indexval

Indexed access to arrays and tables without evaluation

Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

Syntax

indexval(x, i)
indexval(x, i1, i2, …)

Description

indexval(x, i) and indexval(x, i1, i2, ...) yields the entry of x corresponding to the indices i and i1, i2, ..., respectively, without evaluation.

The three calls indexval(x, i), _index(x, i), and x[i] all return the element of index i in the array or hfarray or list or table x. In contrast to _index and the equivalent index operator [ ], however, indexval returns the corresponding entry without evaluating it. This is sometimes desirable for efficiency reasons.

The arguments i or i1, i2, ... must be a valid indices of x, otherwise an error message is printed (see Example 3). When several indices i1, i2, ... are given, they are interpreted as a higher-dimensional index (see Example 4).

The first argument x may also be a set, a string, or an expression sequence. However, in these cases indexval behaves exactly like _index and the index operator [ ]: it returns the evaluation of the corresponding element. In particular, indexval does not flatten its first argument.

For all other basic domains, indexval behaves exactly like _index: either an error occurs, or a symbolic indexval call is returned (see Example 3).

Examples

Example 1

indexval works with tables:

T := table("1" = a, Be = b, `+` = a + b):
a := 1: b := 2:
indexval(T, Be), indexval(T, "1"), indexval(T, `+`)

In contrast _index evaluates returned entries:

_index(T, Be), _index(T, "1"), _index(T, `+`)

The next input line has the same meaning as the last:

T[Be], T["1"], T[`+`]

indexval works with arrays, too. The behavior is the same, but the indices must be positive integers:

delete a, b:
A := array(1..2, 1..2, [[a, a + b], [a - b, b]]):
a := 1: b := 2:
indexval(A, 2, 2), indexval(A, 1, 1), indexval(A, 1, 2)

_index(A, 2, 2), _index(A, 1, 1), _index(A, 1, 2)

A[2, 2], A[1, 1], A[1, 2]

delete A, T, a, b:

indexval works lists, too:

delete a, b:
L := [a, b, 2]:
b := 5:
L[2], _index(L, 2), indexval(L, 2), op(L, 2)

Example 2

However, there is no difference between indexval and _index for all other valid objects, e.g., sets:

delete a, b:
S := {a, b, 2}:
b := 5:
S[2], _index(S, 2), indexval(S, 2), op(S, 2)

Similarly, there is no difference when the first argument is an expression sequence (which is not flattened by indexval):

delete a, b: S := a, b, 2:
b := 5:
S[2], _index(S, 2), indexval(S, 2), op(S, 2)

delete L, S, a, b:

Example 3

If the second argument is not a valid index, an error occurs:

A := array(1..2, 1..2, [[a, b], [a, b]]):
indexval(A, 3)
Error: Index dimension mismatch. [array]
indexval(A, 1, 0)
Error: The argument is invalid. [array]
indexval("12345", 6)
Error: The index is invalid. [string]

However, the result of indexval can also be a symbolic indexval call:

T := table(1 = a, 2 = b):
indexval(T, 3)

delete X, i:
indexval(X, i)

delete A, T:

Example 4

For arrays the number of indices must be equal to the number of dimensions of the array:

A := array(1..2, 1..2, [[a, b], [a, b]]):
a := 1: b := 2:
indexval(A, 1, 2), indexval(A, 2, 1)

Otherwise an error occurs:

indexval(A, 1)
Error: Index dimension mismatch. [array]

Tables can have expression sequences as indices, too:

delete a, b:
T := table((1, 1) = a, (2, 2) = b):
a := 1: b := 2:
indexval(T, 1, 1), indexval(T, 2, 2)

delete A, T, a, b:

Parameters

x

Essentially a table, a list, or an array. Also allowed: a hfarray, a finite set, an expression sequence, or a character string

i, i1, i2, …

Indices. For most "containers" x, indices must be integers. If x is a table, arbitrary MuPAD® objects can be used as indices.

Return Values

Entry of x corresponding to the index. When x is a table, a list or an array, the returned entry is not evaluated again.

Overloaded By

x

See Also

MuPAD Domains

MuPAD Functions

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