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 vector'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 vector 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 analysis 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 specifying the index, or the set the entire array by providing a list of index and value pairs for each element. The disadvantages of associative 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 values 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 element 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 vector 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 operation can be invoked in one of three forms:

vector create vecName

This creates a new vector vecName which initially has no components.

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"

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

vecName matrix numcols 3
puts vecName(0,2)

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

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

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

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

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

VECTOR OPERATIONS

vector configure ? -flush bool -watchunset bool -oldcreate bool -maxsize int -novariable bool -nocommand bool?

The configure operation sets the default options used in creating vectors: these options are global to the interpreter. The -maxsize option, when non-zero, limits creation size. The -oldcreate 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 vector is updated to reflect the changes. When the variable vecName 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:

vector destroy vecName ?vecName...?

Destroy vectors.

vector expr expression

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 

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 operation 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 supported:

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 compacted after all the indices have been deleted.

vecName dup destName

Copies vecName to destName. DestName is the name of a destination vector. If a vector destName already exists, it is overwritten 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 vectors.

vecName index index ?value?...

Get/set individual vector values. This provides element updating 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 truncated. 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 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.

vecName populate destName ?density?

Creates a vector destName which is a superset of vecName. DestName 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 distributed 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 components 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 components 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 vectors 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 vectors 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 vector. 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

int Blt_CreateVector (interp, vecName, length, vecPtrPtr)

Tcl_Interp *interp;
char *vecName;
int length;
Blt_Vector **vecPtrPtr;

Blt_DeleteVectorByName

int Blt_DeleteVectorByName (interp, vecName)

Tcl_Interp *interp;
char *vecName;

Blt_DeleteVector

int Blt_DeleteVector (vecPtr)

Blt_Vector *vecPtr;

Blt_GetVector

int Blt_GetVector (interp, vecName, vecPtrPtr)

Tcl_Interp *interp;
char *vecName;
Blt_Vector **vecPtrPtr;

Blt_ResetVector

int Blt_ResetVector (vecPtr, dataArr, 
	numValues, arraySize, freeProc)

Blt_Vector *vecPtr;
double *dataArr;
int *numValues;
int *arraySize;
Tcl_FreeProc *freeProc;

Blt_ResizeVector

int Blt_ResizeVector (vecPtr, newSize)

Blt_Vector *vecPtr;
int newSize;

int Blt_VectorExists (interp, vecName)

Tcl_Interp *interp;
char *vecName;

typedef void (Blt_VectorChangedProc) (Tcl_Interp *interp, 

ClientData clientData, Blt_VectorNotify notify);

typedef enum {


    BLT_VECTOR_NOTIFY_UPDATE=1,


    BLT_VECTOR_NOTIFY_DESTROY=2
} Blt_VectorNotify;

Blt_VectorId Blt_AllocVectorId (interp, vecName)

Tcl_Interp *interp;
char *vecName;

int Blt_GetVector (interp, clientId, vecPtrPtr)

Tcl_Interp *interp;
Blt_VectorId clientId;
Blt_Vector **vecPtrPtr;

void Blt_SetVectorChangedProc (clientId, proc, clientData);

Blt_VectorId clientId;
Blt_VectorChangedProc *proc;
ClientData *clientData;

void Blt_FreeVectorId (clientId);

Blt_VectorId clientId;

char *Blt_NameOfVectorId (clientId);

Blt_VectorId clientId;

void Blt_InstallIndexProc (indexName, procPtr)

char *indexName;
Blt_VectorIndexProc *procPtr;

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 procedure 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