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vector(n)		     BLT Built-In Commands		     vector(n)

______________________________________________________________________________

NAME
       vector -	 Vector data type for Tcl

SYNOPSIS
       vector configure option value ...

       vector create vecName ?vecName...? ?switches?

       vector destroy vecName ?vecName...?

       vector expr expression

       vector names ?pattern...?

       vector op operation vecName ?arg?...
_________________________________________________________________

DESCRIPTION
       The vector command creates a vector of floating point values.  The vec‐
       tor's components can be manipulated in three ways: through a Tcl	 array
       variable, a Tcl command, or the C API.

INTRODUCTION
       A vector is simply an ordered set of numbers.  The components of a vec‐
       tor are real numbers, indexed by counting numbers.

       Vectors are common data structures for many applications.  For example,
       a  graph	 may  use  two vectors to represent the X-Y coordinates of the
       data plotted.  The graph will automatically be redrawn when the vectors
       are  updated or changed. By using vectors, you can separate data analy‐
       sis from the graph widget.  This makes it easier, for example,  to  add
       data  transformations, such as splines.	It's possible to plot the same
       data to in multiple graphs, where each graph presents a different  view
       or scale of the data.

       You  could  try to use Tcl's associative arrays as vectors.  Tcl arrays
       are easy to use.	 You can access individual elements randomly by speci‐
       fying  the  index,  or  the set the entire array by providing a list of
       index and value pairs for each element.	The disadvantages of  associa‐
       tive  arrays  as	 vectors  lie in the fact they are implemented as hash
       tables.

       · There's no implied ordering to the associative arrays.	 If  you  used
	 vectors  for  plotting, you would want to insure the second component
	 comes after the first, an so on.  This isn't  possible	 since	arrays
	 are actually hash tables.  For example, you can't get a range of val‐
	 ues between two indices.  Nor can you sort an array.

       · Arrays consume lots of memory when the	 number	 of  elements  becomes
	 large	(tens of thousands).  This is because each element's index and
	 value are stored as strings in the hash table.

       · The C programming interface is unwieldy.  Normally with vectors,  you
	 would	like to view the Tcl array as you do a C array, as an array of
	 floats or doubles.  But with hash tables, you must convert  both  the
	 index	and  value to and from decimal strings, just to access an ele‐
	 ment in the array.  This makes it cumbersome to perform operations on
	 the array as a whole.

       The  vector  command  tries to overcome these disadvantages while still
       retaining the ease of use of Tcl arrays.	 The  vector  command  creates
       both a new Tcl command and associate array which are linked to the vec‐
       tor components.	You can randomly access vector components  though  the
       elements	 of  array.   Not  all indices are generated for the array, so
       printing the array (using the parray procedure) does not print out  all
       the  component values.  You can use the Tcl command to access the array
       as a whole.  You can copy, append, or sort vector  using	 its  command.
       If  you need greater performance, or customized behavior, you can write
       your own C code to manage vectors.

EXAMPLE
       You create vectors using the vector command and its create operation.

	      # Create a new vector.
	      vector create y(50)

       This creates a new  vector  named  y.   It  has	fifty  components,  by
       default, initialized to 0.0.  In addition, both a Tcl command and array
       variable, both named y, are created.  You can use either the command or
       variable to query or modify components of the vector.

	      # Set the first value.
	      set y(0) 9.25
	      puts "y has [y length] components"

       The  array  y  can  be used to read or set individual components of the
       vector.	Vector components are indexed from zero.  The array index must
       be  a  number less than the number of components.  For example, it's an
       error if you try to set the 51st element of y.

	      # This is an error. The vector only has 50 components.
	      set y(50) 0.02

       You can also specify a range of indices using a colon (:)  to  separate
       the first and last indices of the range.

	      # Set the first six components of y
	      set y(0:5) 25.2

       If you don't include an index, then it will default to the first and/or
       last component of the vector.

	      # Print out all the components of y
	      puts "y = $y(:)"

       There are special non-numeric indices.  The index  end,	specifies  the
       last  component	of the vector.	It's an error to use this index if the
       vector is empty (length is zero).  The  index  ++end  can  be  used  to
       extend  the  vector  by	one  component and initialize it to a specific
       value.  You can't read from the array using this index, though.

	      # Extend the vector by one component.
	      set y(++end) 0.02

       The other special indices are min and max.   They  return  the  current
       smallest and largest components of the vector.

	      # Print the bounds of the vector
	      puts "min=$y(min) max=$y(max)"

       To  delete  components  from  a	vector, simply unset the corresponding
       array element. In the following example, the first component  of	 y  is
       deleted.	  All  the remaining components of y will be moved down by one
       index as the length of the vector is reduced by one.

	      # Delete the first component
	      unset y(0)
	      puts "new first element is $y(0)"

       The vector's Tcl command can also be used to query or set the vector.

	      # Create and set the components of a new vector
	      vector create x
	      x set { 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 }

       Here we've created a vector x without a initial	length	specification.
       In this case, the length is zero.  The set operation resets the vector,
       extending it and setting values for each new component.

       There are several operations for vectors.  The  range  operation	 lists
       the components of a vector between two indices.

	      # List the components
	      puts "x = [x range 0 end]"

       You  can	 search for a particular value using the search operation.  It
       returns a list of indices of the components with the same value.	 If no
       component has the same value, it returns "".

	      # Find the index of the biggest component
	      set indices [x search $x(max)]

       Other operations copy, append, or sort vectors.	You can append vectors
       or new values onto an existing vector with the append operation.

	      # Append assorted vectors and values to x
	      x append x2 x3 { 2.3 4.5 } x4

       The sort operation sorts the vector.  If	 any  additional  vectors  are
       specified,  they	 are  rearranged in the same order as the vector.  For
       example, you could use it to sort data points represented by  x	and  y
       vectors.

	      # Sort the data points
	      x sort y

       The vector x is sorted while the components of y are rearranged so that
       the original x,y coordinate pairs are retained.

       The expr operation lets you perform arithmetic on vectors.  The	result
       is stored in the vector.

	      # Add the two vectors and a scalar
	      x expr { x + y }
	      x expr { x * 2 }

       When  a	vector	is modified, resized, or deleted, it may trigger call-
       backs to notify the clients of the vector.  For example, when a	vector
       used  in the graph widget is updated, the vector automatically notifies
       the widget that it has changed.	The graph can then redrawn  itself  at
       the  next  idle	point.	By default, the notification occurs when Tk is
       next idle.  This way you can  modify  the  vector  many	times  without
       incurring  the  penalty	of the graph redrawing itself for each change.
       You can change this behavior using the notify operation.

	      # Make vector x notify after every change
	      x notify always
		...
	      # Never notify
	      x notify never
		...
	      # Force notification now
	      x notify now

	      # Set Tcl callback for update of Tktable widget .t.
	      x notify callback {.t conf -padx [.t cget -padx]; .t reread}

       To delete a vector, use the vector delete command.  Both the vector and
       its corresponding Tcl command are destroyed.

	      # Remove vector x
	      vector destroy x

       The  psuedo  vector  last  can  be  used at the end of an expression to
       implement running totals.  During execution it resolves to  the	result
       from the previous vector element evaluation.

	      vector create A(10)
	      vector create B(10)
	      vector create S(10)
	      vector create T(10)
	      S expr A+B
	      T expr S+last; # Running total

SYNTAX
       Vectors are created using the vector create operation.  Th create oper‐
       ation can be invoked in one of three forms:

       vector create vecName
	      This creates a new vector vecName which initially has no	compo‐
	      nents.

       vector create vecName(size)
	      This  second  form  creates a new vector which will contain size
	      number of components.  The components will be  indexed  starting
	      from zero (0). The default value for the components is 0.0.

       vector create vecName(rows,columns)
	      This form allows creation of a matrix with the specified columns
	      and rows*columns elements.  See  the  matrix  section  for  more
	      details.

       vector create vecName(first:last)
	      The  last	 form  creates	a  new vector of indexed first through
	      last.  First and last can be any integer value so long as	 first
	      is less than last.

       Vector  names  must start with a letter and consist of letters, digits,
       or underscores.

	      # Error: must start with letter
	      vector create 1abc

       You can automatically generate vector names using  the  "#auto"	vector
       name.  The create operation will generate a unique vector name.

	      set vec [vector create #auto]
	      puts "$vec has [$vec length] components"

   VECTOR INDICES
       Vectors	are indexed by integers.  You can access the individual vector
       components via its array variable or Tcl command.   The	string	repre‐
       senting	the index can be an integer, a numeric expression, a range, or
       a special keyword.

       The index must lie within the current range of the vector, otherwise an
       an  error  message  is  returned.  Normally the indices of a vector are
       start from 0.  But you can use the offset operation to  change  a  vec‐
       tor's indices on-the-fly.

	      puts $vecName(0)
	      vecName offset -5
	      puts $vecName(-5)

       When  matrix  numcols  is  >  1, 2D indexes are supported using ROW,COL
       form.

	      vecName matrix numcols 3
	      puts vecName(0,2)

       You can also use numeric expressions as indices.	  The  result  of  the
       expression must be an integer value.

	      set n 21
	      set vecName($n+3) 50.2

       The following special non-numeric indices are available: min, max, end,
       and ++end.

	      puts "min = $vecName($min)"
	      set vecName(end) -1.2

       The indices min and max will return the minimum and maximum  values  of
       the  vector.   Also available are: prod,	 sum, and mean.	 The index end
       returns the value of the last component in the vector.  he index	 end,0
       returns the value of the last row in column 0 of the vector.  The index
       ++end is used to append new value onto the  vector.   It	 automatically
       extends the vector by numcols and sets its value.

	      # Append an new component to the end
	      set vecName(++end) 3.2

       A range of indices can be indicated by a colon (:).

	      # Set the first six components to 1.0
	      set vecName(0:5) 1.0

       If no index is supplied the first or last component is assumed.

	      # Print the values of all the components
	      puts $vecName(:)

VECTOR OPERATIONS
       vector  configure  ? -flush bool -watchunset bool -oldcreate bool -max‐
       size int -novariable bool -nocommand bool?
	      The configure operation sets the default options used in	creat‐
	      ing  vectors:  these options are global to the interpreter.  The
	      -maxsize option, when non-zero, limits creation size.  The -old‐
	      create  enable the creation shortcut: vector vec1 vec2 ....  See
	      the create command for details on the others.  By default, these
	      are all disabled or zero.

       vector create vecName?(size)?... ?switches?
	      The  create operation creates a new vector vecName. The size may
	      be an integer, a START:END range or ROW,COL (see matrix).	  This
	      creates  both  a	Tcl command and array variable called vecName.
	      The name vecName must be unique, so another Tcl command or array
	      variable	can  not  already exist in the current scope.  You may
	      access the components of the vector using the  variable.	If you
	      change a value in the array, or unset an array element, the vec‐
	      tor is updated to reflect the changes.  When the	variable  vec‐
	      Name  is	unset,	the  vector  and  its  Tcl  command  are  also
	      destroyed.

	      The vector has optional switches that affect how the  vector  is
	      created. They are as follows:

	      -variable varName
		     Specifies	the name of a Tcl variable to be mapped to the
		     vector. If the  variable  already	exists,	 it  is	 first
		     deleted, then recreated.  If varName is the empty string,
		     then no variable will be mapped.  You can	always	map  a
		     variable  back  to the vector using the vector's variable
		     operation.

	      -command cmdName
		     Maps a Tcl command to  the	 vector.  The  vector  can  be
		     accessed  using  cmdName  and  one of the vector instance
		     operations.  A Tcl command by that	 name  cannot  already
		     exist.   If  cmdName is the empty string, no command map‐
		     ping will be made.

	      -watchunset boolean
		     Indicates that the	 vector	 should	 automatically	delete
		     itself  if	 the  variable	associated  with the vector is
		     unset.  By default, the vector will not be deleted.  This
		     is	 different  from  previous  releases.	Set boolean to
		     "true" to get the old behavior.

	      -flush boolean
		     Indicates that the vector should automatically flush  the
		     cached variable elements which unsets all the elements of
		     the Tcl array variable associated with the vector,	 free‐
		     ing  memory  associated  with the variable. This includes
		     both the hash table and the hash keys.  The down side  is
		     that  this effectively flushes the caching of vector ele‐
		     ments in the array.  This means that the subsequent reads
		     of the array will require a decimal to string conversion.
		     By default, flushing is disabled.

       vector destroy vecName ?vecName...?
	      Destroy vectors.

       vector expr expression
	      All binary operators take vectors	 as  operands  (remember  that
	      numbers  are  treated as one-component vectors).The exact action
	      of binary operators depends upon the length of the second	 oper‐
	      and.   If	 the  second operand has only one component, then each
	      element of the first vector operand is computed by  that	value.
	      For  example,  the  expression "x * 2" multiples all elements of
	      the vector x by 2.  If the second operand has more than one com‐
	      ponent,  both  operands  must  be the same length.  Each pair of
	      corresponding elements are computed.  So "x + y"	adds  the  the
	      first components of x and y together, the second, and so on.

	      The  valid  operators  are  listed  below, grouped in decreasing
	      order of precedence:

	      -	 !		  Unary minus  and  logical  NOT.   The	 unary
				  minus	 flips	the  sign of each component in
				  the  vector.	 The  logical	not   operator
				  returns  a vector of whose values are 0.0 or
				  1.0.	For each  non-zero  component  1.0  is
				  returned, 0.0 otherwise.

	      ^			  Exponentiation.

	      *	 /  %		  Multiply, divide, remainder.

	      +	 -		  Add and subtract.

	      <<  >>		  Left and right shift.	 Circularly shifts the
				  values of the vector

	      <	 >  <=	>=	  Boolean less, greater, less than  or	equal,
				  and  greater	than  or equal.	 Each operator
				  returns a vector of ones and zeros.  If  the
				  condition  is	 true,	1.0  is	 the component
				  value, 0.0 otherwise.

	      ==  !=		  Boolean equal and not equal.	Each  operator
				  returns  a vector of ones and zeros.	If the
				  condition is	true,  1.0  is	the  component
				  value, 0.0 otherwise.

	      &&		  Logical  AND.	  Produces  a 1 result if both
				  operands are non-zero, 0 otherwise.

	      ||		  Logical OR.  Produces a 0 result if both op‐
				  erands are zero, 1 otherwise.

	      x?y:z		  If-then-else, as in C.

	      See  the	C  manual  for more details on the results produced by
	      each operator.  All of the binary operators group	 left-to-right
	      within the same precedence level.

	      Several  mathematical functions are supported for vectors.  Each
	      of the following functions invokes the math library function  of
	      the  same name; see the manual entries for the library functions
	      for details on what they do.  The operation is  applied  to  all
	      elements	of  the	 vector returning the results.	 All functions
	      take a vector operand.  If no vector  operand  is	 used  in  the
	      call, the current vector is assumed. eg.

		     vector create aVec
		     aVec seq 0 100
		     aVec expr {2*abs(aVec)-1}
		     aVec length 100
		     aVec expr {2*row()}
		     vector expr {2*row()} ; # ERROR!

		     acos	 cos	     hypot	sinh
		     asin	 cosh	     log	sqrt
		     atan	 exp	     log10	tan
		     ceil	 floor	     sin	tanh

	      Additional functions are:

	      abs	Returns the absolute value of each component.

	      random	Returns a vector of non-negative values uniformly dis‐
			tributed between [0.0, 1.0) using drand48.   The  seed
			comes from the internal clock of the machine or may be
			set manual with the srandom function.

	      round	Rounds each component of the vector.

	      srandom	Initializes the random number generator using srand48.
			The high order 32-bits are set using the integral por‐
			tion of the first vector component. All	 other	compo‐
			nents  are  ignored.  The low order 16-bits are set to
			an arbitrary value.

	      The following functions return a single value.

	      adev	Returns the average deviation (defined as the  sum  of
			the  absolute values of the differences between compo‐
			nent and the mean, divided by the length of  the  vec‐
			tor).

	      kurtosis	Returns	 the  degree  of peakedness (fourth moment) of
			the vector.

	      length	Returns the number of components in the vector.

	      max	Returns the vector's maximum value.

	      mean	Returns the mean value of the vector.

	      median	Returns the median of the vector.

	      min	Returns the vector's minimum value.

	      q1	Returns the first quartile of the vector.

	      q3	Returns the third quartile of the vector.

	      prod	Returns the product of the components.

	      sdev	Returns the standard deviation (defined as the	square
			root of the variance) of the vector.

	      skew	Returns	 the skewness (or third moment) of the vector.
			This characterizes the degree of asymmetry of the vec‐
			tor about the mean.

	      sum	Returns the sum of the components.

	      var	Returns	 the  variance	of  the vector. The sum of the
			squared differences between  each  component  and  the
			mean  is computed.  The variance is the sum divided by
			the length of the vector minus 1.

	      This last set of functions returns a vector of the  same	length
	      as the argument.

	      invert	Returns vector with elements in reversed order.

	      norm	Scales	the  values  of the vector to lie in the range
			[0.0..1.0].

	      row	Psuedo function to get the current row.

	      sort	Returns the  vector  components	 sorted	 in  ascending
			order.

	      shift(nVec,N)
			This  is  the  only  function taking a second arg.  It
			provides a version of nvec shifted by N places.	  When
			N  is  a scalar or vector with only one element, shift
			fills vacant area with 0. Otherwise the second element
			of  nVec is used for the fill value.  One use for this
			is providing running totals.

       vector names ?pattern?
	      Return names of all defined vectors.

       vector op operation vecName ?arg?...
	      Invoke instance operation.  Supported operations are defined  in
	      the  next section.  Op is the only way to invoke instance opera‐
	      tion sub-commands when -command is defined as empty in a vector.
	      It also allows writing vector code that is checkable by a syntax
	      checkers.	 eg.

	      vector create v1
	      v1 op append {1 2 3}
	      v1 op modify 1 2.1

INSTANCE OPERATIONS
       You can also use the vector's Tcl command to query or modify  it.   The
       general	form is vecName operation ?arg?...  Note this is equivalent to
       the form: vector op operation vecName ?arg?...  Both operation and  its
       arguments  determine the exact behavior of the command.	The operations
       available for vectors are listed below.

       vecName + item
	      vecName - item vecName * item vecName / item Perform  binary  op
	      and return result as a list.

       vecName append item ?item?...
	      Appends  the component values from item to vecName.  Item can be
	      either the name of a vector or a list of numeric values.

       vecName binread channel ?length? ?switches?
	      Reads binary values  from	 a  Tcl	 channel.  Values  are	either
	      appended	to  the	 end  of the vector or placed at a given index
	      (using the -at option), overwriting existing  values.   Data  is
	      read  until EOF is found on the channel or a specified number of
	      values length are read (note that this is	 not  necessarily  the
	      same  as	the  number of bytes). The following switches are sup‐
	      ported:

	      -swap  Swap bytes and words.  The default	 endian	 is  the  host
		     machine.

	      -at index
		     New  values  will start at vector index index.  This will
		     overwrite any current values.

	      -format format
		     Specifies the format of the data.	Format can be  one  of
		     the  following:  "i1", "i2", "i4", "i8", "u1, "u2", "u4",
		     "u8", "r4", "r8", or "r16".   The	number	indicates  the
		     number  of	 bytes	required  for  each value.  The letter
		     indicates the type: "i" for signed, "u" for unsigned, "r"
		     or real.  The default format is "r16".

       vecName binwrite channel ?length? ?-at index?
	      Like binread, but writes data.

       vecName clear
	      Clears  the  element  indices from the array variable associated
	      with vecName.  This doesn't affect the components of the vector.
	      By default, the number of entries in the Tcl array doesn't match
	      the number of components in the vector.  This is because its too
	      expensive	 to  maintain  decimal	strings for both the index and
	      value for each component.	 Instead,  the	index  and  value  are
	      saved  only  when you read or write an element with a new index.
	      This command removes the index and value strings from the array.
	      This is useful when the vector is large.

       vecName delete index ?index?...
	      Deletes the indexth component from the vector vecName.  Index is
	      the index of the element to be deleted.  This  is	 the  same  as
	      unsetting	 the array variable element index.  The vector is com‐
	      pacted after all the indices have been deleted.

       vecName dup destName
	      Copies vecName to destName. DestName is the name of  a  destina‐
	      tion  vector.   If a vector destName already exists, it is over‐
	      written with the components of vecName.  Otherwise a new	vector
	      is created.

       vecName expr expression
	      Computes	the  expression	 and  resets  the values of the vector
	      accordingly.   Both  scalar  and	vector	math  operations   are
	      allowed.	 All  values in expressions are either real numbers or
	      names of vectors.	 All numbers are treated as one component vec‐
	      tors.

       vecName index index ?value?...
	      Get/set  individual vector values.  This provides element updat‐
	      ing when -variable is set to empty.

       vecName insert index item ?item?...
	      Inserts the component values from item to vecName at index  Item
	      can be either the name of a vector or a list of numeric values.

       vecName length ?newSize?
	      Queries  or resets the number of components in vecName.  NewSize
	      is a number specifying the new size of the vector.   If  newSize
	      is  smaller  than	 the current size of vecName, vecName is trun‐
	      cated.  If newSize is greater, the vector is  extended  and  the
	      new  components  are initialized to 0.0.	If no newSize argument
	      is present, the current length of the vector is returned.

       vecName matrix  ...
	      Matrix provides a 2D array  view	into  1D  data.	  It  provides
	      indexing	operations  in ROW,COL form making it suitable for use
	      with TkTable.  Data storage remains unchanged: vectors are still
	      just  a  single  long  array.  For example, here are two ways to
	      create a 3 column by 10 row matrix:

	      vector create aVec(10,3)
	      vector create bVec(30)
	      bVec matrix numcols 3
	      set aVec(0,0) 99
	      set bVec(29,2) -99
	      aVec append {5 6 7}; # aVec now has 11 rows.
	      aVec append 1 2;	   # Now aVec has 13 rows!

       Note that data is appended only in increments of numcols.  Elements 0-2
       make  up the first row, 3-5 the second, etc.  Elements will appear only
       in increments of the column size.

	      vecName matrix copy dstcolumn srccolumn ?srcVec?
		     Copy a column of element values to column dstcolumn  from
		     srccolumn.	  If  vector srcVec is given, and not the same
		     as vecName, the columns numbers must  be  different.   If
		     the  srcVec  column  is longer, vecName will be extended.
		     If shorter, remaining destination values  are  not	 over‐
		     written.

	      vecName matrix delete column.
		     Delete  elements  in  a column.  Note that numcols, which
		     must be greater than 1, will be decremented.

	      vecName matrix get column
		     Get the element in a column:  this number	must  be  less
		     than numcols.  Note that numcols must be non-zero.

	      vecName matrix insert column ?initvalue? .
		     Insert  a	new  column of elements at column (default 0).
		     The new column is initialized with initvalue, or  0.0  if
		     not specified.  Note that numcols will be incremented.

	      vecName matrix multiply srcVec ?dstVec?
		     Perform   matrix  multiplication  using  srcVec,  placing
		     results either in dstVec, or returned  as	a  list.   The
		     numrows  of  srcVec  must	equal numcols in vecName.  One
		     application for multiply is coordinate transformation.

	      vecName matrix numcols ?size?
		     Get or set the number of  columns	for  a	vectors	 data.
		     Values  >1	 enable	 array	variables  to accept 2d matrix
		     indexes.  For example with a numcols  of  10,  $vec1(1,2)
		     refers  to the 13th element in the vector. A vectors size
		     is also constrained to multiples of numcols, as  is  it's
		     offset.  By default, numcols is 1.

	      vecName matrix numrows ?size?
		     Get  or set the length of rows in a columns for a vector.
		     By default, this is just the vector length/numcols.  Set‐
		     ting  this	 value	simply	provides  a  convenient way to
		     increase or decrease the vector size by multiples of num‐
		     cols.

	      vecName matrix set column ?valuelist?
		     Set  value	  elements  in	a column:  this number must be
		     less than numcols.	 The valuelist is a list  values.   If
		     this  list is shorter than the column, it's last value is
		     used for all remaining columns. The column	 gets  set  to
		     the values of item, or 0.0 by default.

	      vecName matrix shift column amount ?startoffset?
		     Shifts  the  values  of  a column by integer inamount.  A
		     negative value shifts upward.  The startoffset  indicates
		     where to start shifting from.

	      vecName matrix sort column ?-reverse?
		     Sort the vector by the given column.

	      vecName matrix transpose
		     Transpose	all  columns  with  rows in matrix.  Note that
		     this is a no-op if numcols is 1.  Otherwise, numcols will
		     change to vectorLength/numcols.

       vecName merge srcName ?srcName?...
	      Merges  the  named  vectors into a single vector.	 The resulting
	      vector is formed by merging the components of each source vector
	      one index at a time.

       vecName notify ?keyword? ?script?
	      Queries  or  controls how vector clients are notified of changes
	      to the vector.  Also allows setting a  notifier  callback.   The
	      exact behavior is determined by keyword.

	      always Indicates	that  clients  are  to be notified immediately
		     whenever the vector is updated.

	      never  Indicates that no clients are to be notified.

	      whenidle
		     Indicates that clients are to be  notified	 at  the  next
		     idle point whenever the vector is updated.

	      now    If	 any  client  notifications is currently pending, they
		     are notified immediately.

	      cancel Cancels pending notifications of clients using  the  vec‐
		     tor.

	      pending
		     Returns 1 if a client notification is pending, and 0 oth‐
		     erwise.

	      callback ?script?
		     Query or set a Tcl callback script that is evaluated when
		     a vector is updated.

       vecName populate destName ?density?
	      Creates a vector destName which is a superset of vecName.	 Dest‐
	      Name will include all the components of vecName, in addition the
	      interval	between each of the original components will contain a
	      density number of new components, whose values are  evenly  dis‐
	      tributed between the original components values.	This is useful
	      for generating abscissas to be interpolated along a spline.

       vecName range firstIndex ?lastIndex?...
	      Returns a list of numeric values representing the vector	compo‐
	      nents  between  two  indices.  Both firstIndex and lastIndex are
	      indices representing the range of components to be returned.  If
	      lastIndex	 is less than firstIndex, the components are listed in
	      reverse order.

       vecName search value ?value?
	      Searches for a value or range of values among the components  of
	      vecName.	 If  one value argument is given, a list of indices of
	      the components which equal value is returned.  If a second value
	      is  also	provided, then the indices of all components which lie
	      within the range of the two values are returned.	If  no	compo‐
	      nents are found, then "" is returned.

       vecName set item
	      Resets  the components of the vector to item. Item can be either
	      a list of numeric expressions or another vector.

       vecName seq start ?finish? ?step?
	      Generates a sequence of values starting with  the	 value	start.
	      Finish  indicates	 the  terminating  value of the sequence.  The
	      vector is automatically resized to contain  just	the  sequence.
	      If three arguments are present, step designates the interval.

	      With  only two arguments (no finish argument), the sequence will
	      continue until the vector is filled.   With  one	argument,  the
	      interval defaults to 1.0.

       vecName sort ?-reverse? ?argName?...
	      Sorts  the  vector vecName in increasing order.  If the -reverse
	      flag is present, the vector is sorted in decreasing  order.   If
	      other  arguments argName are present, they are the names of vec‐
	      tors which will be rearranged in the  same  manner  as  vecName.
	      Each  vector  must be the same length as vecName.	 You could use
	      this to sort the x vector of a graph, while still retaining  the
	      same x,y coordinate pairs in a y vector.

       vecName split dstName ?dstName?...
	      Split  the vector into a multiple vectors.  The resulting N vec‐
	      tors each contain the mod-Nth element from source.

       vecName variable varName
	      Maps a Tcl variable to the vector, creating  another  means  for
	      accessing the vector.  The variable varName can't already exist.
	      This overrides any current variable mapping the vector may have.

C LANGUAGE API
       You can create, modify, and destroy vectors from C code, using  library
       routines.   You	need to include the header file blt.h. It contains the
       definition of the structure Blt_Vector, which  represents  the  vector.
       It appears below.

	      typedef struct {
		  double *valueArr;
		  int numValues;
		  int arraySize;
		  double min, max;
	      } Blt_Vector;

       The field valueArr points to memory holding the vector components.  The
       components are stored in a double precision array, whose size  size  is
       represented by arraySize.  NumValues is the length of vector.  The size
       of the array is always equal to or larger than the length of  the  vec‐
       tor.  Min and max are minimum and maximum component values.

LIBRARY ROUTINES
       The following routines are available from C to manage vectors.  Vectors
       are identified by the vector name.

       Blt_CreateVector

	 Synopsis:

		   int Blt_CreateVector (interp, vecName, length, vecPtrPtr)
				Tcl_Interp *interp;
				char *vecName;
				int length;
				Blt_Vector **vecPtrPtr;

	 Description:
		   Creates a new vector	 vecName  with	a  length  of  length.
		   Blt_CreateVector  creates  both a new Tcl command and array
		   variable vecName.  Neither a	 command  nor  variable	 named
		   vecName  can	 already  exist.   A  pointer to the vector is
		   placed into vecPtrPtr.

	 Results:  Returns TCL_OK if the vector is successfully	 created.   If
		   length  is  negative,  a  Tcl  variable  or command vecName
		   already exists, or memory cannot be allocated for the  vec‐
		   tor,	 then  TCL_ERROR  is  returned and interp->result will
		   contain an error message.

       Blt_DeleteVectorByName

	 Synopsis:

		   int Blt_DeleteVectorByName (interp, vecName)
				Tcl_Interp *interp;
				char *vecName;

	 Description:
		   Removes the vector vecName.	VecName is the name of a  vec‐
		   tor	which  must  already  exist.  Both the Tcl command and
		   array variable vecName are destroyed.  All clients  of  the
		   vector  will	 be  notified  immediately that the vector has
		   been destroyed.

	 Results:  Returns TCL_OK if the vector is successfully	 deleted.   If
		   vecName  is	not  the  name	a  vector,  then  TCL_ERROR is
		   returned and interp->result will contain an error message.

       Blt_DeleteVector

	 Synopsis:

		   int Blt_DeleteVector (vecPtr)
				Blt_Vector *vecPtr;

	 Description:
		   Removes the vector pointed  to  by  vecPtr.	 VecPtr	 is  a
		   pointer  to	a  vector,  typically  set by Blt_GetVector or
		   Blt_CreateVector.  Both the Tcl command and array  variable
		   of  the  vector  are	 destroyed.  All clients of the vector
		   will be notified  immediately  that	the  vector  has  been
		   destroyed.

	 Results:  Returns  TCL_OK  if the vector is successfully deleted.  If
		   vecName is  not  the	 name  a  vector,  then	 TCL_ERROR  is
		   returned and interp->result will contain an error message.

       Blt_GetVector

	 Synopsis:

		   int Blt_GetVector (interp, vecName, vecPtrPtr)
				Tcl_Interp *interp;
				char *vecName;
				Blt_Vector **vecPtrPtr;

	 Description:
		   Retrieves  the  vector  vecName.   VecName is the name of a
		   vector which must already exist.  VecPtrPtr will  point  be
		   set to the address of the vector.

	 Results:  Returns TCL_OK if the vector is successfully retrieved.  If
		   vecName is not the name of  a  vector,  then	 TCL_ERROR  is
		   returned and interp->result will contain an error message.

       Blt_ResetVector

	 Synopsis:

		   int Blt_ResetVector (vecPtr, dataArr,
		     numValues, arraySize, freeProc)
				Blt_Vector *vecPtr;
				double *dataArr;
				int *numValues;
				int *arraySize;
				Tcl_FreeProc *freeProc;

	 Description:
		   Resets  the	components of the vector pointed to by vecPtr.
		   Calling Blt_ResetVector will trigger the vector to dispatch
		   notifications  to its clients. DataArr is the array of dou‐
		   bles which represents the vector  data.  NumValues  is  the
		   number  of  elements	 in the array. ArraySize is the actual
		   size of the array (the array may be bigger than the	number
		   of values stored in it). FreeProc indicates how the storage
		   for the vector component array (dataArr) was allocated.  It
		   is used to determine how to reallocate memory when the vec‐
		   tor is resized  or  destroyed.   It	must  be  TCL_DYNAMIC,
		   TCL_STATIC,	TCL_VOLATILE,  or  a  pointer to a function to
		   free the memory allocated for the vector array. If freeProc
		   is  TCL_VOLATILE,  it indicates that dataArr must be copied
		   and saved.  If freeProc is TCL_DYNAMIC, it  indicates  that
		   dataArr  was dynamically allocated and that Tcl should free
		   dataArr if necessary.  Static indicates that nothing should
		   be done to release storage for dataArr.

	 Results:  Returns  TCL_OK  if the vector is successfully resized.  If
		   newSize is negative, a vector vecName does  not  exist,  or
		   memory  cannot  be allocated for the vector, then TCL_ERROR
		   is returned and interp->result will contain an  error  mes‐
		   sage.

       Blt_ResizeVector

	 Synopsis:

		   int Blt_ResizeVector (vecPtr, newSize)
				Blt_Vector *vecPtr;
				int newSize;

	 Description:
		   Resets  the	length	of  the vector pointed to by vecPtr to
		   newSize.  If newSize is smaller than the  current  size  of
		   the	vector,	 it  is truncated.  If newSize is greater, the
		   vector is extended and the new components  are  initialized
		   to 0.0.  Calling Blt_ResetVector will trigger the vector to
		   dispatch notifications.

	 Results:  Returns TCL_OK if the vector is successfully	 resized.   If
		   newSize  is negative or memory can not be allocated for the
		   vector, then TCL_ERROR is returned and interp->result  will
		   contain an error message.

	 Blt_VectorExists

	    Synopsis:

		      int Blt_VectorExists (interp, vecName)
				  Tcl_Interp *interp;
				  char *vecName;

	    Description:
		      Indicates if a vector named vecName exists in interp.

	    Results:  Returns 1 if a vector vecName exists and 0 otherwise.

	 If  your  application	needs to be notified when a vector changes, it
	 can allocate a unique client identifier for itself.  Using this iden‐
	 tifier,  you  can  then  register a call-back to be made whenever the
	 vector is updated or destroyed.  By default, the call-backs are  made
	 at the next idle point.  This can be changed to occur at the time the
	 vector is modified.  An application can allocate more than one	 iden‐
	 tifier	 for any vector.  When the client application is done with the
	 vector, it should free the identifier.

	 The call-back routine must of the following type.

		       typedef void (Blt_VectorChangedProc) (Tcl_Interp *interp,
			  ClientData clientData, Blt_VectorNotify notify);

	 ClientData is passed to this routine whenever it is called.  You  can
	 use  this  to pass information to the call-back.  The notify argument
	 indicates whether the vector has been updated of destroyed. It is  an
	 enumerated type.

		       typedef enum {
			   BLT_VECTOR_NOTIFY_UPDATE=1,
			   BLT_VECTOR_NOTIFY_DESTROY=2
		       } Blt_VectorNotify;

	 Blt_AllocVectorId

	    Synopsis:

		      Blt_VectorId Blt_AllocVectorId (interp, vecName)
				  Tcl_Interp *interp;
				  char *vecName;

	    Description:
		      Allocates	 an client identifier for with the vector vec‐
		      Name.  This identifier can be used to  specify  a	 call-
		      back  which  is  triggered when the vector is updated or
		      destroyed.

	    Results:  Returns a client identifier if successful.   If  vecName
		      is  not  the name of a vector, then NULL is returned and
		      interp->result will contain an error message.

	 Blt_GetVectorById

	    Synopsis:

		      int Blt_GetVector (interp, clientId, vecPtrPtr)
				  Tcl_Interp *interp;
				  Blt_VectorId clientId;
				  Blt_Vector **vecPtrPtr;

	    Description:
		      Retrieves the vector used by clientId.   ClientId	 is  a
		      valid    vector	 client	   identifier	allocated   by
		      Blt_AllocVectorId.  VecPtrPtr will point be set  to  the
		      address of the vector.

	    Results:  Returns TCL_OK if the vector is successfully retrieved.

	 Blt_SetVectorChangedProc

	    Synopsis:

		      void Blt_SetVectorChangedProc (clientId, proc, clientData);
				  Blt_VectorId clientId;
				  Blt_VectorChangedProc *proc;
				  ClientData *clientData;

	    Description:
		      Specifies	 a call-back routine to be called whenever the
		      vector associated with clientId is updated  or  deleted.
		      Proc  is	a  pointer to call-back routine and must be of
		      the type Blt_VectorChangedProc.  ClientData  is  a  one-
		      word  value  to  be  passed  to  the  routine when it is
		      invoked. If proc is NULL, then the client is  not	 noti‐
		      fied.

	    Results:  The  designated call-back procedure will be invoked when
		      the vector is updated or destroyed.

	 Blt_FreeVectorId

	    Synopsis:

		      void Blt_FreeVectorId (clientId);
				  Blt_VectorId clientId;

	    Description:
		      Frees the client identifier.  Memory allocated  for  the
		      identifier  is  released.	  The client will no longer be
		      notified when the vector is modified.

	    Results:  The designated call-back procedure will be no longer  be
		      invoked when the vector is updated or destroyed.

	 Blt_NameOfVectorId

	    Synopsis:

		      char *Blt_NameOfVectorId (clientId);
				  Blt_VectorId clientId;

	    Description:
		      Retrieves	 the  name  of	the vector associated with the
		      client identifier clientId.

	    Results:  Returns the name of the vector associated with clientId.
		      If  clientId is not an identifier or the vector has been
		      destroyed, NULL is returned.

	 Blt_InstallIndexProc

	    Synopsis:

		      void Blt_InstallIndexProc (indexName, procPtr)
				  char *indexName;
				  Blt_VectorIndexProc *procPtr;

	    Description:
		      Registers a function to be called to retrieved the index
		      indexName from the vector's array variable.

		      typedef double Blt_VectorIndexProc(Vector *vecPtr);

		      The  function  will  be  passed a pointer to the vector.
		      The function must return a double representing the value
		      at the index.

	    Results:  The new index is installed into the vector.

C API EXAMPLE
       The  following  example opens a file of binary data and stores it in an
       array of doubles. The array size is computed from the size of the file.
       If the vector "data" exists, calling Blt_VectorExists, Blt_GetVector is
       called to get  the  pointer  to	the  vector.   Otherwise  the  routine
       Blt_CreateVector is called to create a new vector and returns a pointer
       to it. Just like the Tcl interface, both a new Tcl  command  and	 array
       variable	 are created when a new vector is created. It doesn't make any
       difference what the initial size of the vector  is  since  it  will  be
       reset  shortly.	The  vector  is updated when lt_ResetVector is called.
       Blt_ResetVector makes the changes visible  to  the  Tcl	interface  and
       other vector clients (such as a graph widget).

	      #include <tcl.h>
	      #include <blt.h>
	      Blt_Vector *vecPtr;
	      double *newArr;
	      FILE *f;
	      struct stat statBuf;
	      int numBytes, numValues;

	      f = fopen("binary.dat", "r");
	      fstat(fileno(f), &statBuf);
	      numBytes = (int)statBuf.st_size;

	      /* Allocate an array big enough to hold all the data */
	      newArr = (double *)malloc(numBytes);
	      numValues = numBytes / sizeof(double);
	      fread((void *)newArr, numValues, sizeof(double), f);
	      fclose(f);

	      if (Blt_VectorExists(interp, "data"))  {
		  if (Blt_GetVector(interp, "data", &vecPtr) != TCL_OK) {
		return TCL_ERROR;
		  }
	      } else {
		 if (Blt_CreateVector(interp, "data", 0, &vecPtr) != TCL_OK) {
		return TCL_ERROR;
		 }
	      }
	      /*
	       * Reset the vector. Clients will be notified when Tk is idle.
	       * TCL_DYNAMIC tells the vector to free the memory allocated
	       * if it needs to reallocate or destroy the vector.
	       */
	      if (Blt_ResetVector(vecPtr, newArr, numValues, numValues,
		TCL_DYNAMIC) != TCL_OK) {
		  return TCL_ERROR;
	      }

INCOMPATIBILITIES
       In previous versions, if the array variable isn't global (i.e. local to
       a Tcl procedure), the vector is automatically destroyed when the proce‐
       dure returns.

	      proc doit {} {
		  # Temporary vector x
		  vector x(10)
		  set x(9) 2.0
		    ...
	      }

       This has changed.  Variables are not automatically destroyed when their
       variable is unset.  You can restore the old  behavior  by  setting  the
       "-watchunset" switch.

KEYWORDS
       vector, graph, widget

BLT				      2.5			     vector(n)
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