  Builtin Tela functions
  Pekka	Janhunen, Pekka.Janhunen@fmi.fi
  Version 1.22,	Thu May	25 16:29:25 EDT	1995

  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.


  1.1.	BatchMode



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


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



  1.2.	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





  1.3.	DebugQueryMode












  [;y] = DebugQueryMode(;x)
   DebugQueryMode() returns 1 if the debug query mode
     has been set, otherwise 0.
     DebugQueryMode(on)	and DebugQueryMode(off)	change
     the current setting.

     If	debug query mode is on,	the program will ask whether
     the user wants to enter debug mode	if control-C is
     pressed (INT signal sent).	Otherwise the program simply
     stops on pressing control-C.
     Error codes:
     1:	Argument not integer





  1.4.	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.

	  For vector u,	f=FFT(u) is equivalent with

	  n = length(u); f = czeros(n);
	  for (j=1; j<=n; j++)
	      f[j] = sum(u*exp(-(j-1)*(0:n-1)*2i*pi/n));

	  All Fourier transform	functions in Tela can take the transform
	  along	any dimension in a multidimensional array, and the transform
	  length is not	restricted. The	function FFT should be used only in
	  case of complex input	data. Use realFFT for real input array.

	  Functions FFT, realFFT, sinqFFT, cosFFT and their inverses
	  are the most efficient when the transform length n is	a product
	  of small primes.

	  Functions sinFFT and invsinFFT are efficient when n+1	is
	  a product of small primes

	  Functions cosFFT and invcosFFT are efficient when n-1	is
	  a product of small primes



       See also: ``invFFT'', ``realFFT'', ``sinFFT'', ``cosFFT'', ``sin-
       qFFT'', ``cosqFFT''.

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






  1.5.	GetInstructionData



       [Ninstructions,Noperations] = GetInstructionData(p,mnemo)
	[Ninstr,Nops] =	GetInstructionData(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






  1.6.	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





  1.7.	Im



       [y] = Im(x)
	y = Im(x) takes	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





  1.8.	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'', ``chol'', ``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)






  1.9.	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





  1.10.	 Re



       [y] = Re(x)
	y = Re(x) takes	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

  1.11.	 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'', ``chol''.

	  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)






  1.12.	 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''.



  1.13.	 UsingReadline



       [y] = UsingReadline()
	UsingReadline()	returns	1 if this Tela was compiled
	  to use the GNU readline library, otherwise 0.


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



  1.14.	 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





  1.15.	 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), except that
	  the latter would produce a complex result with zero or tiny
	  (because of possible roundoff	error) imaginary part.
	  If x is an array, the	operation is applied componentwise.
	  Error	codes:
	  -1: Nonnumeric input argument





  1.16.	 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.





  1.17.	 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.

	  Conditional statements (if, while, for, until) assume
	  implicit all,	for example saying
	      if (A > 0) ...
	  is equivalent	of saying
	      if (all(A	> 0)) ... ,
	  thus you will	need all less frequently than you need any.



       See also: ``any''.

	  Error	codes:
	  1: Argument not integer or IntArray






  1.18.	 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.

	  --------------------------------------------
	  Here may be the proper place to list the most	frequently used
	  PlotMTV options. These are used by giving them as optional args
	  (option-value	pairs) to graphics functions.

	  Option name(s)       Possible	value(s)	 Explanation
	  "xlabel"	       string			 X-axis	label
	  "ylabel"	       string			 Y-axis	label
	  "zlabel"	       string			 Z-axis	label
	  "toplabel"	       string			 Plot title
	  "subtitle"	       string			 Text below title
	  "comment"	       string			 Text on right corner
	  "xmin","xmax"	       real number		 X-axis	scale
	  "ymin","ymax"	       real number		 Y-axis	scale
	  "zmin","zmax"	       real number		 Z-axis	scale
	  "cmin","cmax"	       real number		 Contour min/max
	  "nsteps"	       integer			 Number	of contours
	  "cstep"	       real number		 Contour spacing
	  "contstyle"	       1: normal contours, 2: colored (pcolor),
			       3: 3D surface
	  "hiddenline"	       "true": colored 3D surface, "false": wireframe
	  "linecolor"	       color value (integer)
	  "linewidth"	       integer
	  "linestyle"	       solid,dashed etc.; integers; 0 is no line
	  "markertype"	       integers; 0 is no marker	(the default)
	  "markersize"	       real number
	  "markercolor"	       color value (integer)

	  Some color (red,green,blue,pink etc.)	names have been	defined
	  in telainit.t. Use them for clarity if possible.

	  The most usual PlotMTV command line options (always start with
	  minus	sign):
	  -3d		       Initially view in 3D
	  -colorps	       Produce color PostScript
	  -landscape	       Produce landscape (rotated) PostScript
	  -scale s	       PostScript scale	factor,	default	1
	  -nodate	       Drop the	date from PostScript figure
	  -title 'my title'    PlotMTV window title

	  For an example in using the annotations, see e.g. the	file
	  "3windows.t",	usual location is /usr/local/lib/tela/t/.



       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





  1.19.	 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.

	  Conditional statements (if, while, for, until) default
	  to implicit all, thus	you sometimes need to use any
	  with these statements.



       See also: ``all''.

	  Error	codes:
	  1: Argument not integer or IntArray





  1.20.	 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: Argument has undefined value
	  1: Nonnumeric	argument





  1.21.	 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.





  1.22.	 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''.



  1.23.	 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





  1.24.	 autoglobal



       [y] = autoglobal(...)
	autoglobal("sym1","sym2",...) sets the 'autoglobal' attribute
	  to given symbols. The	symbols	are then globally accessible
	  from inside packages and functions without need to explicitly
	  declaring them global. Constants such	as pi carry the	autoglobal
	  attribute automatically, but with this function it is	possible
	  for the user to define more autoglobal symbols.

	  Warning: This	function is for	experts	only. It is not	advisable
	  to say autoglobal("x"), for instance,	because	many existing code
	  may then break down.


       See also: ``hide''.

	  Error	codes:
	  1: Argument not a string





  1.25.	 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





  1.26.	 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






  1.27.	 cd



       [] = cd(fn)
	cd("pathname") will change the current directory to "pathname".
	  cd("") will change to	home directory.
	  cd("~/my/dir") will change to	directory "my/dir" in the
	  home directory.


       See also: ``getenv''.

	  Error	codes:
	  1: Input argument not	a string
	  2: Directory not found
	  3: This system does not support cd








  1.28.	 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





  1.29.	 chol



       [B] = chol(A)
	B=chol(A) returns the Cholesky decomposition of	a
	  positive definite square matrix A: B'**B == A.
	  A may	be integer, real or complex valued.
	  Only the upper half of A is referenced, the lower half
	  is assumed to	be Hermitian symmetric.


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

	  Error	codes:
	  -1: Input arg	is not a matrix
	  -2: Input matrix is not square
	  -3: Input matrix is not positive definite





  1.30.	 closefig



       [] = closefig(n)
	closefig(n) (n>1) closes the nth graphics window.
	  The active window is not changed, so if n is the active
	  window, subsequent plot commands will	reopen it.
	  If the window	has never been opened or has already been
	  closed, closefig is silent about it.


       See also: ``figure''.

	  Error	codes:
	  1: Argument not an integer
	  2: Argument not positive
	  3: This Tela installation does not support the closefig command
	  4: No	n>1 figures are	currently open (and X11	initialization has failed)




  1.31.	 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''.



  1.32.	 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?





  1.33.	 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?





  1.34.	 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.





  1.35.	 cosFFT



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

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

	  For vector u,	f=cosFFT(u) is equivalent with

	  n = length(u); f = zeros(n);
	  for (j=1; j<=n; j++)
	      f[j] = u[1] - (-1)^j*u[n]	+ 2*sum(u[2:n-1]*cos((1:n-2)*(j-1)*pi/(n-1)));

	  Note that cosFFT is most efficient when n-1 is a product of small
	  primes, where	n is the transform length.



       See also: ``invcosFFT'',	``sinFFT'', ``cosqFFT'', ``sinqFFT'',
       ``realFFT'', ``FFT''.

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






  1.36.	 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.





  1.37.	 cosqFFT





  [f] =	cosqFFT(u; dim)
   cosqFFT computes the	quarter-wave cosine Fourier transform.
     Except for	the quarter-wave cosine	character, it works similarly to cosFFT.

     For vector	u, f=cosqFFT(u)	is equivalent with

     n = length(u); f =	zeros(n);
     for (j=1; j<=n; j++)
	 f[j] =	u[1] + 2*sum(u[2:n]*cos((2*j-1)*(1:n-1)*pi/(2*n)));

     cosqFFT is	most efficient when the	transform length is a product
     of	small primes.



  See also: ``invcosqFFT'', ``realFFT'', ``sinqFFT'', ``FFT''.

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






  1.38.	 cot



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





  1.39.	 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()





  1.40.	 csc



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

  1.41.	 cumprod



       [y] = cumprod(x)
	y = cumprod(x) forms an	array of partial products
	  y = #(x[1],x[1]*x[2],...,prod(x[1:n]),...).
	  The result y has the same size and type as x.	Unlike
	  prod,	cumprod	does not try to	avoid integer overflows.
	  The array x is logically flattened, to apply
	  along	a specified dimension use map(cumsum,...).
	  If x is scalar, it is	returned as such.


       See also: ``prod'', ``cumsum'', ``map''.

	  Error	codes:
	  -1: Nonnumeric input arg





  1.42.	 cumsum



       [y] = cumsum(x)
	y = cumsum(x) forms an array of	partial	sums
	  y = #(x[1],x[1]+x[2],...,sum(x[1:n]),...).
	  The result y has the same size and type as x.
	  The array x is logically flattened, to apply
	  along	a specified dimension use map(cumsum,...).
	  If x is scalar, it is	returned as such.


       See also: ``sum'', ``cumprod'', ``map''.

	  Error	codes:
	  -1: Nonnumeric input arg





  1.43.	 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








  1.44.	 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. M need not necessarily be square.
	  Error	codes:
	  -1: Input array not vector or	matrix






  1.45.	 disasm



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





  1.46.	 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






  1.47.	 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





  1.48.	 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





  1.49.	 exit



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





  1.50.	 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.





  1.51.	 export_PBM












  [] = export_PBM(fn,r;g,b)
   export_PBM("file.pbm",x) writes integer matrix x in
     binary PBM	(actually PGM) file "file.pbm".	Matrix elements
     are truncated to the range	0..255.	If all elements	are
     equal to 0	or 1 a black and white PBM file	will be	written.

     export_PBM("file.pbm",r,g,b) creates a 24-bit PBM file.
     The integer matrices r,g and b represent the red, green
     and blue values. They must	have equal dimensions.


  See also: ``import_PBM''.

     Error codes:
     1:	First arg not a	string
     2:	Argument is not	integer	matrix
     3:	export_PBM must	be called with 2 or 4 input args
     4:	Dimensions of R,G,B matrices must be equal





  1.52.	 export_RIS8



       [] = export_RIS8(fn,x)
	export_RIS8("file.hdf",x) writes (appends) integer matrix x
	  to HDF file "file.hdf" as a raster-8 image (Raster Image Set,	RIS).
	  When the file	is opened with default settings	using the usual
	  HDF viewers such as Spyglass products, the first dimension grows
	  vertically downward and the second dimension grows from left to
	  right.

	  The RIS8 HDF files can be read back using import.


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

	  Error	codes:
	  1: First argument not	a string
	  2: Second argument not an integer matrix






  1.53.	 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. Hidden Tela	variables are not saved.

     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






  1.54.	 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









  1.55.	 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






  1.56.	 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





  1.57.	 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




  1.58.	 figure



       [] = figure(n)
	figure(n) causes subsequent plot commands to use
	  window (figure) number n (n=1,2,...).	Figures	with
	  n>1 are drawn	over by	each new plot command.

	  figure(-1) restores the default behavior, which is
	  to create standalone windows.	These plots are	never
	  replaced by new graphics and are quit	only by	the user.

	  Using	this command for n>1 requires that you use the
	  Tela-compatible PlotMTV version.


       See also: ``closefig''.

	  Error	codes:
	  1: Argument is not an	integer
	  2: Figure number zero	is reserved, don't use it
	  3: This Tela installation does not support the figure	command
	  4: Failed X11	initialization,	cannot synchronize with	PlotMTV





  1.59.	 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.

	  Example: If V=#(1,-2.3,4,5,-8.2), find(V < 0)	returns
	  #(2, 5).



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

	  Error	codes:
	  1: Argument not integer vector





  1.60.	 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.

     Example: flatten(#(1,2; 3,4)) returns #(1,2,3,4).

     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.





  1.61.	 flip



       [y] = flip(x;d)
	flip(A)	reverses the first dimension of	array A.
	  flip(A,d) reverses the d'th dimension. For example,
	  flip(#(1,6,2;	7,9,2.3),2) returns #(2,6,1; 2.3,9,7).
	  If A is non-array it is returned as such, regardless of d.


       See also: ``transpose''.

	  Error	codes:
	  -1: Second argument not an integer scalar
	  -2: Second argument out of range





  1.62.	 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





  1.63.	 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





  1.64.	 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





  1.65.	 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






  1.66.	 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.

	  For example, getenv("LOGNAME") returns the login name	of
	  the owner of the Tela	prcess.
	  (If Unix functions are not available,	getenv will always
	  return VOID.)


       See also: ``getpid'', ``cd''.

	  Error	codes:
	  -1: Argument not a string






  1.67.	 getpid



       [y] = getpid()
	getpid() returns the process ID	of the Tela process.
	  This can be used e.g.	to generate unique temporary
	  file names. If Unix functions	are not	available,
	  getpid() returns 0.





  1.68.	 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





  1.69.	 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





  1.70.	 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





  1.71.	 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'', ``flip'', ``conj''.

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





  1.72.	 hide



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


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

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






  1.73.	 hist



       [;ndata,xdata] =	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.
	  [ndata,xdata]	= hist(args) returns the count and abscissa vectors
	  but does not draw anything. bar(xdata,ndata,"lab") can be used to draw
	  the histogram	later. Graphics	options	are ignored in this case.


       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






  1.74.	 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.

	  hold(-1) can be used to reset	the internal counter.
	  Use it in emergency.



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

	  Error	codes:
	  1: Argument not an integer





  1.75.	 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


  1.76.	 import



       [] = import(filename; appendix)
	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
	  (SDS and 8-bit raster	image files) as	well as	MATLAB binary
	  files	(MAT-files).

	  import("file","app") appends the string "app"	to the name
	  of every variable imported.

	  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.
	  3) If	file is	HDF-file, import first tries to	read all SDSs.
	  Only if none was found, it tries to read all RIS8 datasets.
	  The variable names are taken from the	HDF labels, if the labels
	  have been set. If there are no labels, the variables are named
	  "Dataset1", "Dataset2", ... and "Image1", "Image2",... for
	  SDS and RIS8 imports,	respectively.

	  For filename conventions, see	load.


       See also: ``load'', ``save'', ``import1'', ``export_matlab'',
       ``export_RIS8'',	``import_PBM''.


	  (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: First arg not string or char
	  2: First arg 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
	  11: Second argument not a string






  1.77.	 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






  1.78.	 import_PBM














  [r;g,b] = import_PBM(fn)
   x = import_PBM("file.pbm") reads PBM	format image file.
     x will become integer matrix.
     [r,g,b] = import_PBM("file.pbm") reads a color image
     and assigns the red, green	and blue components to
     matrices r,g,b.
     All six PBM formats (P1-P6) are recognized. If a color
     image (P3 or P6) is loaded	using only one output argument,
     the average of color components is	computed and assigned
     to	x. If a	greyscale image	is loaded using	three output
     args, only	the first (r) output arg will be filled,
     g and b are assigned the VOID value. You might use
     a code like

     [r,g,b] = import_PBM("file.pbm");
     if	(isvoid(g)) {g=r; b=r};

     to	continue processing in 24-bit mode.


  See also: ``import'',	``export_PBM''.

     Error codes:
     -1: First arg not a string
     -2: Could not open	input file
     -3: Input file is not PBM file
     -4: Width or height not positive -	improper PBM file
     -5: Color range not in 1..255
     -6: Two output args, give 1 or 3
     -7: Error when rading ASCII data
     -8: Pixel not 0 or	1 in 1-bit image
     -9: Pixel out of range 0..255
     -10: Could	not read all binary data






  1.79.	 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.





  1.80.	 input_string



       [s] = input_string(;prompt)
	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.

	  input_string("prompt") displays prompt first.
	  Error	codes:
	  -1: EOF encountered.


  1.81.	 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. The result y	is of same
	  rank and size	as each	of the index arguments.

	  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.

	  Currently intpol uses	linear interpolation.
	  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





  1.82.	 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'', ``chol'', ``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





  1.83.	 invFFT











  [f] =	invFFT(u; dim)
   invFFT() is the inverse of FFT().
     For vector	f, u=invFFT(f) is equivalent with

     n = length(f); u =	czeros(n);
     for (j=1; j<=n; j++)
	 u[j] =	(1/n)*sum(f*exp((j-1)*(0:n-1)*2i*pi/n));

     Differences with 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






  1.84.	 invcosFFT



       [f] = invcosFFT(u; dim)
	invcosFFT() is the inverse of cosFFT().
	  Actually invcosFFT differs from cosFFT only by normalization,
	  but it is provided as	a separate function for	convenience.

	  For vector f,	u=invcosFFT(f) is equivalent with

	  n = length(f); u = zeros(n);
	  for (j=1; j<=n; j++)
	      u[j] = (f[1] - (-1)^j*f[n] + 2*sum(f[2:n-1]*cos((1:n-2)*(j-1)*pi/(n-1))))/(2*n-2)



       See also: ``cosFFT''.

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






  1.85.	 invcosqFFT












  [f] =	invcosqFFT(u; dim)
   invcosqFFT()	is the inverse of cosqFFT()
     (inverse quarter-wave cosine Fourier transform).

     For vector	f, u=invcosqFFT(f) is equivalent with

     n = length(f); u =	zeros(n);
     for (j=1; j<=n; j++)
	 u[j] =	(1/n)*sum(f*cos((2*(1:n)-1)*(j-1)*pi/(2*n)));



  See also: ``cosqFFT''.

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






  1.86.	 invrealFFT



       [f] = invrealFFT(u; dim,oddevenspec)
	invrealFFT() is	the inverse of realFFT().
	  invrealFFT(u,dim,"even") and invrealFFT(u,dim,"odd") specifies
	  even or odd transform	length,	respectively.
	  invrealFFT(u,dim,N) uses the same evenness as	the integer N has.

	  If the evenness is not specified explicitly, the imaginary parts
	  of the highest frequency components are tested. If they are all zero
	  the transform	length is even,	otherwise odd. However,	this automatic
	  method will fail if the imaginary parts are not EXACTLY zero.	If you
	  use multiple FFTs to solve a PDE, for	example, you should probably
	  specify the evenness explicitly.


       See also: ``realFFT''.

	  Error	codes:
	  -1: First argument not a complex array
	  -2: Second argument not integer
	  -3: Second argument out of range
	  -4: Third argument not "even", "odd" or an integer






  1.87.	 invsinFFT










  [f] =	invsinFFT(u; dim)
   invsinFFT() is the inverse of sinFFT().
     Actually invsinFFT	differs	from sinFFT only by normalization,
     but it is provided	as a separate function for convenience.

     For vector	f, u=invsinFFT(f) is equivalent	with

     n = length(f); u =	zeros(n);
     for (j=1; j<=n; j++)
	 u[j] =	(1/(n+1))*sum(f*sin((1:n)*j*pi/(n+1)));



  See also: ``sinFFT''.

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






  1.88.	 invsinqFFT



       [f] = invsinqFFT(u; dim)
	invsinqFFT() is	the inverse of sinqFFT()
	  (inverse quarter-wave	sine Fourier transform).

	  For vector f,	u=invsinqFFT(f)	is equivalent with

	  n = length(f); u = zeros(n);
	  for (j=1; j<=n; j++)
	      u[j] = (1/n)*sum(f*sin((2*(1:n)-1)*j*pi/(2*n)));



       See also: ``sinqFFT''.

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






  1.89.	 isCfunction



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


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



  1.90.	 isTfunction



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


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



  1.91.	 isarray



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


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



  1.92.	 ischar



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


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



  1.93.	 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''.



  1.94.	 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''.




  1.95.	 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.





  1.96.	 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''.



  1.97.	 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''.



  1.98.	 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''.



  1.99.	 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''.



  1.100.  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''.



  1.101.  isscalar



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


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



  1.102.  isstr



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


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



  1.103.  isstring



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


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



  1.104.  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''.



  1.105.  isvector



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


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



  1.106.  isvoid



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





  1.107.  length



       [L] = length(x)
	length(x) returns the total number of elements in array	x.
	  If x is scalar, length(x) is 1. If x is undefined, an	error
	  results. Notice that if x is e.g. a matrix, its length is
	  equal	to the product of the row and column dimensions,
	  which	is different from e.g. the Matlab convention.


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

	  Error	codes:
	  -1: Argument has undefined value





  1.108.  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






  1.109.  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






  1.110.  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






  1.111.  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.





  1.112.  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
	  or a vector when called with one vector argument. The	type and length
	  of the returned value	must not change	from call to call.

	  For example, map(mean,A,1) computes the columnwise means
	  of matrix A, returning a vector. map(sort,A,2) sorts all rows
	  of matrix A in ascending order. Notice than many standard
	  functions, including mean, have a builtin mapping capabability;
	  using	map in these cases is unnecessary.

  See also: ``mapmin'',	``mapmax'', ``flip''.

     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 numerical object
     -6: First arg (function) unexpectedly changed its return type
     -7: First arg is an intrinsic function; it	is no good
     -8: Function returned rank>1 array	when first called





  1.113.  mapmax



       [y;P] = mapmax(x;d)
	mapmax(x,d) finds maximum along	d'th dimension in array	x.
	  The result is	an array with rank one less than rank(x).
	  The array may	not be complex.
	  [M,p]	= mapmax(x,d) returns the maximum positions p along with
	  the maximums m. The array p is of the	same shape as M, but is
	  integer-valued.

	  mapmax(x) is a flattened form	which returns a	scalar result.
	  It is	equivalent to max(x). [M,p] = mapmax(x)	also works.

	  Using	mapmax is faster than using map	and max	together.
	  In the latter	case you would also have to define another function:
	      function y=max1(x) {y=max(x)}
	  because being	intrinsic function, max	can not	be passed
	  to map directly.



       See also: ``mapmin'', ``map''.

	  Error	codes:
	  -1: First arg	not a numerical	array
	  -2: Second arg not an	integer	scalar
	  -3: Second arg (the dimension) out of	range
	  -4: First arg	is complex





  1.114.  mapmin














  [y;P]	= mapmin(x;d)
   mapmin(x,d) finds minimum along d'th	dimension in array x.
     The result	is an array with rank one less than rank(x).
     The array x may not be complex.
     [m,p] = mapmin(x,d) returns the minimum positions p along with
     the minimum values	m. The array p is of the same shape as m,
     but is integer-valued.

     mapmin(x) is a flattened form which returns a scalar result.
     It	is equivalent to min(x). [m,p] = mapmin(x) also	works.

     Using mapmin is faster than using map and min together.
     In	the latter case	you would also have to define another function:
	 function y=min1(x) {y=min(x)}
     because being intrinsic function, min can not be passed
     to	map directly.



  See also: ``mapmax'',	``map''.

     Error codes:
     -1: First arg not a numerical array
     -2: Second	arg not	an integer scalar
     -3: Second	arg (the dimension) out	of range
     -4: First arg is complex





  1.115.  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








  1.116.  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






  1.117.  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)






  1.118.  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






  1.119.  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






  1.120.  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






  1.121.  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'






  1.122.  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








  1.123.  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?





  1.124.  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)), works 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






  1.125.  pause



       [] = pause(;seconds)
	pause()	will wait for a	keypress on keyboard.
	  pause(n) will	pause for n seconds and	then continue.
	  The argument n may be	integer	or real.

	  Note:	some systems implicitly	round a	real argument
	  to nearest whole number.
	  Error	codes:
	  1: Argument not a real scalar
	  2: Argument is negative
	  3: This system does not support pausing for n	seconds




  1.126.  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?





  1.127.  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).





  1.128.  pixmap



       [] = pixmap(flag)
	pixmap(off) tells PlotMTV not to use pixmaps for faster	redraw.
	  pixmap(on) turns the pixmap mode on, which is	the default.

	  If your X server uses	backing	store, you can save memory
	  by turning pixmap(off) without hurting performance.
	  Error	codes:
	  1: Argument is not an	integer





  1.129.  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






  1.130.  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






  1.131.  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. All graphics	function optional string args which start with minus sign
     are assumed to be PlotMTV command line options.

     Error codes:
     1:	Argument not a string





  1.132.  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






  1.133.  prod



       [y] = prod(x;d)
	prod(x)	multiplies all the elements of x, if x is an array.
	  prod(x,d) takes the product along d'th dimension only, returning
	  an array of rank one less than rank(x).
	  If x is scalar, it is	returned as such.
	  If I is integer array, prod(I) will be of type real if the product
	  would	cause integer overflow.	In all other cases, including prod(I,d),
	  the type of y	equals the component type of x.


       See also: ``sum'', ``cumprod''.

	  Error	codes:
	  -1: Nonnumeric input arg
	  -2: Second argument not an integer
	  -3: Second argument (dimension spec) out of range






  1.134.  quit



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





  1.135.  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.


       See also: ``srand''.

	  Error	codes:
	  -1: Tried to create too high rank array
	  -2: Argument not an integer
	  -3: Non-positive integer argument





  1.136.  rank



       [y] = rank(x)
	rank(A)	returns	the number of dimensions of array A.
	  The rank of a	scalar is 0. The rank of a nonnumeric
	  object, including undefined value, is	-1. The	rank function
	  never	generates an error.


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



  1.137.  realFFT


















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

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

     The result	of realFFT() is	the same as FFT() except that only
     nonnegative frequency components are returned. The	result is
     always complex array. The first component (0 frequency) has always
     zero imaginary part. If the transform length is even, the last
     component has zero	imaginary part as well.	Notice that these
     conventions are different from some generally used	C and Fortran
     library routines, which return a real array force-fitted
     in	the same space as the input array by not storing the zero
     imaginary parts. The Tela convention allows you to	manipulate the
     result in k-space more easily because it is already complex.

     realFFT is	the most efficient when	the transform length is
     a product of small	primes.



  See also: ``invrealFFT'', ``FFT'', ``sinFFT'', ``cosFFT'', ``sin-
  qFFT'', ``cosqFFT''.

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






  1.138.  remove



       [] = remove(fn)
	remove("file") removes the named file.
	  If the file does not exist or	some other error occurs,
	  no warning or	error message is given.
	  Error	codes:
	  1: Argument not a string






  1.139.  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.

     Example: reshape(#(1,2,3,4,5,6), 2,3) returns
	 #(1, 2, 3;
	       4, 5, 6)
     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






  1.140.  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





  1.141.  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()
	  -7: wait(2) returned error
	  -8: pipe(2) returned error
	  -9: cannot fork(2) a child process




  1.142.  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. Hidden variables are	not saved.

	  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






  1.143.  sec



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





  1.144.  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







  1.145.  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






  1.146.  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





  1.147.  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.





  1.148.  sinFFT









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

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

     For vector	u, f=sinFFT(u) is equivalent with

     n = length(u); f =	zeros(n);
     for (j=1; j<=n; j++)
	 f[j] =	2*sum(u*sin((1:n)*j*pi/(n+1)));

     Note that sinFFT is the most efficient when n+1 is	a product of
     small primes, where n is the transform length.



  See also: ``invsinFFT'', ``cosFFT'', ``sinqFFT'', ``cosqFFT'',
  ``realFFT'', ``FFT''.

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






  1.149.  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.





  1.150.  sinqFFT



       [f] = sinqFFT(u;	dim)
	sinqFFT	computes the quarter-wave sine Fourier transform of array u.
	  Except for the quarter-wave sine character, it works similarly to sinFFT.

	  For vector u,	f=sinqFFT(u) is	equivalent with

	  n = length(u); f = zeros(n);
	  for (j=1; j<=n; j++)
	      f[j] = (-1)^(j-1)*u[n] + 2*sum(u[1:n-1]*sin((2*j-1)*(1:n-1)*pi/(2*n)));

	  sinqFFT is most efficient when the transform length is a product
	  of small primes.




  See also: ``invsinqFFT'', ``realFFT'', ``cosqFFT'', ``FFT''.

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






  1.151.  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
	  -2: Argument has undefined value
	  1: More than one output arg but non-array input arg
	  2: Too many output args relative to input arg	rank





  1.152.  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





  1.153.  sort









  [y;I]	= sort(x)
   sort(x) returns array x sorted in ascending order.
     If	x is complex, it is sorted by the real parts.
     If	x is not an array, it is returned as is.
     [y,I] = sort(x) returns also an index vector I such that
     y == x[I].

     To	sort with user-defined comparisons, do the following.
     For example, if you want to sort a	complex	vector z by
     absolute value as Matlab does, first sort a vector	of
     absolute values saving the	index information:

     [y,I] = sort(abs(z));

     Then y=z[I] is the	wanted result.

     If	x is multidimensional, it is implicitly	flattened.
     Use the map function to get around	this problem.





  1.154.  source



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


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

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





  1.155.  source_silent



       [] = source_silent(fn)
	source_silent("file.t")	is similar to source("file.t"),
	  but it does not complain if e.g. the file does not exist.


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

	  Error	codes:
	  1: Argument not a string





  1.156.  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






  1.157.  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.





  1.158.  srand



       [] = srand(seed)
	srand(seed) seeds the random number generator.
	  The same seed	will always produce the	same random
	  number sequence. The argument	must be	an integer.


       See also: ``rand''.

	  Error	codes:
	  1: Argument not an integer





  1.159.  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





  1.160.  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''.



  1.161.  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





  1.162.  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



  1.163.  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''.



  1.164.  sum



       [y] = sum(x;d)
	sum(x) sums all	the elements of	x, if x	is an array.
	  The result type is always the	same as	the component type
	  of x.	If x is	scalar,	it is returned as such.
	  sum(x,d) sums	only along d'th	dimension, returning array
	  of rank one less than	rank(x).


       See also: ``cumsum'', ``prod'', ``map''.

	  Error	codes:
	  -1: Nonnumeric input arg
	  -2: Second argument not an integer
	  -3: Second argument (dimension spec) out of range





  1.165.  system



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





  1.166.  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




  1.167.  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.





  1.168.  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.





  1.169.  telapath



       [s] = telapath()
	telapath() returns the currently set effective Tela path
	  as a string.





  1.170.  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.





  1.171.  toc




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


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



  1.172.  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






  1.173.  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 according
	  to 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].

	  The second argument is meaningful only if rank(A) is greater than 2.

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


       See also: ``herm'', ``flip''.

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





  1.174.  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






  1.175.  version



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





  1.176.  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





  1.177.  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








































































