Creates an \(n\)-dimensional array. \(n\) may be less than or equal to 5. The subscripts for the \(i\)’th dimension are the integers running from 0 to dim_i.
array (name, dim_1, ..., dim_n) creates a general
array.
array (name, type, dim_1, ..., dim_n) creates
an array, with elements of a specified type. type can be fixnum
for integers of limited size or flonum for floating-point numbers.
array ([name_1, ..., name_m], dim_1, ..., dim_n)
creates \(m\) arrays, all of the same dimensions.
See also arraymake, arrayinfo and make_array.
Evaluates A [i_1, ..., i_n],
where A is an array and i_1, …, i_n are integers.
This is reminiscent of apply, except the first argument is an array
instead of a function.
Returns information about the array A.
The argument A may be a declared array, a hashed array,
a memoizing function, or a subscripted function.
For declared arrays, arrayinfo returns a list comprising the atom
declared, the number of dimensions, and the size of each dimension.
The elements of the array, both bound and unbound, are returned by
listarray.
For undeclared arrays (hashed arrays), arrayinfo returns a list
comprising the atom hashed, the number of subscripts,
and the subscripts of every element which has a value.
The values are returned by listarray.
For memoizing functions, arrayinfo returns a list comprising the atom
hashed, the number of subscripts,
and any subscript values for which there are stored function values.
The stored function values are returned by listarray.
For subscripted functions, arrayinfo returns a list comprising the atom
hashed, the number of subscripts,
and any subscript values for which there are lambda expressions.
The lambda expressions are returned by listarray.
See also listarray.
Examples:
arrayinfo and listarray applied to a declared array.
(%i1) array (aa, 2, 3); (%o1) aa
(%i2) aa [2, 3] : %pi; (%o2) %pi
(%i3) aa [1, 2] : %e; (%o3) %e
(%i4) arrayinfo (aa); (%o4) [declared, 2, [2, 3]]
(%i5) listarray (aa);
(%o5) [#####, #####, #####, #####, #####, #####, %e, #####,
#####, #####, #####, %pi]
arrayinfo and listarray applied to an undeclared array (hashed array.).
(%i1) bb [FOO] : (a + b)^2;
2
(%o1) (b + a)
(%i2) bb [BAR] : (c - d)^3;
3
(%o2) (c - d)
(%i3) arrayinfo (bb); (%o3) [hashed, 1, [BAR], [FOO]]
(%i4) listarray (bb);
3 2
(%o4) [(c - d) , (b + a) ]
arrayinfo and listarray applied to a memoizing function.
(%i1) cc [x, y] := y / x;
y
(%o1) cc := -
x, y x
(%i2) cc [u, v];
v
(%o2) -
u
(%i3) cc [4, z];
z
(%o3) -
4
(%i4) arrayinfo (cc); (%o4) [hashed, 2, [4, z], [u, v]]
(%i5) listarray (cc);
z v
(%o5) [-, -]
4 u
Using arrayinfo in order to convert an undeclared array to a declared array:
(%i1) for i:0 thru 10 do a[i]:i^2$
(%i2) indices:map(first,rest(rest(arrayinfo(a)))); (%o2) [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
(%i3) array(A,fixnum,length(indices)-1)$ (%i4) fillarray(A,map(lambda([x],a[x]),indices))$
(%i5) listarray(A); (%o5) [0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100]
arrayinfo and listarray applied to a subscripted function.
(%i1) dd [x] (y) := y ^ x;
x
(%o1) dd (y) := y
x
(%i2) dd [a + b];
b + a
(%o2) lambda([y], y )
(%i3) dd [v - u];
v - u
(%o3) lambda([y], y )
(%i4) arrayinfo (dd); (%o4) [hashed, 1, [b + a], [v - u]]
(%i5) listarray (dd);
b + a v - u
(%o5) [lambda([y], y ), lambda([y], y )]
Returns the expression A[i_1, ..., i_n].
The result is an unevaluated array reference.
arraymake is reminiscent of funmake, except the return value
is an unevaluated array reference instead of an unevaluated function call.
Examples:
(%i1) arraymake (A, [1]);
(%o1) A
1
(%i2) arraymake (A, [k]);
(%o2) A
k
(%i3) arraymake (A, [i, j, 3]);
(%o3) A
i, j, 3
(%i4) array (A, fixnum, 10); (%o4) A
(%i5) fillarray (A, makelist (i^2, i, 1, 11)); (%o5) A
(%i6) arraymake (A, [5]);
(%o6) A
5
(%i7) ''%; (%o7) 36
(%i8) L : [a, b, c, d, e]; (%o8) [a, b, c, d, e]
(%i9) arraymake ('L, [n]);
(%o9) L
n
(%i10) ''%, n = 3; (%o10) c
(%i11) A2 : make_array (fixnum, 10);
(%o11) {Lisp Array: #(0 0 0 0 0 0 0 0 0 0)}
(%i12) fillarray (A2, [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]);
(%o12) {Lisp Array: #(1 2 3 4 5 6 7 8 9 10)}
(%i13) arraymake ('A2, [8]);
(%o13) A2
8
(%i14) ''%; (%o14) 9
Default value: []
arrays is a list of arrays that have been allocated.
These comprise arrays declared by array, hashed arrays that can be
constructed by implicit definition (assigning something to an element that isn’t yet
declared as a list or an array),
and memoizing functions defined by := and define.
Arrays defined by make_array are not included.
See also
array, arrayapply, arrayinfo,
arraymake, fillarray, listarray, and
rearray.
Examples:
(%i1) array (aa, 5, 7); (%o1) aa
(%i2) bb [FOO] : (a + b)^2;
2
(%o2) (b + a)
(%i3) cc [x] := x/100;
x
(%o3) cc := ---
x 100
(%i4) dd : make_array ('any, 7);
(%o4) {Lisp Array: #(NIL NIL NIL NIL NIL NIL NIL)}
(%i5) arrays; (%o5) [aa, bb, cc]
Assigns x to A[i_1, ..., i_n],
where A is an array and i_1, …, i_n are integers.
arraysetapply evaluates its arguments.
Fills array A from B, which is a list or an array.
If a specific type was declared for A when it was created, it can only be filled with elements of that same type; it is an error if an attempt is made to copy an element of a different type.
If the dimensions of the arrays A and B are different, A is filled in row-major order. If there are not enough elements in B the last element is used to fill out the rest of A. If there are too many, the remaining ones are ignored.
fillarray returns its first argument.
Examples:
Create an array of 9 elements and fill it from a list.
(%i1) array (a1, fixnum, 8); (%o1) a1
(%i2) listarray (a1); (%o2) [0, 0, 0, 0, 0, 0, 0, 0, 0]
(%i3) fillarray (a1, [1, 2, 3, 4, 5, 6, 7, 8, 9]); (%o3) a1
(%i4) listarray (a1); (%o4) [1, 2, 3, 4, 5, 6, 7, 8, 9]
When there are too few elements to fill the array, the last element is repeated. When there are too many elements, the extra elements are ignored.
(%i1) a2 : make_array (fixnum, 8);
(%o1) {Lisp Array: #(0 0 0 0 0 0 0 0)}
(%i2) fillarray (a2, [1, 2, 3, 4, 5]);
(%o2) {Lisp Array: #(1 2 3 4 5 5 5 5)}
(%i3) fillarray (a2, [4]);
(%o3) {Lisp Array: #(4 4 4 4 4 4 4 4)}
(%i4) fillarray (a2, makelist (i, i, 1, 100));
(%o4) {Lisp Array: #(1 2 3 4 5 6 7 8)}
Multiple-dimension arrays are filled in row-major order.
(%i1) a3 : make_array (fixnum, 2, 5);
(%o1) {Lisp Array: #2A((0 0 0 0 0) (0 0 0 0 0))}
(%i2) fillarray (a3, [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]);
(%o2) {Lisp Array: #2A((1 2 3 4 5) (6 7 8 9 10))}
(%i3) a4 : make_array (fixnum, 5, 2);
(%o3) {Lisp Array: #2A((0 0) (0 0) (0 0) (0 0) (0 0))}
(%i4) fillarray (a4, a3);
(%o4) {Lisp Array: #2A((1 2) (3 4) (5 6) (7 8) (9 10))}
Returns a list of the elements of the array A.
The argument A may be an array, an undeclared array (hashed array),
a memoizing function, or a subscripted function.
Elements are listed in row-major order.
That is, elements are sorted according to the first index, then according to
the second index, and so on. The sorting order of index values is the same as
the order established by orderless.
For undeclared arrays (hashed arrays), memoizing functions, and subscripted functions,
the elements correspond to the index values returned by arrayinfo.
Unbound elements of general arrays (that is, not fixnum and not
flonum) are returned as #####.
Unbound elements of fixnum or flonum arrays
are returned as 0 or 0.0, respectively.
Unbound elements of hashed arrays, memoizing functions,
and subscripted functions are not returned.
Examples:
listarray and arrayinfo applied to a declared array.
(%i1) array (aa, 2, 3); (%o1) aa
(%i2) aa [2, 3] : %pi; (%o2) %pi
(%i3) aa [1, 2] : %e; (%o3) %e
(%i4) listarray (aa);
(%o4) [#####, #####, #####, #####, #####, #####, %e, #####,
#####, #####, #####, %pi]
(%i5) arrayinfo (aa); (%o5) [declared, 2, [2, 3]]
listarray and arrayinfo applied to an undeclared array (hashed array).
(%i1) bb [FOO] : (a + b)^2;
2
(%o1) (b + a)
(%i2) bb [BAR] : (c - d)^3;
3
(%o2) (c - d)
(%i3) listarray (bb);
3 2
(%o3) [(c - d) , (b + a) ]
(%i4) arrayinfo (bb); (%o4) [hashed, 1, [BAR], [FOO]]
listarray and arrayinfo applied to a memoizing function.
(%i1) cc [x, y] := y / x;
y
(%o1) cc := -
x, y x
(%i2) cc [u, v];
v
(%o2) -
u
(%i3) cc [4, z];
z
(%o3) -
4
(%i4) listarray (cc);
z v
(%o4) [-, -]
4 u
(%i5) arrayinfo (cc); (%o5) [hashed, 2, [4, z], [u, v]]
listarray and arrayinfo applied to a subscripted function.
(%i1) dd [x] (y) := y ^ x;
x
(%o1) dd (y) := y
x
(%i2) dd [a + b];
b + a
(%o2) lambda([y], y )
(%i3) dd [v - u];
v - u
(%o3) lambda([y], y )
(%i4) listarray (dd);
b + a v - u
(%o4) [lambda([y], y ), lambda([y], y )]
(%i5) arrayinfo (dd); (%o5) [hashed, 1, [b + a], [v - u]]
Creates and returns a Lisp array. type may
be any, flonum, fixnum, hashed or
functional.
There are \(n\) indices,
and the \(i\)’th index runs from 0 to dim_i - 1.
The advantage of make_array over array is that the return value
doesn’t have a name, and once a pointer to it goes away, it will also go away.
For example, if y: make_array (...) then y points to an object
which takes up space, but after y: false, y no longer
points to that object, so the object can be garbage collected.
Examples:
(%i1) A1 : make_array (fixnum, 10);
(%o1) {Lisp Array: #(0 0 0 0 0 0 0 0 0 0)}
(%i2) A1 [8] : 1729; (%o2) 1729
(%i3) A1;
(%o3) {Lisp Array: #(0 0 0 0 0 0 0 0 1729 0)}
(%i4) A2 : make_array (flonum, 10);
(%o4) {Lisp Array: #(0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0)}
(%i5) A2 [2] : 2.718281828; (%o5) 2.718281828
(%i6) A2;
(%o6)
{Lisp Array: #(0.0 0.0 2.718281828 0.0 0.0 0.0 0.0 0.0 0.0 0.0)}
(%i7) A3 : make_array (any, 10);
(%o7) {Lisp Array: #(NIL NIL NIL NIL NIL NIL NIL NIL NIL NIL)}
(%i8) A3 [4] : x - y - z; (%o8) (- z) - y + x
(%i9) A3;
(%o9) {Lisp Array: #(NIL NIL NIL NIL
((MPLUS SIMP) $X ((MTIMES SIMP) -1 $Y) ((MTIMES S\
IMP) -1 $Z))
NIL NIL NIL NIL NIL)}
(%i10) A4 : make_array (fixnum, 2, 3, 5);
(%o10) {Lisp Array: #3A(((0 0 0 0 0) (0 0 0 0 0) (0 0 0 0 0))
((0 0 0 0 0) (0 0 0 0 0) (0 0 0 0 0)))}
(%i11) fillarray (A4, makelist (i, i, 1, 2*3*5));
(%o11) {Lisp Array: #3A(((1 2 3 4 5) (6 7 8 9 10) (11 12 13 14 1\
5))
((16 17 18 19 20) (21 22 23 24 25) (26 27 28 29\
30)))}
(%i12) A4 [0, 2, 1]; (%o12) 12
Changes the dimensions of an array.
The new array will be filled with the elements of the old one in
row-major order. If the old array was too small,
the remaining elements are filled with
false, 0.0 or 0,
depending on the type of the array. The type of the array cannot be
changed.
Removes arrays and array associated functions and frees the storage occupied.
The arguments may be declared arrays, hashed arrays, array
functions, and subscripted functions.
remarray (all) removes all items in the global list arrays.
It may be necessary to use this function if it is
desired to clear the cache of a memoizing function.
remarray returns the list of arrays removed.
remarray quotes its arguments.
Evaluates the subscripted expression x[i].
subvar evaluates its arguments.
arraymake (x, [i]) constructs the expression
x[i], but does not evaluate it.
Examples:
(%i1) x : foo $ (%i2) i : 3 $
(%i3) subvar (x, i);
(%o3) foo
3
(%i4) foo : [aa, bb, cc, dd, ee]$
(%i5) subvar (x, i); (%o5) cc
(%i6) arraymake (x, [i]);
(%o6) foo
3
(%i7) ''%; (%o7) cc
Returns true if expr is a subscripted variable, for example
a[i].
Default value: false
When use_fast_arrays is true,
arrays declared by array are values instead of properties,
and undeclared arrays (hashed arrays) are implemented as Lisp hashed arrays.
When use_fast_arrays is false,
arrays declared by array are properties,
and undeclared arrays are implemented with Maxima’s own hashed array implementation.
Note that the code use_fast_arrays switches to is not necessarily faster
than the default one; Arrays created by make_array are not affected by
use_fast_arrays.
See also translate_fast_arrays.
Default value: false
When translate_fast_arrays is true,
the Maxima-to-Lisp translator generates code that assumes arrays are values instead of properties,
as if use_fast_arrays were true.
When translate_fast_arrays is false,
the Maxima-to-Lisp translator generates code that assumes arrays are properties,
as if use_fast_arrays were false.