vector(n) manual page

Synopsis

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

vector destroy vecName ?vecName...?

vector expr expression

vector names ?pattern...?

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 have 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

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

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(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 representing 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 vector's indices on-the-fly.
puts $vecName(0) vecName offset -5 puts $vecName(-5)

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. The index end returns the value of the last component in the vector. The index ++end is used to append new value onto the vector. It automatically extends the vector by one component 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 create vecName?(size)?... ?switches?: The create operation creates a new vector vecName. Both a Tcl command and array variable vecName are also created. The name vecName must be unique, so another Tcl command or array variable can not already exist in that scope. You can access the components of the vector using its 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:
-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 mapping 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.

vector destroy vecName ?vecName...?
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 operand. 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 component, 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 (not implemented yet).
< > <= >=: 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.
|: Bit-wise OR. (Not implemented).
&&: Logical AND. Produces a 1 result if both operands are non-zero, 0 otherwise.
||: Logical OR. Produces a 0 result if both operands are zero, 1 otherwise.
x?y:z: If-then-else, as in C. (Not implemented yet).

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.

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 distributed 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 portion of the first vector component. All other components 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 component and the mean, divided by the length of the vector).
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 vector 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.

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

norm: Scales the values of the vector to lie in the range [0.0..1.0].
sort: Returns the vector components sorted in ascending order.

vector names ?pattern?

Instance Operations

You can also use the vector's Tcl command to query or modify it. The general form is

vecName operation ?arg?...

Both operation and its arguments determine the exact behavior of the command. The operations available for vectors are listed below.

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 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 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 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: Controls how vector clients are notified of changes to the vector. 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 vector.
pending: Returns 1 if a client notification is pending, and 0 otherwise.

vecName offset ?value?: Shifts the indices of the vector by the amount specified by value. Value is an integer number. If no value argument is given, the current offset is returned.
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 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

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 vector, 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 vector 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 doubles 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 vector 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 message.

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 identifier, 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 identifier 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 vecName. 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 notified.
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>

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

Table of Contents

Name
Synopsis
Description
Introduction
Example
Syntax

Vector Indices

Vector Operations
Instance Operations
C Language API
Library Routines
C API Example
Incompatibilities
Keywords