precise the output type.

Mathematical array functions using GSL

template<class T>
Array< typename idil::largest
< float, T >::type > & 		bessel (const Array< T > &t, int n)
 Apply the cylindrical Bessel function $ J_n $ on each element and return the result.
template<class T>
Array< typename idil::largest
< float, T >::type > & 		airy (Array< T > &t)
 Apply the Airy function on each element and return the result.
template<class T>
Array< typename idil::largest
< float, T >::type > & 		erf (Array< T > &t)
 Apply the error function erf on each element and return the result.
template<class T>
Array< typename idil::largest
< float, T >::type > & 		gamma (Array< T > &t)
 Apply the the gamma function on each element and return the result.

Detailed Description

Mathematical functions on Array.

A few mathematical functions have been directly implemented for the class Array. More mathematical functions are available with the GSL Library, via IDIL_GSL.h.

Example: 

 Array<float> af1, af2;
 af1 = findgen(1000)/100.;
 af2 = sin(af1);

!

Todo:
Linear algebra section

Function Documentation

template<class T>
Array<typename idil::largest<float,T>::type>& acos ( const Array< T > &  t  )  [inline]

Returns an Array containing the arc cosinus of each elements.

template<class T>
Array<typename idil::largest<float,T>::type>& acosh ( const Array< T > &  t  )  [inline]

Returns an Array containing the acosh of each elements.

template<class T, class F>
Array<T>& applyFunction ( F *  op,
const Array< T > &  t 
) [inline]

Applies the function op to all the elements of the array t. Returns an array of type T.

template<class T>
Array<typename idil::largest<float,T>::type>& asin ( const Array< T > &  t  )  [inline]

Returns an Array containing the arc sinus of each elements.

template<class T>
Array<typename idil::largest<float,T>::type>& asinh ( const Array< T > &  t  )  [inline]

Returns an Array containing the asinh of each elements.

template<class T>
Array<typename idil::largest<float,T>::type>& atan ( const Array< T > &  t  )  [inline]

Returns an Array containing the arc tan of each elements.

template<class T>
Array<typename idil::largest<float,T>::type>& atanh ( const Array< T > &  t  )  [inline]

Returns an Array containing the atanh of each elements.

template<class T>
Array<typename idil::largest<float,T>::type>& cos ( const Array< T > &  t  )  [inline]

Returns an Array containing the cos of each elements.

template<class T>
Array<typename idil::largest<float,T>::type>& cosh ( const Array< T > &  t  )  [inline]

Returns an Array containing the cosh of each elements.

template<class T, class T2, class T3>
void diagonalize ( Array< T > &  matrix,
Array< T2 > &  eigenvectors,
Array< T3 > &  eigenvalues 
) [inline]

Matrix Diagonalization.

Parameters:
matrix : matrix to diaganalize,
eigenvectors : matrix which will contain the eigenvectors.
eigenvalues : vector which will contain the eigenvalues. We use C-style conventions for matrix index: A(column, line). AxB -> C(b1,a2).

template<class T>
Array<typename idil::largest<float,T>::type>& exp ( const Array< T > &  t  )  [inline]

Returns an Array containing the exp of each elements.

template<class T>
Array<float>& histobins ( const Array< T > &  t,
long  nbin = -1,
float  mn = 0,
float  mx = 0 
) [inline]

Returns the bins positions.

Parameters:
t : Array, any type and dimension,
nbin : number of bins in the histogram.
mn : low bound of the histogram,
mx : high bound of the histogram. If nbin is negative, it is set to the default value (30). If mx<=mn, the limits are calculated from the min and max values of the array t.

template<class T>
Array<long>& histogram ( const Array< T > &  t,
long  nbin = -1,
float  mn = 0,
float  mx = 0 
) [inline]

Returns the histogram of an Array.

Parameters:
t : Array, any type and dimension,
nbin : number of bins in the histogram.
mn : low bound of the histogram,
mx : high bound of the histogram. If nbin is negative, it is set to the default value (30). If mx<=mn, the limits are calculated from the min and max values of the array t.

template<class T>
Array<typename idil::largest<float,T>::type>& log ( const Array< T > &  t  )  [inline]

Returns an Array containing the log of each elements.

template<class T>
Array<typename idil::largest<float,T>::type>& log10 ( const Array< T > &  t  )  [inline]

Returns an Array containing the log10 of each elements.

template<class T, class T2>
Array<double>& matmul ( Array< T > &  A,
Array< T2 > &  B 
) [inline]

Matrix multiplication.

Parameters:
A : matrix (a1,a2),
B : matrix (b1,b2). We use C-style conventions for matrix index: A(column, line). AxB -> C(b1,a2). Example: 
//     [ 0.11 0.12 0.13 ]  [ 1011 1012 ]     [ 367.76 368.12 ]
//     [ 0.21 0.22 0.23 ]  [ 1021 1022 ]  =  [ 674.06 674.72 ]
//                         [ 1031 1032 ]

   Array<float> A,B,C;
   A = vector(0.11, 0.12, 0.13,
              0.21, 0.22, 0.23);   A.setdim(3,2);
   B = vector(1011, 1012,
              1021, 1022,
              1031, 1032);         B.setdim(2,3);
   C = matmul(A,B);

template<class T>
Array<typename idil::largest<float,T>::type>& sin ( const Array< T > &  t  )  [inline]

Returns an Array containing the sin of each elements.

template<class T>
Array<typename idil::largest<float,T>::type>& sinc ( const Array< T > &  t  )  [inline]

Returns an Array containing the sin cardinal of each elements.

template<class T>
Array<typename idil::largest<float,T>::type>& sinh ( const Array< T > &  t  )  [inline]

Returns an Array containing the sinh of each elements.

template<class T, class T2>
Array<double>& solve ( Array< T > &  A,
Array< T2 > &  Y 
) [inline]

Solve a linear system A X = Y, return X.

Parameters:
A : square matrix,
Y : vector. Solve uses the GSL LU decomposition.

template<class T>
Array<typename idil::largest<float,T>::type>& sqrt ( const Array< T > &  t  )  [inline]

Returns an Array containing the square root of each elements.

template<class T>
Array<typename idil::largest<float,T>::type>& tan ( const Array< T > &  t  )  [inline]

Returns an Array containing the tan of each elements.

template<class T>
Array<typename idil::largest<float,T>::type>& tanh ( const Array< T > &  t  )  [inline]

Returns an Array containing the tanh of each elements.

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