Table functions

For building a table, the grid rules, editing keys and the toolbar, see Tables.

lookup

lookup(T, key)
lookup(T, key, col)

Finds the row of T whose key-column cell equals key, and returns the row, or one cell of it when col is given. The header row is never searched.

Parameters

Parameter	Meaning
T	A table: a table block’s name, or any matrix with a header row (row 1) and a key column (column 1).
key	The value to find in the key column. Text matches text exactly; a number or quantity matches by value, converting units, so a key of $10\mathrm{minute}$ is found by $600\mathrm{s}$. Text and numbers never match each other.
col	Optional. Which cell of the row: a 1-based position counting the key column, or a header label as text.

Returns

Without col, the matching row as a vector, key included. With col, that one cell.

Errors

Message	When
lookup needs a table with a header row and a key column (a matrix with rows and columns)	T is not a 2-D grid
No row of T has key M24 — keys: M12, M16, M20	No key matches; the keys the table has are listed
5 kg can’t be compared with T’s keys	key is of a type that can’t be compared with the keys
T’s columns are numbered from 1	col is not a positive whole number
T has only 3 columns	col is beyond the last column
No column of T is labelled p — columns: size, d, A_s	No header matches col
Say which column of T by its position (a number) or its header (a text label)	col is neither a number nor text

Example

With this table named $T$:

size	$d$	$A_s$
M12	$12\mathrm{mm}$	$84.3\mathrm{m}{\mathrm{m}}^2$
M16	$16\mathrm{mm}$	$157\mathrm{m}{\mathrm{m}}^2$
M20	$20\mathrm{mm}$	$245\mathrm{m}{\mathrm{m}}^2$

$$\begin{array}{rl}\mathrm{lookup}(T,\text{M16})& =\left[\begin{array}{ccc}\text{M16}& 16\mathrm{mm}& 157\mathrm{m}{\mathrm{m}}^2\end{array}\right]\\ \mathrm{lookup}(T,\text{M16},3)& =157\mathrm{m}{\mathrm{m}}^2\\ \mathrm{lookup}(T,\text{M16},\text{A\_s})& =157\mathrm{m}{\mathrm{m}}^2\end{array}$$

interp

interp(T, x)
interp(T, x, col)

Interpolates linearly down the key column at x and returns the value from col, or from the second column when T has exactly two columns. An exact key returns that cell unchanged. Never extrapolates.

Parameters

Parameter	Meaning
T	A table whose keys are numbers or quantities, at least two rows of them, in strictly increasing or strictly decreasing order.
x	A number or quantity comparable with the keys, within their range.
col	Optional unless T has more than two columns. A 1-based position counting the key column, or a header label as text. The column must be numeric with no blank cells.

Returns

The interpolated value, carrying the column’s units.

Errors

Message	When
interp needs a table with a header row and a key column (a matrix with rows and columns)	T is not a 2-D grid
T has 3 columns — say which column: interp(T, x, col)	More than two columns and no col
keys of T must be numbers (or quantities with units) to interpolate	A text key
keys of T must be in increasing or decreasing order	Jumbled or repeated keys
keys of T must all share one unit	Mixed units in the key column
T needs at least two rows of keys to interpolate	Only one data row
T’s column 2 holds text, which can’t be interpolated	A text cell in the chosen column
T’s column 2 has a blank cell	A gap in the chosen column
x = 11 is outside T’s keys (0 … 10)	x is out of range, and there is no extrapolation
5 kg can’t be compared with T’s keys	x is of a type that can’t be compared with the keys
T’s columns are numbered from 1, T has only 3 columns, No column of T is labelled p — …	col problems, as for lookup

Example

$$\begin{array}{rl}\mathrm{interp}\left(\left[\begin{array}{cc}x& y\\ 0& 0\\ 10& 1\end{array}\right],5\right)& =0.5\\ \mathrm{interp}\left(\left[\begin{array}{cc}x& y\\ 0& 0\\ 10& 1\\ 20& 5\end{array}\right],15\right)& =3\\ \mathrm{interp}\left(\left[\begin{array}{cc}x& y\\ 0& 0\\ 10& 1\end{array}\right],10\right)& =1\text{(exact key)}\end{array}$$

On a wider table, name the column by position or header: $\mathrm{interp}(T,5,3)$ or $\mathrm{interp}(T,5,\text{b})$.

interp2

interp2(T, x, y)

Interpolates bilinearly: x down the key column and y across the numeric header row. Each column is interpolated at x, then the results are interpolated across the headers at y. Never extrapolates on either axis.

Parameters

Parameter	Meaning
T	A table whose keys are numeric, ordered and at least two, as for interp, and whose column headers after the key column are at least two numbers, also in order.
x	A number or quantity within the range of the keys.
y	A number or quantity within the range of the column headers.

Returns

The interpolated value.

Errors

Message	When
interp2 needs a table with a header row and a key column (a matrix with rows and columns)	T is not a 2-D grid
interp2 needs numeric column headers (T’s are size, d, A_s)	A text header, or fewer than two headers after the key column
keys of T must be numbers (or quantities with units) to interpolate	A text key
keys of T must be in increasing or decreasing order	Jumbled or repeated keys
column headers of T must be in increasing or decreasing order	Jumbled or repeated headers
T needs at least two rows of keys to interpolate	Only one data row
T’s column 2 holds text, which can’t be interpolated / …has a blank cell	A text or blank cell in the body
x = 2 is outside T’s keys (0 … 1)	x out of range, and there is no extrapolation
y = 2 is outside T’s column headers (0 … 1)	y out of range, and there is no extrapolation
keys of T must all share one unit / column headers of T must all share one unit	Mixed units on an axis

Example

$$T=\left[\begin{array}{ccc}p& 0& 1\\ 0& 0& 10\\ 1& 100& 110\end{array}\right]$$ $$\begin{array}{rl}interp2(T,0.5,0.5)& =55\\ interp2(T,1,0.25)& =102.5\end{array}$$