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<H1><A NAME="SEC76" HREF="maxima_toc.html#TOC76">Arrays and Tables</A></H1>
<H2><A NAME="SEC77" HREF="maxima_toc.html#TOC77">Definitions for Arrays and Tables</A></H2>
<P>
<DL>
<DT><U>Function:</U> <B>ARRAY</B> <I>(name, dim1, dim2, ..., dimk)</I>
<DD><A NAME="IDX565"></A>
This sets up a k-dimensional
array. A maximum of five dimensions may be used. The subscripts for
the ith dimension are the integers running from 0 to dimi. If the
user assigns to a subscripted variable before declaring the
corresponding array, an undeclared array is set up. If the user has
more than one array to be set up the same way, they may all be set up
at the same time, by ARRAY([list-of-names],dim1, dim2, ..., dimk).
Undeclared arrays, otherwise known as hashed arrays (because hash
coding is done on the subscripts), are more general than declared
arrays. The user does not declare their maximum size, and they grow
dynamically by hashing as more elements are assigned values. The
subscripts of undeclared arrays need not even be numbers. However,
unless an array is rather sparse, it is probably more efficient to
declare it when possible than to leave it undeclared. The ARRAY
function can be used to transform an undeclared array into a declared
array.
</P>
</DL>
<P>
<DL>
<DT><U>Function:</U> <B>ARRAYAPPLY</B> <I>(array,[sub1, ... ,subk])</I>
<DD><A NAME="IDX566"></A>
is like APPLY except the first
argument is an array.
</P>
</DL>
<P>
<DL>
<DT><U>Function:</U> <B>ARRAYINFO</B> <I>(a)</I>
<DD><A NAME="IDX567"></A>
returns a list of information about the array a. For
hashed arrays it returns a list of "HASHED", the number of subscripts,
and the subscripts of every element which has a value. For declared
arrays it returns a list of "DECLARED", the number of subscripts, and
the bounds that were given the the ARRAY function when it was called
on a. Do EXAMPLE(ARRAYINFO); for an example.
</P>
</DL>
<P>
<DL>
<DT><U>Function:</U> <B>ARRAYMAKE</B> <I>(name,[i1,i2,...])</I>
<DD><A NAME="IDX568"></A>
returns name[i1,i2,...].
</P>
</DL>
<P>
<DL>
<DT><U>Variable:</U> <B>ARRAYS</B>
<DD><A NAME="IDX569"></A>
default: [] a list of all the arrays that have been allocated,
both declared and undeclared. Functions which deal with arrays are:
ARRAY, ARRAYAPPLY, ARRAYINFO, ARRAYMAKE, FILLARRAY, LISTARRAY, and
REARRAY.
</DL>
</P>
<P>
<DL>
<DT><U>Function:</U> <B>BASHINDICES</B> <I>(expr)</I>
<DD><A NAME="IDX570"></A>
- transforms the expression expr by giving each
summation and product a unique index. This gives CHANGEVAR greater
precision when it is working with summations or products. The form of
the unique index is J<number>. The quantity <number> is determined by
referring to GENSUMNUM, which can be changed by the user. For
example, GENSUMNUM:0$ resets it.
</P>
</DL>
<P>
<DL>
<DT><U>Function:</U> <B>FILLARRAY</B> <I>(array,list-or-array)</I>
<DD><A NAME="IDX571"></A>
fills array from list-or-array. If
array is a floating-point (integer) array then list-or-array should be
either a list of floating-point (integer) numbers or another
floating-point (integer) array. If the dimensions of the arrays are
different array is filled in row-major order. If there are not enough
elements in list-or-array the last element is used to fill out the
rest of array. If there are too many the remaining ones are thrown
away. FILLARRAY returns its first argument.
</P>
</DL>
<P>
<DL>
<DT><U>Function:</U> <B>GETCHAR</B> <I>(a, i)</I>
<DD><A NAME="IDX572"></A>
returns the ith character of the quoted string or
atomic name a. This function is useful in manipulating the LABELS
list.
</P>
</DL>
<P>
<DL>
<DT><U>Function:</U> <B>LISTARRAY</B> <I>(array)</I>
<DD><A NAME="IDX573"></A>
returns a list of the elements of a declared or
hashed array. the order is row-major. Elements which you have not
defined yet will be represented by #####.
</P>
</DL>
<P>
<DL>
<DT><U>Function:</U> <B>MAKE_ARRAY</B> <I>(type,dim1,dim2,...,dimn)</I>
<DD><A NAME="IDX574"></A>
- creates an array. "type" may
be 'ANY, 'FLONUM, 'FIXNUM, 'HASHED or 'FUNCTIONAL. This is similar to
the ARRAY command, except that the created array is a functional array
object. The advantage of this over ARRAY is that it doesn't have a
name, and once a pointer to it goes away, it will also go away. e.g.
Y:MAKE_ARRAY(....); Y now points to an object which takes up space,
but do Y:FALSE, and Y no longer points to that object, so the object
will get garbage collected. Note: the "dimi" here are different from
the ARRAY command, since they go from 0 to i-1, i.e. a "dimension"
of 10 means you have elements from 0 to 9.
Y:MAKE_ARRAY('FUNCTIONAL,'F,'HASHED,1) - The second argument to
MAKE_ARRAY in this case is the function to call to calculate array
elements, and the rest of the arguments are passed recursively to
MAKE_ARRAY to generate the "memory" for the array function object.
</P>
</DL>
<P>
<DL>
<DT><U>Function:</U> <B>REARRAY</B> <I>(array,dim1, ... ,dimk)</I>
<DD><A NAME="IDX575"></A>
can be used to change the size or
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, FALSE, 0.0 or 0 will be used to fill the remaining elements,
depending on the type of the array. The type of the array cannot be
changed.
</P>
</DL>
<P>
<DL>
<DT><U>Function:</U> <B>REMARRAY</B> <I>(name1, name2, ...)</I>
<DD><A NAME="IDX576"></A>
removes arrays and array associated
functions and frees the storage occupied. If name is ALL then all
arrays are removed. It may be necessary to use this function if it is
desired to redefine the values in a hashed array.
</P>
</DL>
<P>
<DL>
<DT><U>Variable:</U> <B>USE_FAST_ARRAYS</B>
<DD><A NAME="IDX577"></A>
[TRUE on Lispm] - If TRUE then only two types
of arrays are recognized.
</P>
<P>
1) The art-q array (t in common lisp) which may have several dimensions
indexed by integers, and may hold any lisp or macsyma object as an
entry. To construct such an array, enter A:MAKE_ARRAY(ANY,3,4); then A
will have as value, an array with twelve slots, and the indexing is zero
based.
</P>
<P>
2) The Hash_table array which is the default type of array created if one
does B[X+1]:Y^2 (and B is not already an array,a list, or a matrix-- if
it were one of these an error would be caused since x+1 would not be a
valid subscript for an art-q array,a list or a matrix ). Its indices
(also known as keys) may be any object. It only takes ONE KEY at a time
(B[X+1,U]:Y would ignore the u) Referencing is done by B[X+1]==> Y^2. Of
course the key may be a list, eg B[[x+1,u]]:y would be valid. This is in-
compatible with the old Macsyma hash arrays, but saves consing.
</P>
<P>
An advantage of storing the arrays as values of the symbol is that the
usual conventions about local variables of a function apply to arrays as
well. The Hash_table type also uses less consing and is more efficient
than the old type of macsyma hashar. To obtain consistent behaviour in
translated and compiled code set TRANSLATE_FAST_ARRAYS [TRUE] to be
TRUE.
</DL>
</P>
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