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2023.0.0 - 日本語

brackets [,;]

Concatenation. Recipients of an assignment. Results of a function


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])


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 (if mi are so). structures arrays (if mi are so).

e1, e2,..

Input objects (literals like -1.23 or "abcd", variables, or expressions like a+%pi, etc).


a simple list


Array of Structures with a field named field.

i1, i2,..

Indices of components selected from S.

r1, r2,...

Output variables


[] 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:

  1. boolean < encoded integers < decimal number < complex
  2. 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.
  3. 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.
  4. 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.
  5. Concatenated polynomials or/and rationals must have the same variable name.
  6. Text components can be concatenated (in the set meaning, with brackets) only with other text components or with the empty matrix [].


  • [,]: 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".


  • To concatenate simple lists, please use lstcat.
  • To stack vectors or matrices over some dimension > 2 to build a N-dimensional array, please use cat.

[] 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 because c expects some foods.
  • [a,b,a] = (%pi, %z, "Allo") performs assignments from left to right, such that finally a = "Allo".


// 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]

[%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:

[%F %z]
[%s %z]
[int8(-70), sparse(18)]
[int8(-70), sparse([%T %F])]

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.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  =

 b  =

 c  =

--> [a, b] = (%e, %f, "Hello")
 a  =

 b  =

--> [a, b, a] = (%pi, %t, "test"); a
 a  =

See also

  • cat — 複数の配列を結合する
  • lstcat — リストの結合
  • comma — (,) 列, 命令, 引数セパレータ
  • semicolon — 式の末尾および行セパレータ
  • parentheses — ( ) 左および右括弧
  • empty — empty matrix. Array ranges destructor.
  • overloading — 表示,関数および演算子オーバーロード機能


6.0 Brackets [..] and braces {..} are no longer equivalent
  • Booleans and encoded integers can now be concatenated together, as in [%t, int8(-5)].
  • [a, b, ..] = (A, B,..) now performs assignments from left to right.
  • Concatenations between encoded integers and decimal numbers are now supported.
  • Concatenated polynomials or/and rationals must have the same variable name.
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Last updated:
Tue Mar 07 09:28:37 CET 2023