The matrix language support numerous functions in multiple categories.
The following subsections document each of the currently supported
-functions. In the descriptions, function arguments that must be
-scalars are given names beginning with @var{s}, those that must be
-vectors are given names beginning with @var{v}, and general matrix
-arguments are given names beginning with @var{m}.
+functions. The first letter of each parameter's name indicate the
+required argument type:
+
+@table @samp
+@item s
+Any scalar.
+
+@item n
+A scalar with a nonnegative integer value. (Non-integers are rounded
+down to the nearest integer.)
+
+@item v
+A row or column vector.
+
+@item m
+A matrix.
+@end table
@node Matrix Elementwise Functions
@subsubsection Elementwise Functions
negative.
@end deftypefn
-
@node Matrix Logical Functions
@subsubsection Logical Functions
@node Matrix Construction Functions
@subsubsection Matrix Construction Functions
-@deftypefn {Matrix Function} {} BLOCK (@var{m1}, @var{m2}, @dots{})
+@deftypefn {Matrix Function} {} BLOCK (@var{m1}, @dots{}, @var{mn})
+Returns a block diagonal matrix with as many rows as the sum of its
+arguments' row counts and as many columns as the sum of their columns.
+Each argument matrix is placed along the main diagonal of the result,
+and all other elements are zero.
@end deftypefn
-@deftypefn {Matrix Function} {} IDENT (@var{s})
-@deftypefnx {Matrix Function} {} IDENT (@var{sr}, @var{sc})
+@deftypefn {Matrix Function} {} IDENT (@var{n})
+@deftypefnx {Matrix Function} {} IDENT (@var{nr}, @var{nc})
+Returns an identity matrix, whose main diagonal elements are one and
+whose other elements are zero. The returned matrix has @var{n} rows
+and columns or @var{nr} rows and @var{nc} columns, respectively.
@end deftypefn
-
-@deftypefn {Matrix Function} {} MAGIC (@var{m})
+@deftypefn {Matrix Function} {} MAGIC (@var{n})
+Returns an @math{@var{n}@times{}@var{n}} matrix that contains each of
+the integers @math{1@dots{}@var{n}} once, in which each column, each
+row, and each diagonal sums to @math{n(n^2+1)/2}. There are many
+magic squares with given dimensions, but this function always returns
+the same one for a given value of @var{n}.
@end deftypefn
-
-@deftypefn {Matrix Function} {} MAKE (@var{sr}, @var{sc}, @var{sv})
+@deftypefn {Matrix Function} {} MAKE (@var{nr}, @var{nc}, @var{s})
+Returns an @math{@var{nr}@times{}@var{nc}} matrix whose elements are
+all @var{s}.
@end deftypefn
-
@deftypefn {Matrix Function} {} MDIAG (@var{v})
+Returns a @math{|@var{v}|@times{}|@var{v}|} matrix whose main diagonal
+comes from @var{v} and whose other elements are zero.
@end deftypefn
-@deftypefn {Matrix Function} {} RESHAPE (@var{m}, @var{sr}, @var{sc})
+@deftypefn {Matrix Function} {} RESHAPE (@var{m}, @var{nr}, @var{nc})
+Returns an @math{@var{nr}@times{}@var{nc}} matrix whose elements come
+from @var{m}, which must have the same number of elements as the new
+matrix, copying elements from @var{m} to the new matrix row by row.
@end deftypefn
-@deftypefn {Matrix Function} {} TRANSPOS (@var{m})
-@deftypefnx {Matrix Function} {} T (@var{m})
+@deftypefn {Matrix Function} {} T (@var{m})
+@deftypefnx {Matrix Function} {} TRANSPOS (@var{m})
+Returns @var{m} with rows exchanged for columns.
@end deftypefn
-@deftypefn {Matrix Function} {} UNIFORM (@var{sr}, @var{sc})
+@deftypefn {Matrix Function} {} UNIFORM (@var{nr}, @var{nc})
+Returns a @math{@var{nr}@times{}@var{nc}} matrix in which each element
+is randomly chosen from a uniform distribution of real numbers between
+0 and 1.
@end deftypefn
@node Matrix Minimum and Maximum and Sum Functions
@subsubsection Minimum, Maximum, and Sum Functions
-@deftypefn {Matrix Function} {} CMAX (@var{m})
-@end deftypefn
-
@deftypefn {Matrix Function} {} CMIN (@var{m})
+@deftypefnx {Matrix Function} {} CMAX (@var{m})
+@deftypefnx {Matrix Function} {} CSUM (@var{m})
+@deftypefnx {Matrix Function} {} CSSQ (@var{m})
+Returns a row vector with the same number of columns as @var{m}, in
+which each element is the minimum, maximum, sum, or sum of squares,
+respectively, of the elements in the same column of @var{m}.
@end deftypefn
-@deftypefn {Matrix Function} {} CSSQ (@var{m})
-@end deftypefn
-
-@deftypefn {Matrix Function} {} CSUM (@var{m})
-@end deftypefn
-
-@deftypefn {Matrix Function} {} MMAX (@var{m})
-@end deftypefn
-
-
@deftypefn {Matrix Function} {} MMIN (@var{m})
+@deftypefnx {Matrix Function} {} MMAX (@var{m})
+@deftypefnx {Matrix Function} {} MSUM (@var{m})
+@deftypefnx {Matrix Function} {} MSSQ (@var{m})
+Returns the minimum, maximum, sum, or sum of squares, respectively, of
+the elements of @var{m}.
@end deftypefn
-
-@deftypefn {Matrix Function} {} MSSQ (@var{m})
-@end deftypefn
-
-
-@deftypefn {Matrix Function} {} MSUM (@var{m})
-@end deftypefn
-
-@deftypefn {Matrix Function} {} RMAX (@var{m})
-@end deftypefn
-
-
@deftypefn {Matrix Function} {} RMIN (@var{m})
+@deftypefnx {Matrix Function} {} RMAX (@var{m})
+@deftypefnx {Matrix Function} {} RSUM (@var{m})
+@deftypefnx {Matrix Function} {} RSSQ (@var{m})
+Returns a column vector with the same number of rows as @var{m}, in
+which each element is the minimum, maximum, sum, or sum of squares,
+respectively, of the elements in the same row of @var{m}.
@end deftypefn
-
-@deftypefn {Matrix Function} {} RSSQ (@var{m})
+@deftypefn {Matrix Function} {} SSCP (@var{m})
+Returns @code{T(@var{m}) * @var{m}}.
@end deftypefn
-
-@deftypefn {Matrix Function} {} RSUM (@var{m})
+@deftypefn {Matrix Function} {} TRACE (@var{m})
+Returns the sum of the elements along @var{m}'s main diagonal,
+equivalent to @code{MSUM(DIAG(@var{m}))}.
@end deftypefn
-@deftypefn {Matrix Function} {} SSCP (@var{m})
-@end deftypefn
@node Matrix Property Functions
@subsubsection Matrix Property Functions
-@deftypefn {Matrix Function} {} DIAG (@var{m})
-@end deftypefn
-
-@deftypefn {Matrix Function} {} NCOL (@var{m})
+@deftypefn {Matrix Function} {} NROW (@var{m})
+@deftypefnx {Matrix Function} {} NCOL (@var{m})
+Returns the number of row or columns, respectively, in @var{m}.
@end deftypefn
-@deftypefn {Matrix Function} {} NROW (@var{m})
+@deftypefn {Matrix Function} {} DIAG (@var{m})
+Returns a column vector containing a copy of @var{m}'s main diagonal.
+The vector's length is the lesser of @code{NCOL(@var{m})} and
+@code{NROW(@var{m})}.
@end deftypefn
@node Matrix Rank Ordering Functions
@subsubsection Matrix Rank Ordering Functions
@deftypefn {Matrix Function} {} GRADE (@var{m})
+Returns a matrix with the same dimensions as @var{m} in which each
+elements is a unique integer, from 1 to the number of elements in
+@var{m}, that corresponds to its rank within @var{m}. The smallest
+element in @var{m} corresponds to value 1 in the returned matrix, the
+next smallest to value 2, and so on. When multiple elements in
+@var{m} have the same value, they are assigned consecutive unique
+ranks in the return matrix.
@end deftypefn
+@noindent
+The @code{GRADE} function can be used to sort a vector. For example,
+the following syntax:
+
+@example
+MATRIX.
+COMPUTE v=@{2, 5, 1, 4, 9, 7, 8, 10, 6, 3@}.
+COMPUTE v(GRADE(v))=v.
+PRINT v.
+END MATRIX.
+@end example
+
+@noindent yields the following sorted output:
+
+@example
+v
+ 1 2 3 4 5 6 7 8 9 10
+@end example
+
@deftypefn {Matrix Function} {} RNKORDER (@var{m})
@end deftypefn
-
@node Matrix Algebra Functions
@subsubsection Matrix Algebra Functions
@end deftypefn
-@deftypefn {Matrix Function} {} SWEEP (@var{m}, @var{s})
-@end deftypefn
-
-
-@deftypefn {Matrix Function} {} TRACE (@var{m})
+@deftypefn {Matrix Function} {} SWEEP (@var{m}, @var{n})
@end deftypefn
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