
		      Frequently Asked Questions
			     About Algae
			    (With Answers)

			  28 September 2003

			  K. Scott Hunziker
		      ksh@users.sourceforge.net

What follows is just a start.  It obviously needs help, and you can
provide it.  One way would be for you to take over as the maintainer
of this FAQ.  Another way to help would be to send me new questions,
answers, and improvements.  Thanks in advance.

----------------------------------------------------------------------
			    The Questions
----------------------------------------------------------------------

1.  About Algae
---------------

1.1:   Where can I get Algae?

1.2:   Where should I report bugs and other problems with Algae?

1.3:   Does Algae really only work on Unix machines?

1.4:   What about Algae on DOS, Microsoft Windows, or OS/2?

1.5:   You mean I can't run Algae on my PC?

2.  Installation
----------------

2.1:  How can I compile Algae in 64-bit mode on AIX?

2.2:  Configure reports "Cannot handle floating point exceptions".  Why?

2.3:  Can I use the Apple-supplied BLAS and LAPACK on Mac OS X?

3.  Running Algae
-----------------

3.1:  When I try to run Algae, it fails with the message "Problem
      reading startup file...".  What's wrong?

3.2:  Why does Algae's display not match the width of my terminal?

3.3:  How do I use the `builtin' function to link to code in my own
      shared objects?

4.  The Language
----------------

4.1:  Why do I get inconsistent results when partitioning with labels?

4.2:  How can I create variables A1, A2, A3, etc. in a loop?

5.  Files
---------

5.1:  I can't read my file.  Algae says it's "already open".  Why?

5.2:  Why is Algae leaving temporary files around after it exits?

5.3:  How do I read numbers from a file?

6.  Math
--------

6.1:  Why does Algae only use four significant digits?

6.2:  Why does the transpose operator take the complex conjugate?

6.3:  I need to invert a matrix, but the Algae documentation says that
      the `inv' function isn't very efficient.  Is there a better way?

6.4:  How do I compute the determinant of a matrix?

6.5:  Does Algae have symbolic math capability?

6.6:  The symmetry of my matrix result is wrong.  What gives?

7.  Memory and Speed
--------------------

7.1:  Algae says it's "out of memory", but I think my computer has
      more memory than what it's using.  What's happening?

7.2:  For certain problems, I've noticed unexpectedly large performance
      differences between roughly comparable platforms.  Why?

----------------------------------------------------------------------
			     The Answers
----------------------------------------------------------------------

1.  About Algae
---------------

1.1:  Where can I get Algae?

  You can get Algae from these sites:
      <ftp://algae.sourceforge.net/pub/algae>
      <ftp://ftp.eskimo.com/u/k/ksh/algae>

1.2:  Where should I report bugs and other problems with Algae?

  Please send bug reports to <ksh@users.sourceforge.net>.

1.3:  Does Algae really only work on Unix machines?

  Currently, Algae is set up to configure itself for most Unix
  operating systems.  To run Algae on something else, you'll probably
  have to do some work to port it.  (And if you do, please tell me
  about it so that others can also benefit.)

  Algae uses a number of features that are present in all Unix systems.
  To my knowledge, these features are all incorporated in the family
  of standards known as "POSIX".  Getting Algae running on a POSIX
  system, then, may be relatively easy.  For example, at one time I
  had Algae running on a VAX computer running VMS.

1.4:  What about Algae on DOS, Microsoft Windows, or OS/2?

  As far as I know, Algae has not yet been ported to any of these
  systems.  Although there would likely be some limitations, these
  ports are entirely possible.  If you're interested in taking one of
  these on, I may be able to put you in contact with someone who can
  help.

1.5:  You mean I can't run Algae on my PC?

  Of course you can!  You just need a modern, well-designed operating
  system.  In fact, I do all of the Algae development (as well as real
  work) on "buxom", my 90 MHz Pentium machine running Linux.  (In the
  summer of 2001, "buxom" was replaced by a faster machine, but it's
  still plugging along as a web server.)


2.  Installation
----------------

2.1:  How can I compile Algae in 64-bit mode on AIX?

  On our AIX 4.3 machine, you can do this by making the following
  environment variable assignments before running configure:

	CC=cc
	F77=f77
	CFLAGS="-q64 -O -qmaxmem=8192"
	FFLAGS="-q64 -O -qmaxmem=8192"
	LDFLAGS="-b64"
	ARFLAGS="-X64"

2.2:  Configure reports "Cannot handle floating point exceptions".  Why?

  Unfortunately, there's no standard way to either enable or handle
  floating point exceptions.  What we've done for configuring Algae
  isn't very elegant -- we simply try every file in the "fpe"
  directory, one at a time, looking for one that works.  The message
  you're seeing means that none of them did.

  The good news is that it shouldn't be very hard to fix.  We simply
  need to install a SIGFPE handler and enable exceptions, and
  virtually every system provides a means to do that.  (But see
  below.)  The "config.log" file will contain error messages that may
  help solve the problem.  (Even when it finds an "fpe" file that
  works, there will be error messages from the ones that didn't.)

  By the way, the names of the files in the "fpe" directory are pretty
  lame.  Mostly, they're just the names returned by "config.guess" on
  the machine on which they were developed.  For example, there are
  "i386", "i586", and "i686" files in there, but in reality the
  differences between them have nothing to do with the CPU model.
  There is a generic "fpe.c" file in there, but currently it handles
  only a few machine types.

  Linux has been a moving target, but I think it has finally
  stabilized.  Until glibc 2.2, the Linux libc had no standard way to
  enable floating point exceptions.  The fpsetmask and __setfpucw
  functions came and went, but I don't think either of them was
  documented.  Beginning with glibc 2.2, the function feenableexcept
  is now the standard way to do this.  Unfortunately, glibc 2.1.3
  doesn't appear to provide any of these.  I've been able to grab the
  feenableexcept definition out of recent glibc sources and add it to
  "fpe/i686-pc-linux-gnu.c", but the best approach with glibc 2.1.3 is
  to upgrade to a more recent version.

2.3:  Can I use the Apple supplied BLAS and LAPACK on Mac OS X?

  From Randall Skelton:

  - To use the Apple supplied blas and lapack libraries (based around
    atlas with altivec extensions):
    (1) add -latlas to the linking library list in configure
    (2) set LDFLAGS=-framework veclib

  - Also works with Nagware fortran 95 compiler but this requires a
    bit of fiddling.
    (1) do (1) and (2) from above.
    (2) set F77=/usr/local/bin/f95nag -dcfuns
    (3) set LIBS=/usr/local/lib/NAGWare/libf96.a \
	    /usr/local/lib/NAGWare/quickfit.o
    (4) change configure to include a c-wrapper for erf function.
   3648 
   3649 echo "$as_me:3649: checking whether we can link Fortran" >&5
   3650 echo $ECHO_N "checking whether we can link Fortran... $ECHO_C" >&6
   3651 cat > conftestf.f <<EOF
   3652       DOUBLE PRECISION X
   3653       X=ERF(2.0)
   3654       WRITE(*,*) X
   3655       STOP
   3656       END
   3657 EOF
   3658 cat > conftest.c <<EOF
   3659 double erf_(double x)
   3660 {
   3661       return erf(x);
   3662 }
   3663 EOF
   3664 if eval $f77_c_link; then
   3665   rm -rf conftest*

3.  Running Algae
-----------------

3.1:  When I try to run Algae, it fails with the message "Problem
      reading startup file...".  What's wrong?

  Many of Algae's standard functions are themselves written in Algae.
  So, when it starts up, Algae tries to read them.  There's a startup
  file, usually called "algae.A", which arranges for all the other
  files to be read.  The default name and location of the startup file
  is set when Algae is installed, but you can override that with the
  ALGAE_RC0 environment variable.

  For example, if your startup file is "/tmp/foo" (and you're using a
  Bourne compatible shell), you can start it like this:

	ALGAE_RC0=/tmp/foo algae

3.2:  Why does Algae's display not match the width of my terminal?

  When it starts, Algae attempts to determine the width of the
  terminal on which it is running.  This width, in characters, is set
  in the $term_width variable.  If Algae has trouble determining the
  width, this is set to zero and Algae simply doesn't worry about the
  terminal width.  (And you can get some very long lines.)  Also,
  changing the width of the terminal after Algae is started will not
  change the value of $term_width.

  Changing the value of $term_width will immediately change Algae's
  idea of the terminal width.

3.3:  How do I use the `builtin' function to link to code in my own
      shared objects?

  The `builtin' function itself is simple to use -- the trick is
  writing code to interface with Algae.  There's no programmer's
  manual, so you may need to learn a bit about Algae's source code.
  There's an example of this kind of stuff in a package called
  "shuffle" that's in the "contrib" section of the Algae project at
  Sourceforge (http://sourceforge.net/projects/algae).

  Once you have the shared object set up, you'd run Algae like this:

    $ algae
    > shuffle = builtin ("./shuffle.so"; "bi_shuffle");
    > shuffle (1:6)
	( 6,    1,    3,    4,    5,    2 )

  The first argument to `builtin' is the file name of the shared
  object library, and the second is the name of the symbol you're
  going to call.

4.  The Language
----------------

4.1:  Why do I get inconsistent results when partitioning with labels?

  Here's an example that sometimes causes confusion.

	> x = 1, 2, 3, 4;
	> x.eid = "a", "b", "b", "c";
	> x["e","f"]
	> x["e"]
	algae: stdin: line 3: run time error: Specified label does not
	exist in vector partition operation.

  Why does x["e"] return an error, and x["e","f"] doesn't?  The answer
  lies with the definitions for vector partitioning.

  The expression x["e","f"] uses a single vector to select the elements.
  By definition, this expression returns a vector containing as many
  of those elements as exist, or a zero-length vector if none of them
  do.

  On the other hand, the expression x["e"] uses a scalar to specify
  the selection.  By definition, a scalar is returned.  So, it's an
  error.  (There's no scalar equivalent to a zero-length vector.)
  Also, x["b"] would be an error because "b" isn't unique among the
  labels.  You could, instead, type x[vector("e")] or x[["e"]] and get
  behavior similar to the second and third examples.

  By the way, this behavior is consistent with all partitioning -- not
  just by label.  If `s' is a scalar and `a' is either a vector or a
  matrix (or blank), then here are the results:

	x[s] or x[s;s]		-->	scalar
	x[a], x[a;s] x[s;a]	-->	vector
	x[a;a]			-->	matrix

4.2:  How can I create variables A1, A2, A3, etc. in a loop?

  Are you sure you really want to do that?  Using arrays or tables is
  usually a better choice.  For example, to set up a list of the first
  ten cubes, you could use

	c = 0;
	for (i in 1:9) { c = c, i^3; }

  (Much better, though, to use the simple statement `c=(0:9)^3'.)

  If your variables were to have, say, matrix values, then you could
  use a table instead.  Here's an example where we save several "magic
  squares" in a table:

	t = {};
	for (i in 1:9) { t.(i) = magic (i); }

  If you really need to do what you ask, use the `$$' identifier to
  refer to the global symbol table.  For example, to set A1, A2, A3,
  etc. equal to 1, 2, 3, etc., use

	for (i in 1:9) { $$.(sprintf("A%d";i)) = i; }

  You could also do this with the `exec' function, as in

	for (i in 1:9) { exec (sprintf ("A%d = i;"; i)); }

  By the way, neither of these two approaches is capable of setting
  variables that are local to a function.

5.  Files
---------

5.1:  I can't read my file.  Algae says it's "already open".  Why?

  In Algae, files may be open for either input or output -- not both.
  So, if you've already opened it for output, Algae will complain if
  you try to read it.  Close the file, and then you'll be able to open
  it as you wish.

5.2:  Why is Algae leaving temporary files around after it exits?

  Algae's `tmp_file' function creates temporary files.  They're put in
  the directory /tmp, unless you specify something different with the
  TMPDIR environment variable.  The `plot' function is one of several
  that uses temporary files.

  Algae keeps track of the temporary files it has created, and deletes
  them when it exits.  It does this even if it terminates abnormally.
  However, it is limited in the number of temporary files it can
  handle.  It can usually handle more than 500 files, but the limit is
  system dependent.  If you go over the limit, some or all of the
  files will not be deleted.  (You will not necessarily see an error
  message.)

  Our code for temporary files is clever, but not very robust.
  Someone should improve it.

  In the meantime, I can think of a couple partial workarounds.  One
  possibility is to occasionally execute the statement

	close (tmp_file.cleanup);

  This will immediately delete all temporary files, so of course you
  must be done with them.


5.3:  How do I read numbers from a file?

  If the numbers are in a text file, the `readnum' function is
  probably your best bet, being fast and easy.  The numbers must be
  separated by whitespace, and it simply reads as many numbers as you
  request.

  If it's a text file but the numbers are in a particular format (in
  10 character wide fields, for example), then you may need to use the
  `read' function and then perhaps functions like `split' and `atof'.

  The Algae package called MatrixMarket provides a function to read
  matrices in the Netlib text file format of the same name.

  For binary files, the `get' function reads native Algae data.  These
  files are portable between various computers.

  The `getmat' function reads MATLAB binary files in their v.4
  "Level-1 MAT-file" format.  The `getdyn' function reads matrices
  from binary DYNASTY files.

  At the lowest level, you can use the `fread' function to read the
  file as you like.

6.  Math
--------

6.1:  Why does Algae only use four significant digits?

  It doesn't.  For real and complex numbers, it uses full double
  precision floating point numbers.  By default it only displays four
  digits, but you can change that with the `digits' function.

6.2:  Why does the transpose operator take the complex conjugate?

  With linear algebra on complex matrices, it is usually the complex
  conjugate transpose that's needed, rather than the pure transpose.
  To transpose a complex matrix without taking its complex conjugate,
  use either conj(x') or conj(x)'.

6.3:  I need to invert a matrix, but the Algae documentation says that
      the `inv' function isn't very efficient.  Is there a better way?

  It's not that Algae's implementation is poor.  As any good linear
  algebra text will tell you, it's rarely a good idea to form a matrix
  inverse.

  Consider the linear system `A*x = b'.  You can use the matrix
  inverse to solve this as `x = inv(A)*b'.  A much better way, though,
  is to use the direct solution `x = solve(A;b)'.  The direct approach
  is much faster and behaves better numerically.

  You can use this in many places where it might not be apparent.  For
  example, suppose that you need to compute

	Kaa = K11 - K12 * inv(K22) * K21

  Here again, the right way to solve this is

	Kaa = K11 - K12 * solve (K22; K21)

  If for some reason you really need the inverse, then go right ahead
  and use `inv'.  It simply uses `solve' with an identity matrix on
  the right-hand side.

6.4:  How do I compute the determinant of a matrix?

  The determinant is equal to the product of the singular values.  Use
  `svd' to get the singular values (they're returned in the member
  called "sigma") and multiply them all together with `product'.

  If you're looking for a measure of how well conditioned a matrix is
  (like "is this matrix singular?"), then the determinant is not very
  useful.  It's much better to look at the RCOND condition number
  estimate returned by the `factor' and `chol' functions.

6.5:  Does Algae have symbolic math capability?

  Not at this time.  With Algae's ability to read from and write to
  pipes, implementing something similar to MATLAB's interface to Maple
  would be pretty easy.  It might make a nice little project for
  someone, especially since it wouldn't require any changes to the
  source code.  There are several useful symbolic packages available.
  I'm particularly fond of maxima (www.ma.utexas.edu/users/wfs/maxima.html).

  As an example of this type of interface, consider the following code
  for computing Bessel functions of integer order:

	J = function (n; x)
	{
	  local (fn; r);
	  fn = sprintf ("!echo 'j(%d,%g)' | bc -l"; n; x);
	  r = readnum (; fn);
	  close (fn);
	  return r;
	};

  No symbolic math is involved, but it shows a simple interface to
  another program.  (This function can be improved in many ways, all
  of which are left as an exercise for the reader.  Even then, it's
  going to be slow.)

6.6:  The symmetry of my matrix result is wrong.  What gives?

  Well, it could be a bug.  If you think it is, please report it.

  However, there are many situations where you can get a symmetry that
  you might not expect.  For example, consider the expression

	B = sqrt(-1) * symmetric(A)

  where `A' is a real, square matrix.  If you look at the resulting
  matrix B, you'll see that it is symmetric.  However, `B.symmetry'
  returns "general".  There is a subtle reason for this.

  For complex matrices, Algae has a fundamental preference for
  hermitian symmetry.  When a real, symmetric matrix is cast to
  complex type, it has both ordinary and hermitian symmetry.
  Unfortunately, with Algae it's one or the other -- not both.  As the
  expression is evaluated, the real, symmetric matrix becomes complex
  and hermitian and is then multiplied by a complex scalar.  But, in
  general, that product destroys the symmetry.  At this point, Algae
  does not realize that the imaginary part of the right factor is
  zero.

7.  Memory and Speed
--------------------

7.1:  Algae says it's "out of memory", but I think my computer has
      more memory than what it's using.  What's happening?

  The most common reason is that your processes are being restricted
  to a maximum data size.  This may be increased (up to a hard limit)
  with the ulimit shell command.  For example, I usually use the
  command "ulimit -d 1049600" on our Alpha to set the data size to its
  hard limit.

  Another possibility showed up recently on a new IBM (AIX) machine.
  By default, the linker creates an executable that can use a maximum
  of 256 Mb for heap, stack, and initialized data combined.  The
  linker option "-bmaxdata" may be used to increase this.

  Most 32-bit compilers are limited to about 2 Gb of data.  To get
  more than that, you'll need to use 64-bit mode.

7.2:  For certain problems, I've noticed unexpectedly large performance
      differences between roughly comparable platforms.  Why?

  If your code is not math-intensive, then you may be seeing
  differences in the operating system's memory management
  implementations.  Algae was designed with the assumption that the
  memory management overhead would not be a significant factor.  While
  this is generally true, malloc is so slow on some systems that an
  Algae program can actually spend the majority of its time there.

  As far as I've seen, the dlmalloc package used in Linux's glibc has
  the best performance.  Compared to that, AIX and HP-UX can be more
  than 10 times slower.  The most extreme example (though it can't all
  be attributed to malloc) is the Cray, which took 2 minutes to do
  what my old 0.6 GHz Pentium did in 5 seconds.

  If this is a real issue, you should complain to your vendor and then
  either switch to Linux or else download the dlmalloc code and link
  to it instead.
