  Builtin Tela functions
  Pekka	Janhunen, Pekka.Janhunen@fmi.fi
  Version 1.12,	Fri Nov	 4 09:13:59 EET	1994

  This document	has been automatically generated from the online help
  messages of builtin Tela functions.

  1.  INTRODUCTION

  Negative error codes describe	fatal errors, whereas positive error
  codes	are warnings only. In case of fatal error, the function	output
  arguments have undefined values. If a	function has no	output
  arguments, it	typically has only positive return codes.

  The error code descriptions do normally not appear in	the Tela help
  messages. If an error	occurs,	Tela will however find and display the
  proper textual message.


  2.  std.ct

  This section describes functions from	file std.ct.


  2.1.	BatchMode



       [y] = BatchMode()
	BatchMode() returns 1 if this Tela process is in batch mode
	  (command line	switch -b), otherwise 0.


       See also: ``SilentMode'', ``VerboseMode''.


  2.2.	CheckReadOnlyMode



       [y] = CheckReadOnlyMode(;x)
	CheckReadOnlyMode() returns 1 if this Tela process checks that function
	  input	arguments are not modified by the function. The	check is done by
	  default, but if it causes problems (bugs in Tela) you	can turn it off
	  using	CheckReadOnlyMode(off).
	  CheckReadOnlyMode returns the	old mode setting.


       See also: ``SilentMode'', ``BatchMode'',	``VerboseMode''.

	  Error	codes:
	  1: Argument not integer




  2.3.	GetInstructionData









  [Ninstructions,Noperations] =	GetInstructionData(p,mnemo)
   [Ninstr,Nops] = GetNumberOfInstructions(p,"mnemonic") returns
     the number	of specific instructions executed when p=perf()	was
     gathered, and the number of (floating point) operations associated
     with the instruction.
     The mnemonic must be a string, and	it may be any of the names
     that appear in the	disasm(f) listing. In addition,	mnemonic may
     be	"flop",	which includes all instructions	that may perform floating
     point arithmetic, or it may be "*", which includes	all instructions.
     Error codes:
     -1: Bad first argument, must be obtained from perf()
     -2: Second	arg not	a string
     -3: Second	arg not	a recognized string





  2.4.	HeavisideTheta



       [y] = HeavisideTheta(x)
	y = HeavisideTheta(x) returns 1	if x>=0	and 0 if x<0.
	  x must be real. If x is array, the operation is applied componentwise.


       See also: ``sign''.

	  Error	codes:
	  -1: Complex or nonnumeric input argument




  2.5.	Im



       [y] = Im(x)
	y = Im(x) computes the imaginary part of a complex quantity x.
	  If x is real or integer, the result is zero.
	  If x is an array, the	operation is applied componentwise.


       See also: ``Re'', ``conj'', ``arg''.

	  Error	codes:
	  -1: Nonnumeric input argument




  2.6.	Re



       [y] = Re(x)
	y = Re(x) computes the real part of a complex quantity x.
	  If x is real or integer, it is returned as such.
	  If x is an array, the	operation is applied componentwise.


       See also: ``Im'', ``conj'', ``arg''.


     Error codes:
     -1: Nonnumeric input argument




  2.7.	SilentMode



       [y] = SilentMode()
	SilentMode() returns 1 if this Tela process is in silent mode
	  (command line	switch -s), otherwise 0.


       See also: ``BatchMode'',	``VerboseMode'', ``CheckReadOnlyMode''.


  2.8.	VerboseMode



       [y] = VerboseMode(;x)
	VerboseMode() returns 1	if this	Tela process is	in verbose mode
	  (command line	switch -v), otherwise 0.
	  VerboseMode(on) and VerboseMode(off) set the verbose mode on
	  and off, respectively. They return the old mode setting.


       See also: ``SilentMode'', ``BatchMode''.

	  Error	codes:
	  1: Argument not integer




  2.9.	abs2



       [y] = abs2(x)
	y = abs2(x) computes the square	of the absolute	value of x.
	  If x is real or integer, the result is just the square of x.
	  If x is complex, the result is equal to x*conj(x).
	  If x is an array, the	operation is applied componentwise.
	  Error	codes:
	  -1: Nonnumeric input argument




  2.10.	 acos



       [y] = acos(x)
	y = acos(x) computes the arc cosine of x.
	  If x is complex, the result is complex, otherwise real.
	  If x is an array, the	operation is applied componentwise.






  2.11.	 all



       [y] = all(x)
	all(x) returns 1 if all	elements of x are nonzero,
	  and 0	otherwise.
	  x must be an integer array or	scalar.


       See also: ``any''.

	  Error	codes:
	  1: Argument not integer or IntArray




  2.12.	 any



       [y] = any(x)
	any(x) returns 1 if at least one element of x is nonzero,
	  and 0	otherwise.
	  x must be a integer array or scalar.


       See also: ``all''.

	  Error	codes:
	  1: Argument not integer or IntArray




  2.13.	 arg



       [phi] = arg(z)
	arg(z) returns the argument of a complex quantity
	  (in radians).	The result is between -pi and pi.
	  If z is a complex array, the operation is applied
	  componentwise.


       See also: ``Re'', ``Im'', ``conj''.

	  Error	codes:
	  1: Nonnumeric	argument




  2.14.	 asin



       [y] = asin(x)
	y = asin(x) computes the arc sine of x.
	  If x is complex, the result is complex, otherwise real.
	  If x is an array, the	operation is applied componentwise.



  2.15.	 atan



       [y] = atan(x)
	y = atan(x) computes the arc tangent of	x.
	  If x is complex, the result is complex, otherwise real.
	  If x is an array, the	operation is applied componentwise.


       See also: ``atan2''.


  2.16.	 atan2



       [z] = atan2(y,x)
	z = atan2(y,x) computes	the arcus tangent of y/x using the signs
	  of both arguments to determine the quadrant of the return value.
	  The input argument must be integer or	real scalars and the
	  return value is real.


       See also: ``atan''.

	  Error	codes:
	  -1: Bad input	argument




  2.17.	 autosource



       [] = autosource(fn...)
	autosource("file.t","name1","name2",...) tags symbols
	  name1, name2,... such	that the command source("file.t")
	  is effectively executed when any of the symbols name
	  is used. This	is load-on-demand.


       See also: ``source''.

	  Error	codes:
	  1: Argument not a string




  2.18.	 cd



       [] = cd(fn)
	cd("pathname") will change the current directory to "pathname".
	  Error	codes:
	  1: Input argument not	a string or a char
	  2: Directory not found






  2.19.	 ceil



       [y] = ceil(x)
	ceil(x)	returns	the smallest integer which is larger than x.
	  x must be integer or real scalar or array. If	it is an array,
	  the operation	is applied componentwise.


       See also: ``floor''.

	  Error	codes:
	  -1: Complex or nonnumeric input argument




  2.20.	 conj



       [y] = conj(x)
	y = conj(x) computes the complex conjugate of x.
	  Real and integer arguments are returned as such.
	  If x is an array, the	operation is applied componentwise.


       See also: ``Re'', ``Im'', ``arg''.


  2.21.	 cos



       [y] = cos(x)
	y = cos(x) computes the	cosine function	of x.
	  If x is complex, the result is complex, otherwise real.
	  The argument must be in radians.
	  If x is an array, the	operation is applied componentwise.




  2.22.	 cosh



       [y] = cosh(x)
	y = cosh(x) computes the hyperbolic cosine function of x.
	  If x is complex, the result is complex, otherwise real.
	  If x is an array, the	operation is applied componentwise.




  2.23.	 cot



       [y] = cot(x)
	y = cot(x) is the cotangent function
	  cot(x) = 1/tan(x) = cos(x)/sin(x).



  2.24.	 cputime



       [t] = cputime(;p)
	cputime() returns the CPU time in seconds used by the current
	  tela session.	cputime(p) returns CPU time from performance data
	  array	p, previously obtained from perf().


       See also: ``tic'', ``toc'', ``perf''.

	  Error	codes:
	  -1: Bad argument, must be obtained from perf()




  2.25.	 csc



       [y] = csc(x)
	y = csc(x) is the cosecant function
	  csc(x) = 1/sin(x).




  2.26.	 diag



       [y] = diag(x)
	diag(V)	(V is a	vector)	returns	a square diagonal matrix,
	  whose	diagonal elements are given by V.
	  diag(M) (M is	a matrix) returns the main diagonal of M
	  as a vector.
	  Error	codes:
	  -1: Input array not vector or	matrix





  2.27.	 disasm



       [] = disasm(fn)
	disasm(f) produces disassembly listing of function f.
	  Error	codes:
	  1: Argument not a Tela function




  2.28.	 dump



       [] = dump()
	dump() dumps the stack.	Useful for debugging only.



  2.29.	 echo



       [] = echo(x)
	echo(on) and echo(off) set the echo mode on and	off.
	  The mode is off by default. When echo	mode is	on, the	source
	  code is echoed as it is parsed.

	  *** NOTE: Currently this function has	no effect! ***

	  Error	codes:
	  1: Input argument not	an integer




  2.30.	 eval



       [] = eval(s)
	eval("string") executes	string as a Tela command, as it	had been
	  typed	from the keyboard.
	  The evaluation is done in global context. The	symbols	appearing
	  in the string	refer to the global ones.


       See also: ``evalexpr''.

	  Error	codes:
	  1: Argument not a string or char




  2.31.	 evalexpr



       [y] = evalexpr(s)
	evalexpr("expression") executes	string as a Tela command,
	  returning its	value in y.
	  The evaluation is done in global context. The	symbols	appearing
	  in the string	refer to the global ones.


       See also: ``eval''.

	  Error	codes:
	  1: Argument not a string or char




  2.32.	 exit



       [] = exit()
	exit() stops Tela. quit() is synonym for exit().





  2.33.	 exp



       [y] = exp(x)
	y = exp(x) computes the	exponent function of x.
	  If x is complex, the result is complex, otherwise real.
	  If x is an array, the	operation is applied componentwise.




  2.34.	 find



       [y] = find(x)
	I=find(V) returns the index vector I=(i) for which
	  V[i] is nonzero. V must be an	integer	array. The length
	  of I is equal	to the number of nonzeros in V.
	  If V is multidimensional, it is used in flattened form.


       See also: ``any'', ``all'', ``flatten''.

	  Error	codes:
	  1: Argument not integer vector




  2.35.	 flatten



       [y] = flatten(;x)
	flatten(x) returns the array x flattened to a vector.
	  If x is not an array,	it is returned as is.
	  x = flatten()	flattens x "in place". This is much faster
	  (it works in constant	time) than to do x = flatten(x),
	  since	no data	movement is involved.




  2.36.	 floor



       [y] = floor(x)
	floor(x) returns the largest integer which is smaller than x.
	  x must be integer or real scalar or array. If	it is an array,
	  the operation	is applied componentwise.


       See also: ``ceil''.

	  Error	codes:
	  -1: Complex or nonnumeric input argument







  2.37.	 getenv



       [y] = getenv(varname)
	getenv("envvar") returns the value of environment variable
	  "envvar", or VOID if such variable is	not defined in
	  the UNIX environment.
	  Error	codes:
	  -1: Argument not a string or char





  2.38.	 help



       [] = help(;fn)
	help(function-name) or help("help-item") displays the help information
	  associated with a given function or a	given help item. On command line
	  you may use the abbreviation

	     ?help-item
	  or
	     help help-item

	  These	forms are translated to	help("help-item") before parsing.

	  First	tries:
	  help operators
	  help special
	  help if
	  help for
	  help function
	  ...

	  Error	codes:
	  1: Item not found
	  2: Cannot open help file




  2.39.	 herm



       [B] = herm(A; P)
	herm(A)	is the same as conj(transpose(A)).
	  herm(A,P) is the same	as conj(transpose(A,P)).
	  You can abbreviate "herm(A)" as "A'".


       See also: ``transpose''.

	  Error	codes:
	  -1: Permutation argument not integer array
	  -2: Permutation argument of bad rank or size
	  -3: Permutation argument contains invalid integers





  2.40.	 hide



       [] = hide(...)
	hide("sym-name",...) sets the 'hidden' attribute to
	  specified symbols.


       See also: ``whos'', ``unhide''.

	  Error	codes:
	  1: Argument not a string
	  2: Argument does not name a symbol





  2.41.	 info



       [] = info()
	info() shows information about various class sizes for this Tela implementation.
	  It also prints the total counts of Tnode, Tprg and Tobject objects at	the moment.




  2.42.	 input_string



       [s] = input_string()
	input_string() waits for an input line from the	keyboard
	  and returns it as a string. The newline is not included
	  in the result.
	  If the string	is enclosed in double quotes, they are removed.
	  Error	codes:
	  -1: EOF encountered.




  2.43.	 isCfunction



       [y] = isCfunction(x)
	isCfunction(x) returns 1 if x is a C-tela function.
	  and 0	otherwise.


       See also: ``isfunction'', ``isTfunction''.


  2.44.	 isTfunction



       [y] = isTfunction(x)
	isTfunction(x) returns 1 if x is a function written in Tela
	  and 0	otherwise.


  See also: ``isfunction'', ``isCfunction''.


  2.45.	 isarray



       [y] = isarray(x)
	isarray(x) returns 1 if	x is an	array and 0 if it is not.


       See also: ``isscalar'', ``isvector'', ``ismatrix''.


  2.46.	 ischar



       [y] = ischar(x)
	ischar(x) returns 1 if x is a character	and 0 otherwise.


       See also: ``isstring'', ``isstr''.


  2.47.	 iscomplex



       [y] = iscomplex(x)
	iscomplex(x) returns 1 if x is a complex array or scalar,
	  and 0	if it is real or integer or a nonnumeric object.


       See also: ``isreal'', ``isfloat'', ``isint''.


  2.48.	 isdefined



       [y] = isdefined(x)
	isdefined(x) returns 1 if x is not undefined and 0 if
	  it is	undefined. Optional function arguments are undefined
	  if not assigned by the caller; isdefined can be used
	  inside the function to test whether this is the case.


       See also: ``isundefined''.


  2.49.	 isfinite



       [y] = isfinite(x)
	isfinite(x) returns 1 if x is a	finite number and 0 otherwise.
	  If x is array, the operation is applied componentwise.
	  If x is non-numeric it is considered not finite.
	  Integer and consequently strings and chars are always	finite.






  2.50.	 isfloat



       [y] = isfloat(x)
	isfloat(x) returns 1 if	x is a floating	point array
	  or scalar, and 0 otherwise. Notice the difference between
	  isfloat and isreal. isreal(x)	is 1 for integer objects,
	  while	isfloat(x) is 0.


       See also: ``isreal'', ``isint'',	``iscomplex''.


  2.51.	 isfunction



       [y] = isfunction(x)
	isfunction(x) returns 1	if x is	a function
	  (Tela-function, C-tela function or intrinsic function)
	  and 0	otherwise.


       See also: ``isCfunction'', ``isTfunction''.


  2.52.	 isint



       [y] = isint(x)
	isint(x) returns 1 if x	is integer scalar or array
	  and 0	if it is not.


       See also: ``isreal'', ``isfloat'', ``iscomplex''.


  2.53.	 ismatrix



       [y] = ismatrix(x)
	ismatrix(x) returns 1 if x is a	matrix (2D array)
	  and 0	if it is not.


       See also: ``isscalar'', ``isvector'', ``isarray''.


  2.54.	 isreal



       [y] = isreal(x)
	isreal(x) returns 1 if x is numerical non-complex
	  array	or scalar, and 0 otherwise.


       See also: ``isfloat'', ``isint'', ``iscomplex''.





  2.55.	 isscalar



       [y] = isscalar(x)
	isscalar(x) returns 1 if x is scalar and 0 if it is not.


       See also: ``isvector'', ``ismatrix'', ``isarray''.


  2.56.	 isstr



       [y] = isstr(x)
	isstr(x) returns 1 if x	is a character or string
	  and 0	otherwise.


       See also: ``isstring'', ``ischar''.

	  NOTICE: Usually you want to use isstr, not isstring.




  2.57.	 isstring



       [y] = isstring(x)
	isstring(x) returns 1 if x is a	string and 0 otherwise.


       See also: ``ischar'', ``isstr''.

	  NOTICE: Usually you want to use isstr, not isstring.




  2.58.	 isundefined



       [y] = isundefined(x)
	isundefined(x) returns 1 if x is not undefined and 0 if
	  it is	undefined. Optional function arguments are undefined
	  if not assigned by the caller; isdefined can be used
	  inside the function to test whether this is the case.


       See also: ``isdefined''.


  2.59.	 isvector



       [y] = isvector(x)
	isvector(x) returns 1 if x is a	vector and 0 if	it is not.


       See also: ``isscalar'', ``ismatrix'', ``isarray''.

  2.60.	 isvoid



       [y] = isvoid(x)
	isvoid(x) returns 1 if x is a void value and 0 otherwise.




  2.61.	 length



       [L] = length(x)
	length(x) returns the total number of elements in array	x.
	  If x is scalar, length(x) is 1.


       See also: ``size'', ``rank''.


  2.62.	 log



       [y] = log(x)
	y = log(x) computes the	natural	logarithm of x.
	  If x is complex, the result is complex. If x is real or
	  integer, but negative, the result is complex (purely
	  imaginary). If x is real or integer and non-negative,
	  the result is	real.
	  If x is an array, the	operation is applied componentwise.
	  If some of the components are	negative, all components
	  of the result	are complex.




  2.63.	 map



       [B] = map(fn,A,darg)
	[B] = map(fn,A,d) maps function	fn along d'th dimension
	  in array A. Fn is a functional argument. It must return a scalar
	  when called with one vector argument.	The type of the	scalar
	  returned (integer, real or complex) must not change between
	  calls	on similar type	vectors.

	  For example, map(sum,A,1) sums elements of matrix A along
	  columns, returning a vector.
	  Error	codes:
	  -1: First arg	not a function
	  -2: Second arg not a numerical array
	  -3: Third arg	not an integer scalar
	  -4: Third arg	(the dimension)	out of range
	  -5: First arg	(function) did not return a scalar when	first called
	  -6: First arg	(function) unexpectedly	changed	its return type
	  -7: First arg	is an intrinsic	function; it is	no good






  2.64.	 menu



       [result]	= menu(title...)
	choice = menu("title","choice1","choice2",...) displays
	  a menu of choices and	returns	the number entered by
	  the user.


       See also: ``smenu''.

	  Error	codes:
	  -1: Less than	two input args




  2.65.	 ones



       [y] = ones(...)
	ones(n,m...) returns an	integer	array with all elements
	  equal	to 1 of	size n x m x ... .

	  ones(V) where	V is an	integer	vector,	and thus
	  ones(size(A))	work also.


       See also: ``rand'', ``eye''.


	  Error	codes:
	  -1: Input argument not an integer or IntVector
	  -2: Rank of requested	tensor array exceeds MAXRANK
	  -3: Non-positive input argument
	  -4: Negative input argument
	  -5: Integer array rank not 1





  2.66.	 pause



       [] = pause()
	pause()	will wait for a	keypress on keyboard.




  2.67.	 perf











  [v] =	perf()
   perf() returns an array containing all maintained operation
     counters. To measure performance of a code	segment, do

     p0=perf();	mycode(); p=perf()-p0;

     Now you can apply various performance-related functions to	p:
     for example cputime(p), Mflops(p).




  2.68.	 prod



       [y] = prod(x)
	y = prod(x) multiplies all the elements	of x, is x is an array.
	  If x is scalar, it is	returned as such.


       See also: ``sum''.

	  Error	codes:
	  -1: Nonnumeric input arg




  2.69.	 quit



       [] = quit()
	quit() stops Tela. quit() is synonym for exit().




  2.70.	 rand



       [x] = rand(...)
	rand() returns a random	real x,	0<=x<1.
	  rand(N) (N positive integer) returns a real random vector of length N.
	  rand(N,M) returns a random matrix, and so on.
	  Error	codes:
	  -1: Tried to create too high rank array
	  -2: Argument not an integer
	  -3: Non-positive integer argument




  2.71.	 rank



       [y] = rank(x)
	rank(A)	returns	the number of dimensions of array A.
	  The rank of a	scalar is 0.


       See also: ``length'', ``size''.

  2.72.	 reshape



       [B] = reshape(A...)
	reshape(A,n,m,...) returns the data in array A rearranged
	  to have dimensionality n x m x ... . The product of the indices
	  must equal the length	of A.
	  reshape(A,#(n,m...)) works also.
	  Error	codes:
	  -1: First argument not an array
	  -2: Later argument not an integer
	  -3: Product of dimensions does not equal the length of first argument
	  -4: Number of	input arguments	exceeds	MAXRANK
	  -5: Second arg is array but not integer vector





  2.73.	 round



       [y] = round(x)
	round(x) returns the nearest integer.
	  x must be integer or real scalar or array. If	it is an array,
	  the operation	is applied componentwise.


       See also: ``floor'', ``ceil''.

	  Error	codes:
	  -1: Complex or nonnumeric input argument




  2.74.	 run



       [output]	= run(cmd; input)
	run("cmd","input") runs	operating system (Unix)	command
	  "cmd", using contents	of the second argument string as
	  standard input. It returns the standard output of "cmd"
	  as a string.

	  The form run("cmd") may be used if the command does not
	  read standard	input. The command is executed by /bin/sh.

	  Error	codes:
	  -1: First argument not a string
	  -2: Second argument not a string
	  -3: Error with temporary file
	  -4: Error with internal pipe
	  -5: run not supported: OS does not provide unistd.h nor popen()
	  -6: Executing	the command failed
	  -7: wait(2) returned error
	  -8: pipe(2) returned error






  2.75.	 sec



       [y] = sec(x)
	y = sec(x) is the secant function
	  sec(x) = 1/cos(x).




  2.76.	 showcompiled



       [] = showcompiled(filename...)
	showcompiled("filename.ct",f1,f2,...) compiles functions
	  f1,f2,... to C-tela code, creating "filename.ct".
	  If no	suffix is given	in "filename", the suffix
	  ".ct"	will be	assumed.
	  showcompiled(f1,f2,...) displays on standard output.


       See also: ``t2ct''.

	  NOTE:	STILL UNDER DEVELOPMENT
	  Error	codes:
	  1: One of the	args is	not a Tela-function
	  2: Cannot open output	file





  2.77.	 sign



       [y] = sign(x)
	y = sign(x) returns 1 if x>0, 0	if x==0, and -1	if x<0.
	  x must be real. If x is array, the operation is applied componentwise.


       See also: ``HeavisideTheta''.

	  Error	codes:
	  -1: Complex or nonnumeric input argument




  2.78.	 sin



       [y] = sin(x)
	y = sin(x) computes the	sine function of x.
	  If x is complex, the result is complex, otherwise real.
	  The argument must be in radians.
	  If x is an array, the	operation is applied componentwise.






  2.79.	 sinh



       [y] = sinh(x)
	y = sinh(x) computes the hyperbolic sine function of x.
	  If x is complex, the result is complex, otherwise real.
	  If x is an array, the	operation is applied componentwise.




  2.80.	 size



       [...] = size(x)
	[n,m,...] = size(A) finds out the dimensions of	array A.
	  The number of	n,m... must not	exceed rank(A).	If rank(A)==0
	  (that	is, A is scalar), n=size(A) sets 1 to n.
	  V = size(A) assigns the dimension vector [n,m,..] to V.
	  If A is scalar, V is set to 1, if A is vector, V becomes
	  a one-element	vector.


       See also: ``length'', ``rank''.

	  Error	codes:
	  -1: No output	arguments
	  1: More than one output arg but non-array input arg
	  2: Too many output args relative to input arg	rank




  2.81.	 smenu



       [result]	= smenu(title...)
	choice = smenu("title","choice1","choice2",...)	displays
	  a menu of choices and	returns	the "choice" string corresponding
	  to the number	entered	by the user.


       See also: ``menu''.

	  Error	codes:
	  -1: Less than	two input args




  2.82.	 sort



       [y] = sort(;x)
	sort(x)	returns	array x	sorted in ascending order.
	  If x is not an array,	it is returned as is.
	  x = sort() sorts x in	place.
	  x may	not be complex.
	  Error	codes:
	  1: Complex input arg


  2.83.	 source



       [] = source(fn)
	source("file.t") loads the tela	code from given	file.


       See also: ``autosource'', ``load''.

	  Error	codes:
	  1: Operation did not succeed
	  2: Argument not a string




  2.84.	 sqrt



       [y] = sqrt(x)
	y = sqrt(x) computes the square	root of	x.
	  If x is complex, the result is complex. If x is real or
	  integer, but negative, the result is complex (purely
	  imaginary). If x is real or integer and non-negative,
	  the result is	real.
	  If x is an array, the	operation is applied componentwise.
	  If some of the components are	negative, all components
	  of the result	are complex.




  2.85.	 str2num



       [y] = str2num(s)
	str2num(s) converts a string to	a number.
	  The string must represent a scalar. If an error
	  occurs, str2num returns a void value.
	  Error	codes:
	  1: Argument not a string or char




  2.86.	 streq



       [y] = streq(s1,s2)
	streq("string1","string2") returns 1 if	the argument
	  strings are exactly equal and	0 otherwise. If	one of
	  the args is not a string, the	result is also 0.


       See also: ``strstarteq''.


  2.87.	 strmat




  [x] =	strmat(...)
   strmat("string1","string2",...) makes a string matrix
     ouf of individual strings.	The strings need not be	same length,
     they are padded with zeros	(invisible) if they are	not.


  See also: ``strmat2''.

     Error codes:
     -1: Argument not a	string




  2.88.	 strmat2



       [x] = strmat2(str; sep)
	strmat2("string") creates a string matrix from "string"
	  interpreting the newline character as	row ending marker.
	  strmat2("string",sep)	uses separator sep instead of
	  newline char;	sep may	be either character or string.
	  If sep is a string, any character that is a member of	sep
	  is taken to be a separator. If the rows have unequal lengths,
	  they are padded with zeros.


       See also: ``strmat''.

	  Error	codes:
	  -1: First arg	not a string
	  -2: Second arg not a char or string





  2.89.	 strstarteq



       [y] = strstarteq(s1,s2)
	strstarteq("string1","string2")	returns	1 if the argument
	  strings are equal on the first min(length(s1),length(s2))
	  characters and 0 otherwise.
	  If one of the	the args is not	a string, the result is	also 0.


       See also: ``streq''.


  2.90.	 sum



       [y] = sum(x)
	y = sum(x) sums	all the	elements of x, is x is an array.
	  If x is scalar, it is	returned as such.


       See also: ``prod''.

	  Error	codes:
	  -1: Nonnumeric input arg

  2.91.	 system



       [] = system(s)
	system("string") executes string as an external	operating system
	  (Unix) command.
	  Error	codes:
	  1: Argument not a string or char




  2.92.	 t2ct



       [] = t2ct(fn)
	t2ct("filename.t") translates t-code to	ct-code.
	  Error	codes:
	  1: Operation did not succeed
	  2: Argument not a string
	  3: Could not open output file





  2.93.	 tan



       [y] = tan(x)
	y = tan(x) computes the	tangent	function of x.
	  If x is complex, the result is complex, otherwise real.
	  The argument must be in radians.
	  If x is an array, the	operation is applied componentwise.




  2.94.	 tanh



       [y] = tanh(x)
	y = tanh(x) computes the hyperbolic tangent function of	x.
	  If x is complex, the result is complex, otherwise real.
	  If x is an array, the	operation is applied componentwise.




  2.95.	 tic



       [] = tic()
	tic() marks the	CPU time at which it was invoked.
	  To measure CPU time, use tic() and toc().


       See also: ``cputime'', ``toc''.



     Example:

	a = rand(100,100); tic(); b=inv(a); toc()

    This would measure the CPU time in inverting a 100x100
    random real	matrix.	See also: toc.




  2.96.	 toc



       [t] = toc()
	toc() gives the	CPU seconds used since the last	call to	tic().


       See also: ``tic'', ``cputime''.


  2.97.	 tostring



       [y] = tostring(x)
	tostring(x) converts an	integer	vector to a string.
	  Transfer of characters is stopped if zero element
	  is encountered.
	  tostring(A) where A is geneeral integer array	copies
	  A and	sets the string	flag.
	  Error	codes:
	  -1: Argument not an integer array





  2.98.	 transpose



       [B] = transpose(A; P)
	B = transpose(A) returns a transpose of	array A: B[i,j,k...l] =	A[l...k,j,i].
	  B = transpose(A,P) where P is	integer	vector transposes the indices in the
	  permutation defined by P.
	  For example if A has rank 3, B = transpose(A,[2,1,3])	causes the assignment
	  B[j,i,k] = A[i,j,k] to be carried out. B = transpose(A) would	in this	case
	  correspond to	B[k,j,i] = A[i,j,k].

	  You can abbreviate "transpose(A)" by "A.'".


       See also: ``herm''.

	  Error	codes:
	  -1: Permutation argument not integer array
	  -2: Permutation argument of bad rank or size
	  -3: Permutation argument contains invalid integers







  2.99.	 unhide



       [] = unhide(...)
	hide("sym-name",...) unsets the	'hidden' attribute to
	  specified symbols.


       See also: ``whos'', ``hide''.

	  Error	codes:
	  1: Argument not a string
	  2: Argument does not name a symbol





  2.100.  version



       [x] = version()
	version() returns the Tela version number (real) currently
	  in use.




  2.101.  whos



       [] = whos(;hidden)
	whos() displays	names of variables together with their
	  types	and values, if short. 'Hidden' symbols are not shown.
	  whos("hidden") shows also hidden symbols.


       See also: ``hide'', ``unhide''.

	  Error	codes:
	  1: Bad argument






  3.  files.ct

  This section describes functions from	file files.ct.


  3.1.	export_matlab










  [] = export_matlab(fn...)
   export_matlab("file") saves all variables in	Tela
     workspace in "file". Any previous contents	of "file"
     are overwritten. The data are written in MATLAB
     binary format.

     export_matlab("file","var1","var2"...) saves only the
     specified variables. Notice that you have to give the
     variable names as strings.

     The resulting MAT-file can	be read	using the
     MATLAB 'load' command.

     Limitations (bugs): It is not possible to export
     local variables. If you try, the global ones will
     be	written, if they have numeric values. Use
     export_matlab2 to achieve this, and to have explicit
     control of	variable naming.



  See also: ``export_matlab2'',	``save'', ``load'', ``import''.

     Error codes:
     1:	Too few	arguments
     2:	Argument not a string
     3:	Write error on file





  3.2.	export_matlab2



       [] = export_matlab2(fn...)
	export_matlab2("file", var1,"name1", var2,"name2"...)
	  saves	objects	var1,var2... in	MATLAB binary format in	"file".
	  The objects will be named "name1", "name2"...	.
	  Any previous contents	of "file" are overwritten.
	  workspace in "file". Any previous contents of	"file"
	  is overwritten.

	  The resulting	MAT-file can be	read using the
	  MATLAB 'load'	command.



       See also: ``export_matlab'', ``save'', ``load'',	``import''.

	  Error	codes:
	  1: First arg not a string
	  2: Even number of arguments
	  3: Write error on file
	  4: The 'name'	argument is not	a string





  3.3.	import




  [] = import(filename)
   import("file") tries	to load	the contents of	"file" in Tela workspace.
     All files accepted	by load	are also accepted by import. In	addition,
     import accepts more general HDF files and MATLAB binary files.
     Create these files	using the MATLAB 'save'	command.

     Restrictions:
     1)	Only MATLAB files created on a similar architecture can	be
     correctly imported. If this rule is not followed, the imported
     data will be garbage!
     2)	MATLAB4.0 and higher saves arrays with more than 10000 elements
     as	various	integer	formats, if all	elements are whole numbers.
     Tela cannot read these files. A workaround	is to perturb one element
     in	MATLAB before saving so	that it	is not exactly integer.

     For filename conventions, see load.


  See also: ``load'', ``save'',	``import1'', ``export_matlab''.


     (The difference between import and	import1	is that	import1	reads
      only one object and returns it, whereas import reads several
	  objects and assigns them directly to workspace variables.)
     Error codes:
     1:	Argument not string or char
     2:	Argument is not	an HDF file
     3:	File not found
     4:	Cannot import file
     5:	Unused error message
     6:	Cannot import this Matlab file (O(letter'Oh) !=	0, (can	even Matlab?))
     7:	Cannot import this Matlab file (P != 0). Is your array size >10000 and all integer? Try	perturbing it
     8:	Cannot import this Matlab file (T != 0,	1). Is it a sparse matrix? Make	it full
     10: Bad Matlab binary file, premature end of file





  3.4.	import1


























  [x] =	import1(filename; label)
   import1("file") reads one object from "file". The imported
     object is returned. "File"	can be one of the following:

     1)	HDF file, in which case	the first Scientific Data Set (SDS)
	is imported. The form import1("file.hdf","label") reads	SDS
	with label "label", which is not necessarily the first one.

     2)	D-style	ASCII file of the following format:

	  (line	1)   D=Nt dim1 dim2 ...	dimN
	  (any number M	of blank lines or lines	starting with '#')
	  (line	M+2) data1 data2 ....

	 where N is the	rank of	the dataset and	t is an	optionial
	 type specification letter: t may be either 'r', 'i', or 'c'
	 for real, integer and complex data, respectively. If t	is
	 missing, real data are	asssumed.

     3)	Plain ASCII file of nrows x ncols real numbers.	If nrows or
	ncols is 1, it will be returned	as a vector, otherwise as a
	matrix.	Missing	entries	are treated as zeros. This format
	is similar to Matlab's load for	ASCII, except that '#'
	comments are accepted in the beginning.



  See also: ``import'',	``load'', ``save''.

     See import	for a difference between import	and import1.
     For filename conventions, see load.
     Error codes:
     -1: Input arg not a char or string
     -2: File not found
     -3: Unknown format	in ASCII file
     -4: Unknown format	in ASCII file
     -5: Too high rank ASCII data
     -6: Syntax	error in ASCII file dimension specification
     -7: Syntax	error when reading D-style ASCII data
     -8: Internal error
     -9: Cannot	import file
     -10: Second arg not a string
     -11: Specified label not found
     -12: Premature end	of file	in D-style ASCII
     -13: Syntax error when reading plain ASCII	data





  3.5.	load















  [] = load(filename)
   load("file")	loads the contents of "file"
     in	Tela workspace.
     "file" must have been previously created using
     the 'save'	command; it must be in a certain
     HDF format.

     Filename conventions:
     If	the filename starts with "/", "./" or "..",
     it	is considered absolute.	Otherwise it is	searched
     along TELAPATH. This applies to other file
     operations	as well.

     The counterpart of	load is	save.
     To	read more general HDF files and	ASCII files,
     see import1.
     To	load more general HDF files and	MATLAB binary
     files, see	import.


  See also: ``save'', ``import'', ``import1'', ``export_matlab''.

     Error codes:
     1:	Argument not string or char
     2:	Argument is not	an HDF file
     3:	File not found





  3.6.	save



       [] = save(fn...)
	save("file") saves all variables in Tela workspace
	  in "file". Any previous contents of "file" is
	  overwritten. The data	are written as Scientific
	  Data Sets in HDF format.
	  save("file","var1","var2"...)	saves only the
	  specified variables. Notice that you have to give
	  the variable names as	strings.

	  Limitations (bugs): It is not	possible to save
	  local	variables, since they are not bound to
	  symbols. If you try, the global one, if any,
	  will be saved.



       See also: ``load'', ``export_matlab''.

	  Error	codes:
	  1: Too few arguments
	  2: Argument not a string or char
	  3: Unexpected	HDF error









  4.  plotmtv.ct

  This section describes functions from	file plotmtv.ct.


  4.1.	annotate



       [] = annotate(primitive...)
	annotate("primitive"[,options])	adds MTV annotations to	the previous
	  graph. The plot command(s) and the annotate command(s) must appear
	  inside hold(on) ... hold(off)	in order to work correctly.


       See also: ``plotopt'', ``hold'',	``plot'', ``pcolor'', ``mesh'',
       ``contour'', ``vplot''.

	  Error	codes:
	  1: Could not open temporary MTV file
	  2: First argument not	a string
	  3: Syntax error in graph options




  4.2.	bar



       [] = bar(x,y,z...)
	bar(grouplabels,data,barnames[,options]) produces a bar	chart.
	  Example 1:

	      bar(strmat("DEC","HP"),#(111,150.6),"Speed")


       See also: ``plot'', ``hist''.

	  Error	codes:
	  1: First argument not	int nor	real array
	  2: First argument not	a vector nor matrix
	  3: Second argument not int nor real array
	  4: Second argument not a vector nor matrix
	  5: Dimension mismatch	between	first and second arg
	  6: If	second arg is vector, third arg	must be	a string
	  7: Third arg must be a string	or a string matrix
	  8: If	second arg is matrix, third arg	must be	a string matrix
	  9: Dimension mismatch	between	second and third arg
	  10: Syntax error in graph options
	  11: First arg	must not be real matrix
	  12: Could not	open temporary MTV file





  4.3.	contour



       [] = contour(z...)
	contour(z[,options]) plots the matrix z	as a filled contour plot.



  See also: ``contour3'', ``annotate'',	``plot'', ``mesh'', ``pcolor'',
  ``vplot''.

     Error codes:
     1:	Could not open temporary MTV file
     2:	First argument is not a	numeric	2D array
     3:	Syntax error in	graph options
     4:	Write error in MTV file	- file system full?




  4.4.	contour3



       [] = contour3(z...)
	contour3(z[,options]) plots the	3D array as a
	  "volume" plot. Currently this	only means that	all
	  six faces of the volume are contoured	and colored
	  according to options.


       See also: ``annotate'', ``plot'', ``mesh'', ``pcolor'', ``vplot''.

	  contour.
	  Error	codes:
	  1: Could not open temporary MTV file
	  2: First argument is not a real 3D array
	  3: Syntax error in graph options
	  4: Write error in MTV	file - file system full?




  4.5.	grid



       [X,Y] = grid(x,y)
	[X,Y] =	grid(x,y) produces matrices X,Y	that are formed	from vectors x,y
	  such that X[i,j] = x[i] for all j, and Y[i,j]	= y[j] for all i.


       See also: ``grid3''.

	  Error	codes:
	  -1: Input argument is	array but not a	vector
	  -2: Input argument is	not real array




  4.6.	grid3



       [X,Y,Z] = grid3(x,y,z)
	[X,Y,Z]	= grid3(x,y,z) produces	3D arrays X,Y,Z	that ar
	  formed from vectors x,y,z such that
	  X[i,j,k] = x[i] for all j,k,
	  Y[i,j,k] = y[j] for all i,k, and
	  Z[i,j,k] = z[k] for all i,j.



  See also: ``grid''.

     Error codes:
     -1: Input arg is array but	not a vector
     -2: Input arg not a real array




  4.7.	hist



       [] = hist(x...)
	hist(x)	produces a histogram of	vector x.
	  The range min(x)..max(x) is divided in bins, and the
	  number of x values in	each bin is counted. The count determines
	  the height of	each bin.

	  hist(x) uses 10 bins,	hist(x,n) uses n bins.
	  hist(x,n,a) starts from x=a.
	  hist(x,n,a,b)	ignores	x values outside interval a..b.
	  Rest of the args may contain other MTV options.


       See also: ``plot'', ``bar''.

	  Error	codes:
	  1: First argument not	a (real) vector
	  2: Second arg	not a positive integer
	  3: Third arg not a (real) scalar
	  4: Fourth arg	not a (real) scalar
	  5: Third arg greater of equal	than fourth arg
	  6: Could not open temporary MTV file
	  7: Syntax error in graph options





  4.8.	hold



       [] = hold(flag)
	hold(on) and hold(off) set the graphics	hold mode on and off.
	  When hold is on, all graphics	commands will be accumulated and
	  performed only until hold(off).
	  If hold(on) is called	many times in succession, also hold(off)
	  must be called as many times until the plots are produced.
	  For example, if

	  function f() {hold(on); plot1(); plot2(); hold(off)};

	  and it is called as

	  hold(on); f(); plot3(); hold(off);

	  then all three plots are actually combined in	one plot.


       See also: ``plot'', ``holdmode''.

	  Error	codes:
	  1: Argument not an integer

  4.9.	holdmode



       [result]	= holdmode(;flag)
	holdmode(overlay) causes held plots to be combined in same figure.
	  holdmode(paging) shows them as sequential pages in one window.
	  holdmode(stacking) draws them	as subplots in one window.
	  holdmode() returns the current setting.


       See also: ``hold''.

	  Error	codes:
	  1: Argument not an integer
	  2: Bad value for argument




  4.10.	 mesh



       [] = mesh(z...)
	mesh(z[,options]) plots	the matrix z as	a 3D mesh.


       See also: ``annotate'', ``plot'', ``contour'', ``pcolor'', ``vplot''.

	  Error	codes:
	  1: Could not open temporary MTV file
	  2: First argument is not a numeric 2D	array
	  3: Syntax error in graph options
	  4: Write error in MTV	file - file system full?




  4.11.	 pcolor



       [] = pcolor(z...)
	pcolor(z[,options]) plots the matrix z as a pseudocolor	density	plot.


       See also: ``annotate'', ``plot'', ``contour'', ``mesh'',	``vplot''.

	  Error	codes:
	  1: Could not open temporary MTV file
	  2: First argument is not a numeric 2D	array
	  3: Syntax error in graph options
	  4: Write error in MTV	file - file system full?




  4.12.	 plot







  [] = plot(...)
   plot(x1,y1,[options1], x2,y2,[options2],...)	is the basic 2D	plot function.
     Each vector yi is plotted versus the corresponding	xi. All	curves yi are
     displayed in the same figure. The option sequences	must consist of	keyword-
     value pairs. Example:

	 x = 0:0.1:4*pi;
	 plot(x,sin(x),	"linewidth",3,"linecolor",2);

     The abscissa x may	be missing, in which case the default of 1:length(y)
     is	used. The ordinates y may be matrices; then each row produces one
     curve. If also abscissa x is matrix, the x-value may be different for each
     curve.


  See also: ``plot3'', ``annotate'', ``plotopt'', ``mesh'', ``contour'',
  ``pcolor'', ``vplot''.

     Error codes:
     1:	Could not open temporary MTV file
     2:	Nonnumeric or complex data argument
     3:	Syntax error in	graph options
     4:	The abscissa ("x") must	be a vector or a matrix
     5:	The ordinate ("y") must	be a vector or a matrix
     6:	x and y	dimensions disagree





  4.13.	 plot3



       [] = plot3(x,y,z...)
	plot3(x,y,z[,options]) produces	parametric space curves.
	  The quantities x,y,z must have equal ranks, and they can
	  be either vectors or matrices. If they are vectors, only
	  one space curve is drawn. If they are	matrices, the number
	  of curves produces equals the	number of rows.


       See also: ``plot'', ``annotate''.

	  Error	codes:
	  1: Could not open temporary MTV file
	  2: y dimensionality disagrees	with x dimensionality
	  3: z dimensionality disagrees	with x dimensionality
	  4: Input arrays must be integer or real arrays
	  5: Input arrays must have rank equal to 1 or 2
	  6: Syntax error in graph options





  4.14.	 plotopt



       [] = plotopt(s)
	plotopt("-3d -colorps -landscape...") sets a set of PlotMTV command
	  line options for subsequent graphics commands	(global	setting).



  See also: ``plot'', ``annotate''.


     NOTICE: plotopt is	usually	not required. You can pass the option string
     to	all plot commands directly, for	example:

     plot(x,sin(x),"-3d	-landscape");

     These options affect only the current (or next outputted, if hold is used)
     plot. Include only

     Error codes:
     1:	Argument not a string




  4.15.	 vplot



       [] = vplot(x,y,vx,vy...)
	vplot(x,y,vx,vy[,options]) produces a 2D vector	plot of	the vector
	  field	(vx,vy). All arguments x,y,vx and vy must be 2D	integer	or
	  real arrays and of the same size. Each 2D vector will	be positioned
	  at (x[i,j],y[i,j]) and its direction will be (vx[i,j],vy[i,j]) where
	  (i,j)	run over rows and columns of the matrices.


       See also: ``annotate'', ``plot'', ``mesh'', ``contour'',	``pcolor''.

	  Error	codes:
	  1: Could not open temporary MTV file
	  2: One of first four args is not a numeric array
	  3: One of first four args has	rank not equal to 2
	  4: Dimensions	of first four args disagree
	  5: Syntax error in graph options





  5.  la.ct

  This section describes functions from	file la.ct.


  5.1.	LU



       [L;U,P] = LU(A)
	[L,U,P]	= LU(A)	computes the LU	factorization of matrix	A.
	  The factorization is A = P**L**U, where P is a permutation
	  matrix, L is lower triangular	with unit diagonal and U is
	  upper	triangular.
	  [lu] = LU(A) leaves the factors L and	U packed in one	matrix.
	  [lu,p] = LU(A) returns also the pivoting info	vector p.
	  (Notice that this p is related to the	permutation matrix P
	  but is not the same. You need	this form of LU	if you want to
	  use LUbacksubst later	on.)


       See also: ``LUbacksubst'', ``linsolve'',	``inv'', ``SVD''.


     Error codes:
     1:	Singular matrix	(==> zero in U's diagonal)
     -1: Input arg not an array
     -2: Input arg not a rank-2	array (matrix)





  5.2.	LUbacksubst



       [x] = LUbacksubst(lu,p,b)
	LUbacksubst(lu,p,b) solves the linear system A**x == b,
	  where	A has been previously LU-decomposed using LU:
	  [lu,p] = LU(A).


       See also: ``linsolve'', ``LU''.

	  Error	codes:
	  -1: First input arg is not an	array
	  -2: First input arg is not a square matrix
	  -3: Second input arg is not an integer vector
	  -4: Third input arg is not an	array
	  -5: Third input arg is not a vector or matrix
	  -6: Incompatible dimensions in first/third args
	  -7: Singular matrix
	  -8: Incompatible dimensions in first/second args
	  -9: Internal error




  5.3.	SVD



       [U;S,V] = SVD(A)
	[U,S,V]	= SVD(A) computes the singular value
	  decomposition	of matrix A: A = U**S**V'.
	  U and	V are unitary and S is diagonal.
	  SVD(A) as such returns the vector of singular	values.


       See also: ``LU''.

	  Error	codes:
	  1: No	convergence
	  -1: Input arg	not an array
	  -2: Input array is not a matrix
	  -3: Internal error
	  -4: Two output arg case not supported	(must be 1 or 3)





  5.4.	det






  [d] =	det(A)
   det(A) returns the determinant of a square matrix A.
     A may be integer, real or complex valued.
     If	A is scalar, it	is returned as such.
     Error codes:
     -1: Nonnumeric input arg
     -2: Input array is	not a matrix
     -3: Input matrix is not square
     -4: Singular matrix




  5.5.	eig



       [D;V] = eig(A)
	eig(A) returns the eigenvalues of a square matrix A.
	  [D,V]	= eig(A) returns the eigenvalues in D and the
	  right	eigenvectors as	columns	of V. The eigenvectors
	  satisfy A**V == D*V.


       See also: ``inv'', ``LU''.

	  Error	codes:
	  1: Failed to converge
	  -1: Input arg	is not an array
	  -2: Input array is not a matrix
	  -3: Input matrix is not square
	  -4: Internal error





  5.6.	eye



       [A] = eye(n)
	eye(n) returns the (integer) unit matrix of order n.
	  n must be a non-negative scalar integer.
	  eye(V) where V is a two-element integer vector with
	  both elements	equal and positive works also, thus
	  you can also use eye(size(A)).


       See also: ``ones'', ``inv''.

	  Error	codes:
	  -1: Argument not an integer or IntArray
	  -2: Negative dimension
	  -3: IntArray rank not	1
	  -4: IntArray length not 2
	  -5: Integer vector elements are unequal





  5.7.	inv



  [B] =	inv(A)
   inv(A) returns the inverse of a square matrix A.
     A may be integer, real or complex valued.
     A may also	be a scalar, in	which case its reciprocal
     is	returned.


  See also: ``linsolve'', ``LU'', ``matprod'', ``det'',	``eig''.

     Error codes:
     -1: Nonnumeric input arg
     -2: Input array is	not a matrix
     -3: Input matrix is not square
     -4: Singular matrix
     -5: Singular matrix




  5.8.	linsolve



       [x] = linsolve(A,b)
	linsolve(A,b) solves the linear	system A**x == b.
	  If A is square, the result x is roughly the same as
	  computing inv(A)**b (however,	using linsolve is
	  faster and numerically more accurate). If A is not
	  square, a least-square problem is solved. If the system
	  is overdetermined, the solution x minimizes the quantity
	  |A**x	- b|. If the system is underdetermined,	the
	  solution x minimizes |x| among all x that satisfy
	  A**x==b.
	  The second argument may be a vector or a matrix.
	  If it	is a matrix, several linear systems are	effectively
	  solved simultaneously.


       See also: ``inv'', ``LU'', ``eig'', ``SVD''.

	  Error	codes:
	  -1: First input arg is not an	array
	  -2: First input arg is not a matrix
	  -3: Second input arg is not an array
	  -4: Second input arg is not a	vector or matrix
	  -5: Incompatible dimensions in first/second args
	  -6: Matrix must be square
	  -7: Singular matrix
	  -8: Internal error





  5.9.	matprod











  [C] =	matprod(A,B; Aflag,Bflag)
   matprod(A,B)	returns	the matrix product of A	and B.
     If	at least one of	A and B	is scalar, matprod(A,B)	is the
     same as their ordinary product A*B. If both A and B
     are arrays, their "inner" dimensions must agree.
     That is, the last dimension of A must equal the first
     dimension of B.
     You can abbreviate	matprod(A,B) as	A**B.

     Optional args: matprod(A,B,aflag,bflag) can be used to
     transpose or Hermitian-conjugate the factors before the
     product. 'n' means	no operation, 't' means	transpose and
     'h' means Hermitian conjugate. For	example,

     matprod(A,B,'h') =	A'**B =	herm(A)**B
     matprod(A,B,'n','t') = A**B.' = A**transpose(B)

     Normally you need not use matprod explicitly, but you
     can use the operator **, which is internally translated
     to	matprod. Hermitian conjugates and transposes in
     connection	with **	produce	the corresponding 'h' and
     't' options in matprod. For example,

     A'**B	  generates	  matprod(A,B,'h')
     A.'**B'	  generates	  matprod(A,B,'t','h')
     A**B.'	  generates	  matprod(A,B,'n','t')

     and so on.	The runtime is optimal for all these operations.


  See also: ``inv''.


     Error codes:
     -1: Inner dimensions do not agree
     -2: Resulting array would have too	high rank
     -3: Third arg not one of 'n', 't',	'h'
     -4: Fourth	arg not	one of 'n', 't', 'h'






  6.  fft.ct

  This section describes functions from	file fft.ct.


  6.1.	FFT
















  [f] =	FFT(u; dim)
   FFT(u) gives	the complex Fast Fourier Transform of u.
     If	u's rank is more than one, the transform is computed
     only along	the first dimension (many independent 1D
     transforms).

     FFT(u,dim)	computes the FFT along the specified dimension.
     The first dimension is labeled 1 and so on.

     The forward FFT is	defined	as

     FFT(u)_j =	sum(c_k	* exp(-i*(j-1)*(k-1)*2*pi/n), k=1..n)

     where i = sqrt(-1).



  See also: ``invFFT''.

     Error codes:
     -1: First argument	not a numeric array
     -2: Second	argument not integer
     -3: Second	argument out of	range





  6.2.	invFFT



       [f] = invFFT(u; dim)
	invFFT() is the	inverse	of FFT():

	  invFFT(u)_j =	(1/n) *	sum(c_k	* exp(i*(j-1)*(k-1)*2*pi/n), k=1..n)

	  Differences to FFT: sign of i	is plus, scale factor 1/n.



       See also: ``FFT''.

	  Error	codes:
	  -1: First argument not a numeric array
	  -2: Second argument not integer
	  -3: Second argument out of range






  7.  dld.ct

  This section describes functions from	file dld.ct.


  7.1.	link







  [] = link(filename)
   link("file.o") makes	C-tela functions in "file.o" available
     to	Tela. "file.o" must be compiled	from a C-tela file
     (usually "file.ct").
     Error codes:
     1:	Cannot initialize DLD
     2:	Cannot link-load file
     3:	Argument not string or char
     4:	Cannot find fninfo pointer
     5:	Internal inconsistency
     6:	Undefined symbols remain
     7:	main function returned error code
     8:	Could not dlclose the previous linkage
     9:	Too many dynamically linked modules
     10: File not found






  8.  fileio.ct

  This section describes functions from	file fileio.ct.


  8.1.	fclose



       [] = fclose(fnum)
	fclose(fnum) closes file with given identification number.
	  The fnum must	have been previously obtained from fopen.


       See also: ``fopen'', ``fformat''.

	  Error	codes:
	  -1: Bad argument: not	integer
	  -2: Bad argument: outside range
	  3: File was not open




  8.2.	fformat



       [] = fformat(fnum,str...)
	fformat(fnum,"format-string",arg1,arg2,...) is similar to format,
	  except that it does not output to stdout but to opened file.


       See also: ``format'', ``sformat'', ``fopen''.

	  Error	codes:
	  -1: First argument not integer
	  -2: First argument not a valid file number
	  -3: Second argument not a string or char
	  4: File is not open





  8.3.	fopen



       [fnum] =	fopen(name,mode)
	fopen("filename",mode) opens a file and	returns
	  its identifier (integer). The	mode parameter can be
	  "r" or "w" for reading and writing, respectively.
	  If the open is not succesful,	-1 is returned.


       See also: ``fformat'', ``fclose''.

	  Error	codes:
	  -1: First arg	not a string
	  -2: Second arg not a string
	  -3: Too many open files
	  -4: Bad string for second arg




  8.4.	format



       [] = format(str...)
	format("format-string",arg1,arg2,...) prints "format-string"
	  to standard output, replacing	occurrences of `format-spec`
	  with consecutive args. `Format-spec` is either empty,	i.e. ``,
	  or of	the form

	      `[-]w[.d]`.

	  Here w is the	field width (unsigned integer) and d is	the number
	  of significant digits, also unsigned integer.	By default the
	  argument is printed left-justified, but the optional minus sign
	  dictates right justification.	The backquote character	`  can be
	  produced by writing it three times: ```.

	  Hint:	You can	add any	number of spaces before	the closing backquote,
	  for example `20.7    `.
	  These	spaces do not affect the output. This feature can be used
	  to justify source code lines.


       See also: ``fformat'', ``sformat''.

	  Error	codes:
	  1: First argument not	a string or char




  8.5.	fprintf











  [] = fprintf(fnum,formatstr...)
   fprintf(fnum,"format-string",arg1,arg2,...) is an interface to the C
     fprintf function. The format string should	have a percent slot
     for every arg. The	args may be integer or real scalars or strings.
     The file identifier fnum must have	been obtained from fopen.

     Notice: The stream	is not flushed after every fprintf operation,
     but a flush occurs	whenever you switch from using fprintf to
     fformat on	the same file. Therefore avoid mixing fprintf and fformat
     on	the same file if performance is	an issue for you!



  See also: ``fopen'', ``printf'', ``sprintf'',	``format''.

     Error codes:
     1:	Bad argument type
     2:	Second arg not a string
     3:	First argument not an integer
     4:	Bad file identifier: out of range
     5:	File is	not open
     6:	Internal error:	fdopen failed





  8.6.	printf



       [] = printf(formatstr...)
	printf("format-string",arg1,arg2,...) is an interface to the C
	  printf function. The format string should have a percent slot
	  for every arg. The args may be integer or real scalars or strings.


       See also: ``fprintf'', ``sprintf'', ``format''.

	  Error	codes:
	  1: Bad argument type
	  2: First arg not a string





  8.7.	sformat



       [s] = sformat(formatstr...)
	sformat("format-string",arg1,arg2,...) is similar to format,
	  except that it does not output to stdout but returns a string
	  variable.


       See also: ``format'', ``fformat'', ``sprintf''.

	  Error	codes:
	  -1: First argument not a string or char





  8.8.	sprintf



       [s] = sprintf(formatstr,arg)
	sprintf("format-string",arg1,arg2,...) is an interface to the C
	  sprintf function. The	format string should have a percent
	  slot for every arg. The args may be integer or real scalars
	  or strings.


       See also: ``sformat''.


	  LIMITATIONS:
	      This implementation allows only one arg (arg1).
	      The resulting string may not become larger than
		  500 chars or Tela may	crash.
	  Error	codes:
	  -1: First arg	not a string
	  -2: Args may only be scalar ints or reals, or	strings






  9.  numerics.ct

  This section describes functions from	file numerics.ct.


  9.1.	intpol



       [y] = intpol(A...)
	intpol(A,index1,index2...) is a	general	interpolation
	  function. A must be an array from which values are interpolated.
	  The rank of A	must equal the number of index arguments.
	  Each index argument may be a real scalar or real array.
	  All index arguments must mutually agree in type and rank.
	  The array A may also be complex.

	  intpol(A,i,j,...) is a generalization	of mapped indexing
	  A<[i,j,...]> for non-integral	indices. The function benefits
	  from vectorization even more than most other Tela functions.
	  Error	codes:
	  -1: First arg	not a numerical	array
	  -2: Rank of first arg	does not match number of index args
	  -3: Non-real index arg
	  -4: Dissimilar index args
	  -6: Range overflow





  10.  matlabeng.ct

  This section describes functions from	file local/matlabeng.ct.





  10.1.	 matlab_call



       [...] = matlab_call(fname...)
	[a,b,c,...] = matlab_call("fname",d,e,f,...)
	  calls	a Matlab function in a currently running background
	  Matlab process. Input	arguments (any number) d,e,f,...
	  are sent to Matlab prior to call, and	output arguments
	  (any number) a,b,c,... are collected and returned to Tela
	  after	the function has completed.


       See also: ``matlab_start'', ``matlab_eval'', ``matlab_put'', ``mat-
       lab_get''.

	  Error	codes:
	  1: Unknown error when	sending	input argument
	  2: Function call unsuccessful
	  3: Internal error: No	such output argument in	Matlab workspace
	  4: Output argument is	of unsupported type (not double)
	  5: Output argument is	of unsupported type (not full matrix)
	  -1: Internal error: matlab_put or matlab_get first argument not a string
	  -2: No Matlab	process	running, use matlab_start first
	  -3: Input argument not interpretable as a matrix
	  -4: Input argument has too high (> 2)	rank
	  -5: First argument not a string





  10.2.	 matlab_eval



       [retval]	= matlab_eval(str)
	matlab_eval("command") sends "command" to currently
	  running Matlab background process. It	returns	1
	  if succesful 0 if an error occurred.


       See also: ``matlab_start'', ``matlab_put'', ``matlab_call''.

	  Error	codes:
	  -1: Argument not a string
	  -2: No Matlab	process	running, use matlab_start first





  10.3.	 matlab_get



       [y] = matlab_get(name)
	matlab_get("MatrixName") asks a	currently running background
	  Matlab process for a variable	named "MatrixName", and	returns
	  its value.


       See also: ``matlab_start'', ``matlab_put'', ``matlab_eval''.



     Error codes:
     -1: Argument not a	string
     -2: No Matlab process running, use	matlab_start first
     3:	No such	variable in Matlab workspace
     4:	The variable is	of unsupported type (not double)
     5:	The variable is	of unsupported type (not full matrix)





  10.4.	 matlab_put



       [] = matlab_put(name,value)
	matlab_put("MatrixName",x) tries to interpret x	as
	  a Matlab matrix and sends it to currently running
	  background Matlab process. The matrix	is assigned to
	  variable "MatrixName"	in Matlab side.
	  matlab_put returns 1 if successful and 0 if not.


       See also: ``matlab_start'', ``matlab_get'', ``matlab_eval''.

	  Error	codes:
	  1: Unknown error
	  -1: First argument not a string
	  -2: No Matlab	process	running, use matlab_start first
	  -3: Second argument not interpretable	as a matrix
	  -4: Second argument has too high (> 2) rank





  10.5.	 matlab_start



       [] = matlab_start(;startcmd)
	matlab_start() starts a	new Matlab process on background.
	  You can send to it commands with matlab_eval.
	  matlab_start("startcmd") uses	"startcmd" to start up
	  Matlab. The default "startcmd" is "matlab".
	  If matlab_start() has	already	been called, a new call
	  is harmless and does nothing.


       See also: ``matlab_eval'', ``matlab_call'', ``matlab_stop''.

	  Error	codes:
	  1: Could not start Matlab
	  -1: Argument not a string





  10.6.	 matlab_stop



       [] = matlab_stop()
	matlab_stop() stops a currently	running	Matlab process.

  See also: ``matlab_start'', ``matlab_eval''.

     Error codes:
     1:	No Matlab process running; none	to be stopped
     2:	Unknown	error occurred when trying to stop Matlab process






  11.  tsyganenko.ct

  This section describes functions from	file local/tsyganenko.ct.


  11.1.	 T87



       [Bx,By,Bz] = T87(Kp,x,y,z)
	[Bx,By,Bz] = T87(Kp,x,y,z) computes the	Tsyganenko-87 model
	  magnetic field. The non-truncated version of the model is used.
	  Inputs: Kp, the Kp index; x,y,z, GSM coordinates
	  in Earth radii. Outputs: total magnetic field	in nanotesla in
	  GSM coordinates.


       See also: ``T89'', ``m2i'', ``geotomag''.

	  Error	codes:
	  -1: Bad type of input	arg




  11.2.	 T89



       [Bx,By,Bz] = T89(Kp,x,y,z)
	[Bx,By,Bz] = T89(Kp,x,y,z) computes the	Tsyganenko-89 model
	  magnetic field. Inputs: Kp, the Kp index; x,y,z, GSM coordinates
	  in Earth radii. Outputs: total magnetic field	in nanotesla in
	  GSM coordinates.


       See also: ``T87'', ``m2i'', ``geotomag''.

	  Error	codes:
	  -1: Bad type of input	arg




  11.3.	 ecctogeo



       [lat,longit] = ecctogeo(latmag,longmag)
	[lat,long] = ecctogeo(latecc,longecc) transforms eccentric
	  geomagnetic latitude and longitude to	geographic latitude and	longitude.
	  All angles in	degrees.



  See also: ``geotoecc'', ``ecctogeoXYZ'', ``geotomag'', ``magtogeo''.

     Error codes:
     -1: Bad first arg
     -2: Bad second arg





  11.4.	 ecctogeoXYZ



       [x1,y1,z1] = ecctogeoXYZ(x,y,z)
	[x1,y1,z1] = ecctogeoXYZ(x,y,z)	transforms eccentric dipole
	  point	(x,y,z)	to geographic coordinates (x1,y1,z1).


       See also: ``ecctogeo'', ``geotoeccXYZ'',	``magtogeoXYZ''.

	  Error	codes:
	  -1: Bad first	arg
	  -2: Bad second arg
	  -3: Bad third	arg





  11.5.	 geotoecc



       [latmag,longmag]	= geotoecc(lat,longit)
	[latmag,longmag] = geotoecc(lat,long) transforms geographic
	  latitude and longitude to eccentric geomagnetic latitude and longitude.
	  All angles in	degrees.


       See also: ``ecctogeo'', ``geotoeccXYZ'',	``geotomag'', ``magtogeo''.

	  Error	codes:
	  -1: Bad first	arg
	  -2: Bad second arg





  11.6.	 geotoeccXYZ



       [x1,y1,z1] = geotoeccXYZ(x,y,z)
	[x1,y1,z1] = geotoeccXYZ(x,y,z)	transforms geographic
	  point	(x,y,z)	to eccentric dipole coordinates	(x1,y1,z1).


       See also: ``geotomagXYZ'', ``ecctogeoXYZ'', ``geotoecc''.






     Error codes:
     -1: Bad first arg
     -2: Bad second arg
     -3: Bad third arg





  11.7.	 geotomag



       [latmag,longmag]	= geotomag(lat,longit)
	[latmag,longmag] = geotomag(lat,long) transforms geographic
	  latitude and longitude to geomagnetic	dipole latitude	and longitude.
	  All angles in	degrees.


       See also: ``geotomagXYZ'', ``magtogeo'',	``ecctogeo'', ``geotoecc''.

	  Error	codes:
	  -1: Bad first	arg
	  -2: Bad second arg





  11.8.	 geotomagXYZ



       [x1,y1,z1] = geotomagXYZ(x,y,z)
	[x1,y1,z1] = geotomagXYZ(x,y,z)	transforms geographic
	  point	(x,y,z)	to geomagnetic dipole coordinates (x1,y1,z1).


       See also: ``geotomag'', ``magtogeoXYZ''.

	  Error	codes:
	  -1: Bad first	arg
	  -2: Bad second arg
	  -3: Bad third	arg





  11.9.	 m2i



       [theta,phi] = m2i(Kp,x,y)
	[theta,phi] = m2i(Kp,x,y) maps the equatorial plane point (x,y,z=0)
	  to the northern ionosphere. Inputs: Kp, the Kp index;	x,y,z, GSM
	  coordinates in Earth radii. Outputs: colatitude and longitude	in
	  magnetic coordinates in degrees.


       See also: ``T89'', ``geotomag''.

	  Error	codes:
	  -1: Bad type of input	arg


  11.10.  magtogeo



       [lat,longit] = magtogeo(latmag,longmag)
	[lat,long] = magtogeo(latmag,longmag) transforms geomagnetic
	  latitude and longitude to geographic latitude	and longitude.
	  All angles in	degrees.


       See also: ``geotomag'', ``magtogeoXYZ'',	``geotoecc'', ``ecctogeo''.

	  Error	codes:
	  -1: Bad first	arg
	  -2: Bad second arg





  11.11.  magtogeoXYZ



       [x1,y1,z1] = magtogeoXYZ(x,y,z)
	[x1,y1,z1] = magtogeoXYZ(x,y,z)	transforms geomagnetic dipole
	  point	(x,y,z)	to geographic coordinates (x1,y1,z1).


       See also: ``magtogeo'', ``geotomagXYZ''.

	  Error	codes:
	  -1: Bad first	arg
	  -2: Bad second arg
	  -3: Bad third	arg






  12.  gnuplot.ct

  This section describes functions from	file local/gnuplot.ct.


  12.1.	 gnuplot



       [] = gnuplot(x)
	gnuplot(x) calls GNUPLOT on vector x.
	  Error	codes:
	  -1: Cannot open command pipe to gnuplot
	  -2: Cannot open data pipe











