blt::vectorcreatevecName?vecName...? ?switches?blt::vectordestroyvecName?vecName...?blt::vectorexprexpressionblt::vectornames?pattern...?

Thevectorcommand creates an array 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.

A vector is an ordered set of real numbers. The components of a vector are indexed by integers. 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.oThere'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.oArrays 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.oThe 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. Thevectorcommand tries to overcome these disadvantages while still 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. sety(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 ele- ment of y. # This is an error. The vector only has 50 components. sety(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 = $y(:)" There are special non- numeric indices. The index end, specifies the last component of the vector. It's an error to use this index if the vector is empty (length is zero). The index ++end can be used to extend the vector by one com- ponent and initialize it to a specific value. You can't read from the array using this index, though. # Extend the vector by one component. set y(++end) 0.02 The other special indices are min and max. They return the current smallest and largest components of the vector. # Print the bounds of the vector puts "min=$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 unsety(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 compo- nents of a new vector blt::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. Thesetoperation resets the vector, extending it and setting values for each new component. There are several operations for vectors. Therangeoperation 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 thesearchoperation. 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 $x(max)] Other operations copy, append, or sort vectors. You can append vectors or new values onto an existing vector with theappendoperation. # Append assorted vectors and values to x x append x2 x3 { 2.3 4.5 } x4 Thesortoperation sorts the vector. If any additional vectors are specified, they are rearranged in the same order as the vector. For example, you could use it to sort data points represented by x and y vectors. # Sort the data points x sort y The vector x is sorted while the components of y are rearranged so that the original x,y coordinate pairs are retained. Theexproperation lets you perform arithmetic on vectors. The result is stored in the vector. # Add the two vectors and a scalar x expr { x + y } x expr { x * 2 } When a vector is modified, resized, or deleted, Vectors are created using thevectorcreateoperation. Thcreateoper- ation can be invoked in one of three forms:blt::vectorcreatevecNameThis creates a new vectorvecNamewhich initially has no compo- nents.blt::vectorcreatevecName(size) This second form creates a new vector which will containsizenumber of components. The components will be indexed starting from zero (0). The default value for the components is 0.0.blt::vectorcreatevecName(first:last) The last form creates a new vector of indexedfirstthroughlast.Firstandlastcan be any integer value so long asfirstis less thanlast. Vector names must start with a letter and consist of letters, digits, or underscores. # Error: must start with letter blt::vector create 1abc You can automatically generate vector names using the "#auto" vec- tor name. Thecreateoperation will generate a unique vector name. set vec [blt::vector create #auto] puts "$vec has [$vec length] compo- nents"VECTORINDICESVectors 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 theoffsetoperation to change a vec- tor's indices on-the-fly. puts $vecName(0)vecName offset -5 puts $vecName(-5) You can also use numeric expressions as indices. The result of the expression must be an integer value. set n 21 set vec- Name($n+3) 50.2 The following special non-numeric indices are avail- able: min, max, end, and ++end. puts "min = $vecName($min)" set vec- Name(end) -1.2 The indices min and max will return the minimum and max- imum 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 vec- Name(++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(:)

blt::vectorcreatevecName?(size)?... ?switches? Thecreateoperation creates a new vectorvecName. Both a Tcl command and array variablevecNameare also created. The name then no variable will be mapped. You can always map a variable back to the vector using the vector'svariableoperation.-commandcmdNameMaps a Tcl command to the vector. The vector can be accessed usingcmdNameand one of the vector instance operations. A Tcl command by that name cannot already exist. IfcmdNameis the empty string, no command map- ping will be made.-watchunsetbooleanIndicates 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. Setbooleanto "true" to get the old behavior.blt::vectordestroyvecName?vecName...? Deletes one or more vectors. Both the Tcl command and array variable are removed also.blt::vectorexprexpressionAll 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 (not implemented yet).&&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:zIf-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.acoscoshypotsinhasincoshlogsqrtatanexplog10tanceilfloorsintanhAdditional functions are:absReturns the absolute value of each component.randomReturns a vector of non-negative values uniformly dis- tributed between [0.0, 1.0) usingdrand48. The seed comes from the internal clock of the machine or may be set manual with the srandom function.roundRounds each component of the vector.srandomInitializes the random number generator usingsrand48. 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.adevReturns 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).kurtosisReturns the degree of peakedness (fourth moment) of the vector.lengthReturns the number of components in the vector.maxReturns the vector's maximum value.skewReturns the skewness (or third moment) of the vector. This characterizes the degree of asymmetry of the vec- tor about the mean.sumReturns the sum of the components.varReturns 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 argu- ment.normScales the values of the vector to lie in the range [0.0..1.0].sortReturns the vector components sorted in ascending order.vectornames?pattern?

You can also use the vector's Tcl command to query or modify it. The general form isvecNameoperation?arg?... Bothoperationand its arguments determine the exact behavior of the command. The operations available for vectors are listed below.vecNameappenditem?item?... Appends the component values fromitemtovecName.Itemcan be either the name of a vector or a list of numeric values.vecNamebinreadchannel?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-atoption), overwriting existing values. Data is read until EOF is found on the channel or a specified number of valueslengthare read (note that this is not necessarily the same as the number of bytes). The following switches are sup- ported:-swapSwap bytes and words. The default endian is the host machine.-atindexNew values will start at vector indexindex. This will overwrite any current values.-formatformatSpecifies the format of the data.Formatcan be one of the following: "i1", "i2", "i4", "i8", "u1, "u2", "u4", This is useful when the vector is large.vecNamedeleteindex?index?... Deletes theindexth component from the vectorvecName.Indexis the index of the element to be deleted. This is the same as unsetting the array variable elementindex. The vector is com- pacted after all the indices have been deleted.vecNamedupdestNameCopiesvecNametodestName.DestNameis the name of a destina- tion vector. If a vectordestNamealready exists, it is over- written with the components ofvecName. Otherwise a new vector is created.vecNameexprexpressionComputes 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.vecNamelength?newSize? Queries or resets the number of components invecName.NewSizeis a number specifying the new size of the vector. IfnewSizeis smaller than the current size ofvecName,vecNameis trun- cated. IfnewSizeis greater, the vector is extended and the new components are initialized to 0.0. If nonewSizeargument is present, the current length of the vector is returned.vecNamemergesrcName?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.vecNamenotifykeywordControls how vector clients are notified of changes to the vec- tor. The exact behavior is determined bykeyword. 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.densitynumber 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.vecNamerangefirstIndex?lastIndex?... Returns a list of numeric values representing the vector compo- nents between two indices. BothfirstIndexandlastIndexare indices representing the range of components to be returned. IflastIndexis less thanfirstIndex, the components are listed in reverse order.vecNamesearchvalue?value? Searches for a value or range of values among the components ofvecName. If onevalueargument is given, a list of indices of the components which equalvalueis returned. If a secondvalueis 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.vecNamesetitemResets the components of the vector toitem.Itemcan be either a list of numeric expressions or another vector.vecNameseqstart?finish? ?step? Generates a sequence of values starting with the valuestart.Finishindicates the terminating value of the sequence. The vector is automatically resized to contain just the sequence. If three arguments are present,stepdesignates the interval. With only two arguments (nofinishargument), the sequence will continue until the vector is filled. With one argument, the interval defaults to 1.0.vecNamesort?-reverse? ?argName?... Sorts the vectorvecNamein increasing order. If the-reverseflag is present, the vector is sorted in decreasing order. If other argumentsargNameare present, they are the names of vec- tors which will be rearranged in the same manner asvecName. Each vector must be the same length asvecName. 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.vecNamevariablevarNameMaps a Tcl variable to the vector, creating another means for accessing the vector. The variablevarNamecan't already exist. This overrides any current variable mapping the vector may have.

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 structureBlt_Vector, which represents the vector. It appears below. typedef struct {Blt_CreateVectorSynopsis: intBlt_CreateVector(interp,vecName,length,vecPtrPtr) Tcl_Interp *interp; char *vecName; intlength; Blt_Vec- tor **vecPtrPtr; Description: Creates a new vectorvecNamewith a length oflength.Blt_CreateVectorcreates both a new Tcl command and array variablevecName. Neither a command nor variable namedvecNamecan already exist. A pointer to the vector is placed intovecPtrPtr. Results: Returns TCL_OK if the vector is successfully created. Iflengthis negative, a Tcl variable or commandvecNamealready exists, or memory cannot be allocated for the vec- tor, then TCL_ERROR is returned andinterp->resultwill contain an error message.Blt_DeleteVectorByNameSynopsis: intBlt_DeleteVectorByName(interp,vecName) Tcl_Interp *interp; char *vecName; Description: Removes the vectorvecName.VecNameis the name of a vec- tor which must already exist. Both the Tcl command and array variablevecNameare 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. IfvecNameis not the name a vector, then TCL_ERROR is returned andinterp->resultwill contain an error message.Blt_DeleteVectorSynopsis: intBlt_DeleteVector(vecPtr) Blt_Vector *vecPtr; Description: Removes the vector pointed to byvecPtr.VecPtris a pointer to a vector, typically set byBlt_GetVectororBlt_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. IfvecNameis not the name a vector, then TCL_ERROR is Results: Returns TCL_OK if the vector is successfully retrieved. IfvecNameis not the name of a vector, then TCL_ERROR is returned andinterp->resultwill contain an error message.Blt_ResetVectorSynopsis: intBlt_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 byvecPtr. CallingBlt_ResetVectorwill trigger the vector to dispatch notifications to its clients.DataArris the array of dou- bles which represents the vector data.NumValuesis the number of elements in the array.ArraySizeis the actual size of the array (the array may be bigger than the number of values stored in it).FreeProcindicates 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. IffreeProcis TCL_VOLATILE, it indicates thatdataArrmust be copied and saved. IffreeProcis TCL_DYNAMIC, it indicates thatdataArrwas dynamically allocated and that Tcl should freedataArrif necessary. Static indicates that nothing should be done to release storage fordataArr. Results: Returns TCL_OK if the vector is successfully resized. IfnewSizeis negative, a vectorvecNamedoes not exist, or memory cannot be allocated for the vector, then TCL_ERROR is returned andinterp->resultwill contain an error mes- sage.Blt_ResizeVectorSynopsis: intBlt_ResizeVector(vecPtr,newSize) Blt_Vector *vecPtr; intnewSize; Description: Resets the length of the vector pointed to byvecPtrtonewSize. IfnewSizeis smaller than the current size of the vector, it is truncated. IfnewSizeis greater, the vector is extended and the new components are initialized to 0.0. CallingBlt_ResetVectorwill trigger the vector to dispatch notifications. Results: Returns 1 if a vectorvecNameexists and 0 otherwise. If your application needs to be notified when a vector changes, it can allocate a uniqueclientidentifierfor 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, ClientDataclientData, Blt_VectorNotifynotify);ClientDatais passed to this routine whenever it is called. You can use this to pass information to the call-back. Thenotifyargument 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_AllocVectorIdSynopsis: Blt_VectorIdBlt_AllocVectorId(interp,vecName) Tcl_Interp *interp; char *vecName; Description: Allocates an client identifier for with the vectorvec-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. IfvecNameis not the name of a vector, then NULL is returned andinterp->resultwill contain an error message.Blt_GetVectorByIdSynopsis: intBlt_GetVector(interp,clientId,vecPtrPtr) Tcl_Interp *interp; Blt_VectorIdclientId; Blt_Vector **vecPtrPtr; Description: Retrieves the vector used byclientId.ClientIdis a valid vector client identifier allocated by Specifies a call-back routine to be called whenever the vector associated withclientIdis updated or deleted.Procis a pointer to call-back routine and must be of the typeBlt_VectorChangedProc.ClientDatais a one- word value to be passed to the routine when it is invoked. Ifprocis 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_FreeVectorIdSynopsis: voidBlt_FreeVectorId(clientId); Blt_VectorIdclientId; 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_NameOfVectorIdSynopsis: char *Blt_NameOfVectorId(clientId); Blt_VectorIdclientId; Description: Retrieves the name of the vector associated with the client identifierclientId. Results: Returns the name of the vector associated withclientId. IfclientIdis not an identifier or the vector has been destroyed, NULL is returned.Blt_InstallIndexProcSynopsis: voidBlt_InstallIndexProc(indexName,procPtr) char *indexName; Blt_VectorIndexProc *procPtr; Description: Registers a function to be called to retrieved the indexindexNamefrom the vector's array variable. typedef double Blt_VectorIndexProc(Vector *vecPtr); The function will be passed a pointer to the vector. reset shortly. The vector is updated whenlt_ResetVectoris 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 = (dou- ble *)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; }

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 vectorx(10)setx(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.

vector, graph, widget BLT BLT_VERSION blt::vector(n)

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