  Builtin Tela functions
  Pekka	Janhunen, Pekka.Janhunen@fmi.fi
  Version 1.0, Wed Aug	3 10:38:29 EDT 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.	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




  2.3.	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




  2.4.	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




  2.5.	SilentMode



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


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


  2.6.	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




  2.7.	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




  2.8.	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.




  2.9.	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




  2.10.	 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




  2.11.	 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




  2.12.	 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.




  2.13.	 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''.


  2.14.	 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




  2.15.	 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




  2.16.	 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




  2.17.	 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




  2.18.	 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''.


  2.19.	 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.




  2.20.	 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.




  2.21.	 cot



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




  2.22.	 cputime



       [t] = cputime()
	cputime() returns the CPU time in seconds used by the current
	  tela session.


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


  2.23.	 csc



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




  2.24.	 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





  2.25.	 disasm



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




  2.26.	 dump



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




  2.27.	 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




  2.28.	 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




  2.29.	 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




  2.30.	 exit



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




  2.31.	 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.




  2.32.	 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




  2.33.	 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.




  2.34.	 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




  2.35.	 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: ``sformat''.

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






  2.36.	 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





  2.37.	 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




  2.38.	 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





  2.39.	 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.




  2.40.	 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.




  2.41.	 isCfunction



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


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


  2.42.	 isTfunction



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


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


  2.43.	 isarray



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


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


  2.44.	 ischar




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


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


  2.45.	 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''.


  2.46.	 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''.


  2.47.	 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.




  2.48.	 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''.


  2.49.	 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''.


  2.50.	 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''.


  2.51.	 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''.


  2.52.	 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''.


  2.53.	 isscalar



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


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


  2.54.	 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.




  2.55.	 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.




  2.56.	 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''.


  2.57.	 isvector



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


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


  2.58.	 isvoid



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




  2.59.	 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''.


  2.60.	 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.




  2.61.	 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




  2.62.	 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







  2.63.	 pause



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




  2.64.	 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




  2.65.	 quit



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




  2.66.	 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




  2.67.	 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''.



  2.68.	 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





  2.69.	 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




  2.70.	 sec



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




  2.71.	 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''.

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



  2.72.	 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





  2.73.	 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




  2.74.	 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.




  2.75.	 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.





  2.76.	 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




  2.77.	 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




  2.78.	 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




  2.79.	 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




  2.80.	 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.




  2.81.	 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




  2.82.	 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''.


  2.83.	 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''.



  2.84.	 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




  2.85.	 system



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




  2.86.	 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





  2.87.	 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.




  2.88.	 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.




  2.89.	 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.




  2.90.	 toc



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


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


  2.91.	 tostring



       [y] = tostring(x)
	tostring(x) converts an	integer	vector to a string.
	  Error	codes:
	  -1: Argument not an integer vector





  2.92.	 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




  2.93.	 verbose



       [] = verbose(x)
	THE FUNCTION 'verbose' IS OBSOLETE. USE	'VerboseMode' INSTEAD.
	  Error	codes:
	  1: Input argument not	an integer




  2.94.	 whos



       [] = whos()
	whos() displays	names of variables together with their
	  types.





  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"
     is	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.



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

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





  3.2.	import



       [] = import(filename)
	import("file") tries to	load the contents of "file"
	  into 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





  3.3.	import1



       [x] = import1(filename; label)
	import1("file")	reads one object from "file".
	  The imported object is returned.
	  The "file" can be an HDF file, in which
	  case the first Scientific Data Set (SDS) is
	  loaded.

	  import1("file.hdf","label") reads SDS	with
	  label	"label", which is not necessarily the
	  first	one.

	  The "file" can also be an ASCII file
	  of the following format:

	  (line	1)   D=Nt dim1 dim2 ...	dimN
	  (line	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.


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

	  See 'help 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	ASCII data
	  -8: Internal error
	  -9: Cannot import file
	  -10: Second arg not a	string
	  -11: Specified label not found



  3.4.	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





  3.5.	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.	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?




  4.3.	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?

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




  4.5.	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''.

	  Error	codes:
	  1: Argument not an integer




  4.6.	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?




  4.7.	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?




  4.8.	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





  4.9.	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





  4.10.	 plotopt



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


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

	  Error	codes:
	  1: Argument not a string




  4.11.	 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 permutation matrix	P.


  See also: ``inv'', ``linsolve'', ``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.	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)





  5.3.	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




  5.4.	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





  5.5.	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





  5.6.	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


  5.7.	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 x 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.


       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





  5.8.	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
































