at

Syntax

at(X, [index])

Arguments

If only 1 parameter is specified: X is a Boolean expression or a vector.

If both parameters are specified: X is a scalar/vector (including tuples)/matrix/table/dictionary/pair/function;

index is a Boolean expression/Boolean value/scalar/vector (including tuples)/pair.

Details

In the first case, return the indexes of the elements of X that are true.

In the second case:

  • If index is a Boolean expression, at returns the elements in X that correspond to the elements in Y that are true. Function at is equivalent to brackets operator []. For example, “X.at(X>3) is equivalent to “X[X>3]”.

  • If index is a vector, at retrieves the elements from X at the positions as specified by each element of index.

  • If index is a tuple, each element in the tuple specifies an index into the corresponding dimension of X. at retrieves the element(s) at the specified position as specified by the indices. For example, when X is a matrix, index must be a tuple of two elements - the first element indicates the row index, and the second element indicates the column index.

  • If index is a pair like a:b, at returns the elements from X in the range [a,b).

Note: When index refers to column/row index, or an index range, for elements outside the bounds of the X (i.e. outside of [0,size(X)-1]), the corresponding positions in X will return NULL values.

If X is a function, index specifies the arguments of X.

Examples

$ x=5 7 0 4 2 3
$ at(x>3)
[0,1,3]
// at position 0, 1, and 3, x>3 is true.

// compare with x>3:
$ x>3;
[1,1,0,1,0,0]

$ x[x>3]
[5,7,4]
$ x at x>3
[5,7,4]

$ x=5 7 0 0 0 3
$ at(x==0)
[2,3,4]

$ x[x==0]
[0,0,0]

$ shares=500 1000 1000 600 2000
$ prices=25.5 97.5  19.2 38.4 101.5
$ prices[shares>800]
[97.5,19.2,101.5]
$ prices at shares>800
[97.5,19.2,101.5]

$ m=(1..6).reshape(2:3)
$ m;

0

1

2

1

3

5

2

4

6

 
$ at(m>3)
[3,4,5]

$ m[m>3] // equal to m at m>3

col1

col2

col3

5

4

6

Note the difference between using a vector versus a tuple for index:

$ m at [0,2]  // locate column 0 and 2

0

1

1

5

2

6

 
$ m at (0,2) // locate element at a specific column and a specific row
5

$ m at 0:2 // locate column 0 and 1

0

1

1

3

2

4

When X is a function:

$ (sum)[1..10]
55

$ (corr)[1 3 -1, 2 3 4]
-0.5000