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brackets [,;]
Concatenation. Recipients of an assignment. Results of a function
Syntax
Mh = [m11 m12 m13.. m1N] or [m11, m12, m13,.., m1N] Mv = [m11 ; m21 ; m31..; mN1] M = [m11, m12,...; m21, m22,...;...] [r1, r2,...] = func(...) [r1, r2,.., rN] = (e1, e2, .., eN) [r1, r2,.., rk] = (e1, e2, .., ek,.., eN) [r1, r2,.., rN] = mylist(:) [r1, r2,.., rN] = S.field([i1 i2.. iN])
Arguments
- m11, m12,...
Set of objects to be concatenated (and merged: the former individual containers are removed). The following subsets of types of objects can be mixed in-between, but are mutually exclusive:
- Matrices of booleans, reals, complex numbers, polynomials, rationals: The data type of the concatenated result is set by the rules defined below (see the type conversions rules).
- Matrices of encoded integers of any
inttype.
Encoded integers of different inttypes can't be concatenated together.
- Arrays of cells.
- Arrays of structures with same fields. Fields may be in different orders from an array to other ones.
- Typed lists of type syslin.
- M, Mh, Mv
Matrices with the type of all
m##
(if they all have the same data type). cells arrays (ifmi
are so). structures arrays (ifmi
are so).- e1, e2,..
Input objects (literals like
-1.23
or"abcd"
, variables, or expressions likea+%pi
, etc).- mylist
a simple list
- S.field
Array of Structures with a field named
field
.- i1, i2,..
Indices of components selected from
S
.- r1, r2,...
Output variables
Description
- [] on right-hand side: concatenators
[..] bundle their contents of simple and compatible types into a homogeneous vector, matrix or hypermatrix.
An horizontal or a vertical concatenation is a binary iterated operator. It is performed step-by-step from left-to-right, and from top-to-bottom. Thus,[1 3 5 7]
is performed as[[[1 3] 5] 7]
.Inside brackets,
- spaces (blanks or tabs) or commas are used as columns separators.
Using commas instead of spaces is safer. For instance,
[2 1 +%i]
means[2, 1, %i]
, while[2 1 + %i]
means[2, 1+%i]
- semi-colons or carriage-return are used as rows separators.
Multiple rows do not need the continuation dots
..
Types conversions
In some limits, brackets may be applied on a set of data having different but compatible types. In this case, some data are converted into the dominating type available in the set. The main conversion rules are the following:
- boolean < encoded integers < decimal number < complex
- decimal number < polynomial < rational
booleans and polynomials are not compatible.
[%t 2. %z]
is accepted:[%t 2.]
is first converted into[1. 2.]
, and then[[1. 2.] %z]
is accepted.[%z %t 2.]
is rejected and yields an error. Indeed,[%z %t]
can't be converted first.
- Any encoded integer can be concatenated only with booleans,
decimal numbers, or other integers of the same inttype.
Thus, the expressions
[int8(2), uint8(7)]
,[int8(2), int16(7)]
,[int8(2), 7+0*%z]
,[int8(2), sparse(7)]
, or[int8(2), sparse(%t)]
will yield an error. - The result becomes complex-encoded as soon as a complex-encoded component -- value, polynomial, or rational -- is met in the list (even with a null imaginary part) Similarly, the result becomes sparse-encoded as soon as a sparse-encoded component is met and processed.
- Concatenated polynomials or/and rationals must have the same variable name.
- Text components can be concatenated (in the set meaning,
with brackets) only with other text components or with the
empty matrix
[]
.
Overloading
- [,]: horizontal concatenation:
This operator is binary and automatically
iterated from left to right. Its overloading
code is
"c"
. - [;]: vertical concatenation:
This operator is binary and automatically
iterated from top to bottom. Its overloading
code is
"f"
.
- spaces (blanks or tabs) or commas are used as columns separators.
- [] on left-hand side of a
"="
assignment In this case, brackets are no longer concatenators. They are used as left and right delimiters of a series of variables used as recipients.
- Recipients must be variables. Literal expressions are not accepted.
- Variables shall be separated with commas.
- In a distributive assignment, there must
be at most as many LHS recipients
as output sources, not more. If there are less
recipients on the left than sources on the right,
non-collected data sources are ignored. Examples :
[a,b]=(%pi,"Hi", %z)
is OK, but%z
is ignored.[a,b,c]=(%pi,"Hi")
yields an error becausec
expects some foods.
[a,b,a] = (%pi, %z, "Allo")
performs assignments from left to right, such that finallya = "Allo"
.
Examples
// Horizontal concatenations a = [ %pi 4 -1 ] b1 = grand(3,4,"uin",0,10) b2 = grand(3,2,"uin",0,10) b = [b1 b2] // they must have the same number of rows // Vertical concatenations a = [-2 ; 10 ; 7] b1 = grand(2,4,"uin",0,10) b2 = grand(3,4,"uin",0,10) b = [b1 ; b2] // they must have the same number of columns // Mixed horizontal and vertical concatenations a = [ 3 7 ; 6, 5 ] b = [ 1:3 ; 7:3:13] c = [ a b ; a b] d = [ 3 5 1 4 ] e = [ d d d d d d ] // Concatenation of various types of data: ['this is' ; 'a column' ; 'of texts'] s = poly(0,'s');[1/s,2/s] [tf2ss(1/s),tf2ss(2/s)] [%t %f %f %T %F]
Heterogeneous concatenations with automatical type conversions:
[%T int8(-5)] [%T %pi %f 2] [%pi, 2+%i, %F] [%pi int16(-1000.84) 1.23] v = [%pi+0*%i, %F, %z, (1-%z)^2 ]; typeof(v), isreal(v) v = [10 1/%z], typeof(v) // Special case: int16 and uint8 together, due to initial // conversion to real propagating from left to right [%pi int16(-1000.84) uint8(87)]
Incompatible heterogeneous concatenations => ERRORS:
Concatenation of cells arrays:
// Concatenation of cells arrays: c1 = {%pi %t}; c2 = {%z "abc"}; c = [[{%i} c1] ; [c2, {1/%z^2}]] // comma mandatory, to not parse c2{1/%z^2}
Distributive assignments:
// Output from a function. Most often, output results are serially optional: M = rand(3,3); [u, s] = schur(M) // we expect and use both results u and s u = schur(M) // we expect and store only the first result u // Direct RHS list [a, b, c] = (%pi, %t, "test") [a, b] = (%e, %f, "Hello") [a, b, a] = (%pi, %t, "test"); a // Explicit RHS list L = list(%z, %i, %t, %pi, "Text"); [a, b, c] = L(:) // RHS structure s(2,3).r = %pi; s(2,1).r = %i; s(2,2) = %e; s(2,:).r s.r([2 4 6]) [a, b, c] = s.r([2 4 6]) // Forbidden / Rejected LHS expressions (=> error) [m, n, m+n] = myfun(a,b) // Symbolic expressions like "m+n" are forbidden [p, 4.5, q] = myfun(a,b) // Literal LHS values or expressions like "4.5" are forbidden [r, s+3 ] = myfun(a,b) // Expressions mixing literals and symbols like "s+3" can't be LHS recipients
--> [a, b, c] = (%pi, %t, "test") a = 3.1415927 b = T c = test --> [a, b] = (%e, %f, "Hello") a = 2.7182818 b = F --> [a, b, a] = (%pi, %t, "test"); a a = test
See also
- cat — concatena vários arrays
- lstcat — concatenação de listas
- comma — (,) separador de colunas, instruções e argumentos
- semicolon — (;) fim de expressão e separador de linhas
- parentheses — ( ) parênteses esquerdo e direito
- empty — empty matrix. Array ranges destructor.
- overloading — capacidades de overloading ("sobrecarga") de exibições, funções e operadores
History
Versão | Descrição |
6.0 | Brackets [..] and braces
{..} are no longer equivalent |
6.1.0 |
|
6.1.1 |
|
Report an issue | ||
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