MaskArrMath.h

Classes

Global Functions -- Mathematical operations for MaskedArrays (and with Arrays) (full description)

Mathematical operations for MaskedArrays (and with Arrays) (source)

Interface

const MaskedArray<T> & operator+= (const MaskedArray<T> &left, const Array<T> &other)
const MaskedArray<T> & operator-= (const MaskedArray<T> &left, const Array<T> &other)
const MaskedArray<T> & operator*= (const MaskedArray<T> &left, const Array<T> &other)
const MaskedArray<T> & operator/= (const MaskedArray<T> &left, const Array<T> &other)
Array<T> & operator+= (Array<T> &left, const MaskedArray<T> &other)
Array<T> & operator-= (Array<T> &left, const MaskedArray<T> &other)
Array<T> & operator*= (Array<T> &left, const MaskedArray<T> &other)
Array<T> & operator/= (Array<T> &left, const MaskedArray<T> &other)
const MaskedArray<T> & operator+= (const MaskedArray<T> &left, const MaskedArray<T> &other)
const MaskedArray<T> & operator-= (const MaskedArray<T> &left, const MaskedArray<T> &other)
const MaskedArray<T> & operator*= (const MaskedArray<T> &left, const MaskedArray<T> &other)
const MaskedArray<T> & operator/= (const MaskedArray<T> &left,const MaskedArray<T> &other)
const MaskedArray<T> & operator/= (const MaskedArray<T> &left,const MaskedArray<S> &other)
const MaskedArray<T> & operator+= (const MaskedArray<T> &left,const T &other)
const MaskedArray<T> & operator-= (const MaskedArray<T> &left,const T &other)
const MaskedArray<T> & operator*= (const MaskedArray<T> &left,const T &other)
const MaskedArray<T> & operator/= (const MaskedArray<T> &left,const T &other)
MaskedArray<T> operator+(const MaskedArray<T> &a)
MaskedArray<T> operator-(const MaskedArray<T> &a)
MaskedArray<T> operator+ (const MaskedArray<T> &left, const Array<T> &right)
MaskedArray<T> operator- (const MaskedArray<T> &left, const Array<T> &right)
MaskedArray<T> operator* (const MaskedArray<T> &left, const Array<T> &right)
MaskedArray<T> operator/ (const MaskedArray<T> &left, const Array<T> &right)
MaskedArray<T> operator+ (const Array<T> &left, const MaskedArray<T> &right)
MaskedArray<T> operator- (const Array<T> &left, const MaskedArray<T> &right)
MaskedArray<T> operator* (const Array<T> &left, const MaskedArray<T> &right)
MaskedArray<T> operator/ (const Array<T> &left, const MaskedArray<T> &right)
MaskedArray<T> operator+ (const MaskedArray<T> &left,const MaskedArray<T> &right)
MaskedArray<T> operator- (const MaskedArray<T> &left,const MaskedArray<T> &right)
MaskedArray<T> operator* (const MaskedArray<T> &left,const MaskedArray<T> &right)
MaskedArray<T> operator/ (const MaskedArray<T> &left,const MaskedArray<T> &right)
MaskedArray<T> operator+ (const MaskedArray<T> &left, const T &right)
MaskedArray<T> operator- (const MaskedArray<T> &left, const T &right)
MaskedArray<T> operator* (const MaskedArray<T> &left, const T &right)
MaskedArray<T> operator/ (const MaskedArray<T> &left, const T &right)
MaskedArray<Complex> operator* (const MaskedArray<Complex> &left, const Float &right)
MaskedArray<T> operator+ (const T &left, const MaskedArray<T> &right)
MaskedArray<T> operator- (const T &left, const MaskedArray<T> &right)
MaskedArray<T> operator* (const T &left, const MaskedArray<T> &right)
MaskedArray<T> operator/ (const T &left, const MaskedArray<T> &right)
MaskedArray<Complex> operator* (const Float &left, const MaskedArray<Complex> &right)
MaskedArray<T> sin(const MaskedArray<T> &left)
MaskedArray<T> cos(const MaskedArray<T> &left)
MaskedArray<T> tan(const MaskedArray<T> &left)
MaskedArray<T> asin(const MaskedArray<T> &left)
MaskedArray<T> acos(const MaskedArray<T> &left)
MaskedArray<T> atan(const MaskedArray<T> &left)
MaskedArray<T> sinh(const MaskedArray<T> &left)
MaskedArray<T> cosh(const MaskedArray<T> &left)
MaskedArray<T> tanh(const MaskedArray<T> &left)
MaskedArray<T> exp(const MaskedArray<T> &left)
MaskedArray<T> log(const MaskedArray<T> &left)
MaskedArray<T> log10(const MaskedArray<T> &left)
MaskedArray<T> sqrt(const MaskedArray<T> &left)
MaskedArray<T> abs(const MaskedArray<T> &left)
MaskedArray<T> fabs(const MaskedArray<T> &left)
MaskedArray<T> ceil(const MaskedArray<T> &left)
MaskedArray<T> floor(const MaskedArray<T> &left)
MaskedArray<T> atan2(const MaskedArray<T> &left, const Array<T> &right)
MaskedArray<T> fmod(const MaskedArray<T> &left, const Array<T> &right)
MaskedArray<T> atan2(const Array<T> &left, const MaskedArray<T> &right)
MaskedArray<T> fmod(const Array<T> &left, const MaskedArray<T> &right)
MaskedArray<T> atan2(const MaskedArray<T> &left,const MaskedArray<T> &right)
MaskedArray<T> fmod(const MaskedArray<T> &left,const MaskedArray<T> &right)
MaskedArray<T> atan2(const MaskedArray<T> &left, const T &right)
MaskedArray<T> fmod(const MaskedArray<T> &left, const T &right)
MaskedArray<T> atan2(const T &left, const MaskedArray<T> &right)
MaskedArray<T> fmod(const T &left, const MaskedArray<T> &right)
MaskedArray<T> pow(const MaskedArray<T> &left, const Array<U> &right)
MaskedArray<T> pow(const Array<T> &left, const MaskedArray<U> &right)
MaskedArray<T> pow(const MaskedArray<T> &left,const MaskedArray<U> &right)
MaskedArray<T> pow(const MaskedArray<T> &left, const Double &right)
void minMax(T &minVal, T &maxVal, IPosition &minPos, IPosition &maxPos,const IPosition<T> &marray)
void minMax(T &minVal, T &maxVal,const MaskedArray<T> &marray)
T min(const MaskedArray<T> &left)
MaskedArray<T> min(const MaskedArray<T> &left, const Array<T> &right)
MaskedArray<T> min(const Array<T> &left, const MaskedArray<T> &right)
MaskedArray<T> min(const MaskedArray<T> &left, const MaskedArray<T> &right)
MaskedArray<T> min(const T &left, const MaskedArray<T> &right)
MaskedArray<T> min(const MaskedArray<T> &left, const T &right)
void min(const MaskedArray<T> &result, const Array<T> &left, const Array<T> &right)
T max(const MaskedArray<T> &left)
MaskedArray<T> max(const MaskedArray<T> &left, const Array<T> &right)
MaskedArray<T> max(const Array<T> &left, const MaskedArray<T> &right)
MaskedArray<T> max(const MaskedArray<T> &left, const MaskedArray<T> &right)
MaskedArray<T> max(const T &left, const MaskedArray<T> &right)
MaskedArray<T> max(const MaskedArray<T> &left, const T &right)
void max(const MaskedArray<T> &result,const Array<T> &left, const Array<T> &right)
void indgen(MaskedArray<T> &a, T start, T inc)
void indgen(MaskedArray<T> &a)
void indgen(MaskedArray<T> &a, T start)
T sum(const MaskedArray<T> &a)
T sumsquares(const MaskedArray<T> &a)
T product(const MaskedArray<T> &a)
T mean(const MaskedArray<T> &a)
T variance(const MaskedArray<T> &a)
T variance(const MaskedArray<T> &a, T mean)
T stddev(const MaskedArray<T> &a)
T stddev(const MaskedArray<T> &a, T mean)
T avdev(const MaskedArray<T> &a)
T avdev(const MaskedArray<T> &a,T mean)
inline T median(const MaskedArray<T> &a, Bool sorted = False)
T median(const MaskedArray<T> &a, Bool sorted, Bool takeEvenMean)
MaskedArray<T> square(const MaskedArray<T> &val)
MaskedArray<T> cube(const MaskedArray<T> &val)

Description

Review Status

Programs:
Tests:

Prerequisite

Etymology

MaskArrMath is short for MaskedArrayMath, which is too long by AIPS++ file naming conventions. This file contains global functions which perform element by element mathematical operations on masked arrays.

Synopsis

These functions perform element by element mathematical operations on masked arrays. With two arrays, they must both conform, and the result is done element by element, for those locations where the mask of the MaskedArray is True. For two MaskedArrays, the "and" of the masks is used.

Example

   Vector<Int> a(10);
   Vector<Int> b(10);
   Vector<Int> c(10);
      . . .
   c = a(a>0) + b(b>0);
This example sets those elements of c where ((a>0) && (b>0)) to (a+b). Elements of c where !((a>0) && (b>0)) are unchanged. The result of this operation is a MaskedArray. The assignment from this MaskedArray to the Vector c only assigns those elements where the mask is True.

Example

   Vector<Double> a(10);
   Vector<Double> b(10);
   Vector<Double> c(10);
      . . .
   c = atan2 (a, b(b>0);
This example sets those elements of c where (b>0) to atan2 (a,b). Elements of c where !(b>0) are unchanged. The result of this operation is a MaskedArray. The assignment from this MaskedArray to the Vector c only assigns those elements where the mask is True.

Example

   Vector<Int> a(10);
   Int result;
      . . .
   result = sum (a(a>0));
This example sums a, for those elements of a which are greater than 0.

Motivation

One wants to be able to mask arrays and perform mathematical operations on those masked arrays. Since the masked arrays are only defined where the masks are True, the result must be a MaskedArray, or a simple number.

Member Description

const MaskedArray<T> & operator+= (const MaskedArray<T> &left, const Array<T> &other)
const MaskedArray<T> & operator-= (const MaskedArray<T> &left, const Array<T> &other)
const MaskedArray<T> & operator*= (const MaskedArray<T> &left, const Array<T> &other)
const MaskedArray<T> & operator/= (const MaskedArray<T> &left, const Array<T> &other)
Array<T> & operator+= (Array<T> &left, const MaskedArray<T> &other)
Array<T> & operator-= (Array<T> &left, const MaskedArray<T> &other)
Array<T> & operator*= (Array<T> &left, const MaskedArray<T> &other)
Array<T> & operator/= (Array<T> &left, const MaskedArray<T> &other)
const MaskedArray<T> & operator+= (const MaskedArray<T> &left, const MaskedArray<T> &other)
const MaskedArray<T> & operator-= (const MaskedArray<T> &left, const MaskedArray<T> &other)
const MaskedArray<T> & operator*= (const MaskedArray<T> &left, const MaskedArray<T> &other)
const MaskedArray<T> & operator/= (const MaskedArray<T> &left,const MaskedArray<T> &other)
const MaskedArray<T> & operator/= (const MaskedArray<T> &left,const MaskedArray<S> &other)

Element by element arithmetic modifying left in-place. left and other must be conformant.

Thrown Exceptions

const MaskedArray<T> & operator+= (const MaskedArray<T> &left,const T &other)
const MaskedArray<T> & operator-= (const MaskedArray<T> &left,const T &other)
const MaskedArray<T> & operator*= (const MaskedArray<T> &left,const T &other)
const MaskedArray<T> & operator/= (const MaskedArray<T> &left,const T &other)

Element by element arithmetic modifying left in-place. The scalar "other" behaves as if it were a conformant Array to left filled with constant values.

MaskedArray<T> operator+(const MaskedArray<T> &a)
MaskedArray<T> operator-(const MaskedArray<T> &a)

Unary arithmetic operation.

MaskedArray<T> operator+ (const MaskedArray<T> &left, const Array<T> &right)
MaskedArray<T> operator- (const MaskedArray<T> &left, const Array<T> &right)
MaskedArray<T> operator* (const MaskedArray<T> &left, const Array<T> &right)
MaskedArray<T> operator/ (const MaskedArray<T> &left, const Array<T> &right)
MaskedArray<T> operator+ (const Array<T> &left, const MaskedArray<T> &right)
MaskedArray<T> operator- (const Array<T> &left, const MaskedArray<T> &right)
MaskedArray<T> operator* (const Array<T> &left, const MaskedArray<T> &right)
MaskedArray<T> operator/ (const Array<T> &left, const MaskedArray<T> &right)
MaskedArray<T> operator+ (const MaskedArray<T> &left,const MaskedArray<T> &right)
MaskedArray<T> operator- (const MaskedArray<T> &left,const MaskedArray<T> &right)
MaskedArray<T> operator* (const MaskedArray<T> &left,const MaskedArray<T> &right)
MaskedArray<T> operator/ (const MaskedArray<T> &left,const MaskedArray<T> &right)

Element by element arithmetic on MaskedArrays, returns a MaskedArray.

Thrown Exceptions

MaskedArray<T> operator+ (const MaskedArray<T> &left, const T &right)
MaskedArray<T> operator- (const MaskedArray<T> &left, const T &right)
MaskedArray<T> operator* (const MaskedArray<T> &left, const T &right)
MaskedArray<T> operator/ (const MaskedArray<T> &left, const T &right)
MaskedArray<Complex> operator* (const MaskedArray<Complex> &left, const Float &right)

Element by element arithmetic between a MaskedArray and a scalar, returning a MaskedArray.

MaskedArray<T> operator+ (const T &left, const MaskedArray<T> &right)
MaskedArray<T> operator- (const T &left, const MaskedArray<T> &right)
MaskedArray<T> operator* (const T &left, const MaskedArray<T> &right)
MaskedArray<T> operator/ (const T &left, const MaskedArray<T> &right)
MaskedArray<Complex> operator* (const Float &left, const MaskedArray<Complex> &right)

Element by element arithmetic between a scalar and a MaskedArray, returning a MaskedArray.

MaskedArray<T> sin(const MaskedArray<T> &left)
MaskedArray<T> cos(const MaskedArray<T> &left)
MaskedArray<T> tan(const MaskedArray<T> &left)
MaskedArray<T> asin(const MaskedArray<T> &left)
MaskedArray<T> acos(const MaskedArray<T> &left)
MaskedArray<T> atan(const MaskedArray<T> &left)
MaskedArray<T> sinh(const MaskedArray<T> &left)
MaskedArray<T> cosh(const MaskedArray<T> &left)
MaskedArray<T> tanh(const MaskedArray<T> &left)
MaskedArray<T> exp(const MaskedArray<T> &left)
MaskedArray<T> log(const MaskedArray<T> &left)
MaskedArray<T> log10(const MaskedArray<T> &left)
MaskedArray<T> sqrt(const MaskedArray<T> &left)
MaskedArray<T> abs(const MaskedArray<T> &left)
MaskedArray<T> fabs(const MaskedArray<T> &left)
MaskedArray<T> ceil(const MaskedArray<T> &left)
MaskedArray<T> floor(const MaskedArray<T> &left)

Transcendental function applied to the array on an element-by-element basis. Although a template function, this may not make sense for all numeric types.

MaskedArray<T> atan2(const MaskedArray<T> &left, const Array<T> &right)
MaskedArray<T> fmod(const MaskedArray<T> &left, const Array<T> &right)
MaskedArray<T> atan2(const Array<T> &left, const MaskedArray<T> &right)
MaskedArray<T> fmod(const Array<T> &left, const MaskedArray<T> &right)
MaskedArray<T> atan2(const MaskedArray<T> &left,const MaskedArray<T> &right)
MaskedArray<T> fmod(const MaskedArray<T> &left,const MaskedArray<T> &right)
MaskedArray<T> atan2(const MaskedArray<T> &left, const T &right)
MaskedArray<T> fmod(const MaskedArray<T> &left, const T &right)
MaskedArray<T> atan2(const T &left, const MaskedArray<T> &right)
MaskedArray<T> fmod(const T &left, const MaskedArray<T> &right)
MaskedArray<T> pow(const MaskedArray<T> &left, const Array<U> &right)
MaskedArray<T> pow(const Array<T> &left, const MaskedArray<U> &right)
MaskedArray<T> pow(const MaskedArray<T> &left,const MaskedArray<U> &right)
MaskedArray<T> pow(const MaskedArray<T> &left, const Double &right)

Transcendental functions requiring two arguments applied on an element-by-element basis. Although a template function, this may not make sense for all numeric types.

Thrown Exceptions

void minMax(T &minVal, T &maxVal, IPosition &minPos, IPosition &maxPos,const IPosition<T> &marray)
void minMax(T &minVal, T &maxVal,const MaskedArray<T> &marray)

Find the minimum and maximum values of a MaskedArray. Also find the IPositions of the minimum and maximum values.

Thrown Exceptions

T min(const MaskedArray<T> &left)

The "min" and "max" functions require that the type "T" have comparison operators. The minimum element of the array.

MaskedArray<T> min(const MaskedArray<T> &left, const Array<T> &right)
MaskedArray<T> min(const Array<T> &left, const MaskedArray<T> &right)
MaskedArray<T> min(const MaskedArray<T> &left, const MaskedArray<T> &right)
MaskedArray<T> min(const T &left, const MaskedArray<T> &right)
MaskedArray<T> min(const MaskedArray<T> &left, const T &right)

Return an array that contains the minimum of "left" and "right" at each position.

"left" and "right" must be conformant.

Thrown Exceptions

void min(const MaskedArray<T> &result, const Array<T> &left, const Array<T> &right)

"result" contains the minimum of "left" and "right" at each position. "result", "left", and "right" must be conformant.

Thrown Exceptions

T max(const MaskedArray<T> &left)

The maximum element of the array.

MaskedArray<T> max(const MaskedArray<T> &left, const Array<T> &right)
MaskedArray<T> max(const Array<T> &left, const MaskedArray<T> &right)
MaskedArray<T> max(const MaskedArray<T> &left, const MaskedArray<T> &right)
MaskedArray<T> max(const T &left, const MaskedArray<T> &right)
MaskedArray<T> max(const MaskedArray<T> &left, const T &right)

Return an array that contains the maximum of "left" and "right" at each position.

"left" and "right" must be conformant.

Thrown Exceptions

void max(const MaskedArray<T> &result,const Array<T> &left, const Array<T> &right)

"result" contains the maximum of "left" and "right" at each position. "result", "left", and "right" must be conformant.

Thrown Exceptions

void indgen(MaskedArray<T> &a, T start, T inc)

Fills all elements of "array" where the mask is True with a sequence starting with "start" and incrementing by "inc" for each element where the mask is True. The first axis varies most rapidly.

void indgen(MaskedArray<T> &a)

Fills all elements of "array" where the mask is True with a sequence starting with 0 and incremented by one for each element where the mask is True. The first axis varies most rapidly.

void indgen(MaskedArray<T> &a, T start)

Fills all elements of "array" where the mask is True with a sequence starting with "start" and incremented by one for each element where the mask is True. The first axis varies most rapidly.

T sum(const MaskedArray<T> &a)

Thrown Exceptions

Sum of every element of the MaskedArray where the Mask is True.

T sumsquares(const MaskedArray<T> &a)

Sum of the squares of every element of the MaskedArray where the Mask is True.

T product(const MaskedArray<T> &a)

Product of every element of the MaskedArray where the Mask is True. This could of course easily overflow.

T mean(const MaskedArray<T> &a)

The mean of "a" is the sum of all elements of "a" divided by the number of elements of "a".

T variance(const MaskedArray<T> &a)

The variance of "a" is the sum of (a(i) - mean(a))**2/(a.nelements() - 1). N.B. N-1, not N in the denominator).

T variance(const MaskedArray<T> &a, T mean)

The variance of "a" is the sum of (a(i) - mean(a))**2/(a.nelements() - 1). N.B. N-1, not N in the denominator). Rather than using a computed mean, use the supplied value.

T stddev(const MaskedArray<T> &a)

The standard deviation of "a" is the sqare root of its variance.

T stddev(const MaskedArray<T> &a, T mean)

The standard deviation of "a" is the sqare root of its variance. Rather than using a computed mean, use the supplied value.

T avdev(const MaskedArray<T> &a)

The average deviation of "a" is the sum of abs(a(i) - mean(a))/N. (N.B. N, not N-1 in the denominator).

T avdev(const MaskedArray<T> &a,T mean)

The average deviation of "a" is the sum of abs(a(i) - mean(a))/N. (N.B. N, not N-1 in the denominator). Rather than using a computed mean, use the supplied value.

inline T median(const MaskedArray<T> &a, Bool sorted = False)
T median(const MaskedArray<T> &a, Bool sorted, Bool takeEvenMean)

The median of "a" is a(n/2). When a has an even number of elements and the switch takeEvenMean is set, the median is 0.5*(a(n/2) + a((n+1)/2)). According to Numerical Recipes (2nd edition) it makes little sense to take the mean when the array is large enough (> 100 elements). Therefore the default for takeEvenMean is False when the array has > 100 elements, otherwise it is True.
If "sorted"==True we assume the data is already sorted and we compute the median directly. Otherwise the function GenSort::kthLargest is used to find the median (kthLargest is about 6 times faster than a full quicksort).

MaskedArray<T> square(const MaskedArray<T> &val)

Returns a MaskedArray where every element is squared.

MaskedArray<T> cube(const MaskedArray<T> &val)

Returns a MaskedArray where every element is cubed.