matrix docs

diff --git a/doc/matrices.texi b/doc/matrices.texi
index 459940823f8c1e5edc998e91111796fa77f48b16..5c03eb79c3748841d898cfb43aa298c434fe2595 100644 (file)
--- a/doc/matrices.texi
+++ b/doc/matrices.texi
@@ -2018,6 +2018,19 @@ Each expression on @code{DO IF} and @code{ELSE IF} must evaluate to a
 scalar.  Positive scalars are considered to be true, and scalars that
 are zero or negative are considered to be false.
 
+The following matrix language fragment sets @samp{b} to the term
+following @samp{a} in the
+@url{https://en.wikipedia.org/wiki/Juggler_sequence, Juggler
+sequence}:
+
+@example
+DO IF MOD(a, 2) = 0.
+  COMPUTE b = TRUNC(a &** (1/2)).
+ELSE.
+  COMPUTE b = TRUNC(a &** (3/2)).
+END IF.
+@end example
+
 @node Matrix LOOP and BREAK Commands
 @subsection The @code{LOOP} and @code{BREAK} Commands
 
@@ -2057,12 +2070,61 @@ The optional @code{IF} on @code{END LOOP} is evaluated after each
 iteration through the loop body.  If its expression, which must
 evaluate to a scalar, is zero or negative, then the loop terminates.
 
+The following computes and prints @math{l(n)}, whose value is the
+number of steps in the
+@url{https://en.wikipedia.org/wiki/Juggler_sequence, Juggler sequence}
+for @math{n}, for @math{n} from 2 to 10 inclusive:
+
+@example
+COMPUTE l = @{@}.
+LOOP n = 2 TO 10.
+  COMPUTE a = n.
+  LOOP i = 1 TO 100.
+    DO IF MOD(a, 2) = 0.
+      COMPUTE a = TRUNC(a &** (1/2)).
+    ELSE.
+      COMPUTE a = TRUNC(a &** (3/2)).
+    END IF.
+  END LOOP IF a = 1.
+  COMPUTE l = @{l; i@}.
+END LOOP.
+PRINT l.
+@end example
+
+@node Matrix BREAK Command
+@subsubsection The @code{BREAK} Command
+
 The @code{BREAK} command may be used inside a loop body, ordinarily
 within a @code{DO IF} command.  If it is executed, then the loop
 terminates immediately, jumping to the command just following
 @code{END LOOP}.  When multiple @code{LOOP} commands nest,
 @code{BREAK} terminates the innermost loop.
 
+The following example is a revision of the one above that shows how
+@code{BREAK} could substitute for the index and @code{IF} clauses on
+@code{LOOP} and @code{END LOOP}:
+
+@example
+COMPUTE l = @{@}.
+LOOP n = 2 TO 10.
+  COMPUTE a = n.
+  COMPUTE i = 1.
+  LOOP.
+    DO IF MOD(a, 2) = 0.
+      COMPUTE a = TRUNC(a &** (1/2)).
+    ELSE.
+      COMPUTE a = TRUNC(a &** (3/2)).
+    END IF.
+    DO IF a = 1.
+      BREAK.
+    END IF.
+    COMPUTE i = i + 1.
+  END LOOP.
+  COMPUTE l = @{l; i@}.
+END LOOP.
+PRINT l.
+@end example
+
 @node Matrix READ and WRITE Commands
 @subsection The @code{READ} and @code{WRITE} Commands
 
@@ -2171,6 +2233,74 @@ file.  It is also ineffective just after a command that uses the
 particular file, because @code{EOF} has to try to read the next line
 from the file to determine whether the file contains more input.
 
+@subsubheading Example 1: Basic Use
+
+The following matrix program reads the same matrix @code{@{1, 2, 4; 2,
+3, 5; 4, 5, 6@}} into matrix variables @code{v}, @code{w}, and
+@code{x}:
+
+@example
+READ v /FILE='input.txt' /FIELD=1 TO 100 /SIZE=@{3, 3@}.
+READ w /FIELD=1 TO 100 /SIZE=@{3; 3@} /MODE=SYMMETRIC.
+READ x /FIELD=1 TO 100 BY 1/SIZE=@{3, 3@} /MODE=SYMMETRIC.
+@end example
+
+@noindent
+given that @file{input.txt} contains the following:
+
+@example
+1, 2, 4
+2, 3, 5
+4, 5, 6
+1
+2 3
+4 5 6
+1
+23
+456
+@end example
+
+The @code{READ} command will read as many lines of input as needed for
+a particular row, so it's also acceptable to break any of the lines
+above into multiple lines.  For example, the first line @code{1, 2, 4}
+could be written with a line break following either or both commas.
+
+@subsubheading Example 2: Reading into a Submatrix
+
+The following reads a @math{5@times{}5} matrix from @file{input2.txt},
+reversing the order of the rows:
+
+@example
+COMPUTE m = MAKE(5, 5, 0).
+LOOP r = 5 TO 1 BY -1.
+  READ m(r, :) /FILE='input2.txt' /FIELD=1 TO 100.
+END LOOP.
+@end example
+
+@subsubheading Example 3: Using @code{REREAD}
+
+Suppose each of the 5 lines in a file @file{input3.txt} starts with an
+integer @var{count} followed by @var{count} numbers, e.g.:
+
+@example
+1 5
+3 1 2 3
+5 6 -1 2 5 1
+2 8 9
+3 1 3 2
+@end example
+
+@noindent
+Then, the following reads this file into a matrix @code{m}:
+
+@example
+COMPUTE m = MAKE(5, 5, 0).
+LOOP i = 1 TO 5.
+  READ count /FILE='input3.txt' /FIELD=1 TO 1 /SIZE=1.
+  READ m(i, 1:count) /FIELD=3 TO 100 /REREAD.
+END LOOP.
+@end example
+
 @node Matrix WRITE Command
 @subsubsection The @code{WRITE} Command