Arrays and ranges

A table of results

A range variable takes a run of whole numbers. A statement that uses it is worked out once for each value:

L := 6 m
q := 12 kN/m
i := 0..4
x[i] := i*L/4
M_x[i] := q*x[i]*(L - x[i])/2
x = ?
M_x = ? — As text
L := 6 m q := 12 kN/m i := 0..4 x[i] := i*L/4 M_x[i] := q*x[i]*(L - x[i])/2 x = ? M_x = ?
Open this example · Download .bbm

Type ; for the two dots of a range (i:0;4), and [ for an index (x[i). On the page, x[i] is drawn as x with a subscript i, and the results as columns.

x[i] := … defines one element of the vector x for each value of i.
A range can step by any amount: give the first two values, then the last. s := 0 m, 1.5 m..L is 0, 1.5, 3, 4.5 and 6 m.
A range variable stands for one value at a time, so y := i^2 is an error: define elements (y[i] := i^2) instead.

Vectors and matrices

Ctrl+M asks for the number of rows and columns and makes an empty matrix to fill in. In a file, , separates columns and ; rows:

v := [3; 4; 12]
M := [2, 1; 1, 3]
v[0] = ?
|v| = ?
M^-1 = ?
|M| = ?
M^T = ? — As text
v := [3; 4; 12] M := [2, 1; 1, 3] v[0] = ? |v| = ? M^-1 = ? |M| = ? M^T = ?
Open this example · Download .bbm

Indices start at 0. To count from 1, define ORIGIN := 1 above, or set origin: 1 for the whole sheet.
|v| is a vector’s length, and |M| a square matrix’s determinant. M^-1 is the inverse and M^T the transpose (Ctrl+1).
M^<j> is column j of M (Ctrl+6).

Each element keeps its own unit, so a vector can hold a force and a moment:

F := [10 kN; 2 kN*m]
F = ? — As text
F := [10 kN; 2 kN*m] F = ?
Open this example · Download .bbm

Working on every element

A function that takes one number, such as sqrt, sin or round, works on every element of an array, and gives an array of the same shape:

As text
sqrt(v) = ?
Open this example · Download .bbm

Arithmetic between arrays follows the rules of matrices: M*v is a matrix product, and two vectors multiplied give their dot product. To multiply element by element instead, wrap the expression in vec( ) (Ctrl+-, drawn as an arrow over it):

As text
vec(v*v) = ?
Open this example · Download .bbm

Sums

sum(v) = ?
sum(i^2, i) = ?
sum(k^2, k, 1, 4) = ?
max(v) = ?
rows(M_x) = ? — As text
sum(v) = ? sum(i^2, i) = ? sum(k^2, k, 1, 4) = ? max(v) = ? rows(M_x) = ?
Open this example · Download .bbm

sum(v) adds a vector’s elements; sum(expr, i) adds over a range variable ($); sum(expr, k, a, b) from a to b (Ctrl+Shift+4). prod is the same for products.

The array functions include rows, cols, augment, stack, submatrix, sort, eigenvals and more.

Big arrays

An array with more than 20 rows or columns is shown as a table of 20 at a time, with its row and column numbers. Scroll it with the mouse wheel over it (Shift and the wheel to go sideways).