Tcl does many things well, but handling collections of numbers is not one of them. You could make lists, but for data sets of sizes relevant to scientific graphics which is the primary domain of applicability for PLplot, the extraction time is excessive and burdensome. You could use Tcl arrays, but the storage overhead is astronomical and the lookup time, while better than list manipulation, is still prohibitive.
To cope with this, a Tcl Matrix extension has been created for the purpose of making it feasible to work with large collections of numbers in Tcl, in a way which is storage efficient, reasonably efficient for accesses from Tcl, and reasonably compatible with practices used in compiled code.
Much like the Tk widget creation commands, the Tcl matrix
command considers its first argument to be the name of a new command
to be created, and the rest of the arguments to be modifiers. After
the name, the next argument can be float
or
int
or
contractions thereof. Next follow a variable number of size arguments
which determine the size of the matrix in each of its dimensions. For
example:
matrix x f 100 matrix y i 64 64
constructs two matrices. x
is a float matrix, with one
dimension and 100 elements. y
is an integer matrix, and has 2
dimensions each of size 64.
Additionally a matrix can be initialized when it is created, e.g.,
matrix x f 4 = { 1.5, 2.5, 3.5, 4.5 }
The matrix
command supports subcommands such as
info
which reports the number of elements in each dimension, e.g.,
pltcl> matrix x f 4 pltcl> x info 4 pltcl> matrix y i 8 10 pltcl> y info 8 10
Other useful subcommands are delete
to delete the
matrix (if, for example, you wanted to use that variable name for
something else such as a differently dimensioned matrix) and
help
to document all subcommands possible with
a given matrix.
A Tcl matrix is a command, and as longtime Tcl users know, Tcl
commands are globally accessible. The PLplot Tcl Matrix extension
attempts to lessen the impact of this by registering a variable in the
local scope, and tracing it for insets, and deleting the actual
matrix command when the variable goes out of scope. In this way, a
Tcl matrix appears to work sort of like a variable. It is, however,
just an illusion, so you have to keep this in mind. In particular,
you may want the matrix to outlive the scope in which it was created.
For example, you may want to create a matrix, load it with data, and
then pass it off to a Tk megawidget for display in a spreadsheet like
form. The proc which launches the Tk megawidget will complete, but
the megawidget, and the associated Tcl matrix are supposed to hang
around until they are explicitly destroyed. To achieve this effect,
create the Tcl matrix with the -persist
flag. If present
(can be anywhere on the line), the matrix is not automatically deleted
when the scope of the current proc (method) ends. Instead, you must
explicitly clean up by using either the 'delete' matrix command or renaming
the matrix command name to {}. Now works correctly from within [incr Tcl].
As mentioned above, the result of creating a matrix is that a new command of the given name is added to the interpreter. You can then evaluate the command, providing indices as arguments, to extract the data. For example:
pltcl> matrix x f = {1.5, 2.5, 3.5, 4.5} insufficient dimensions given for Matrix operator "x" pltcl> matrix x f 4 = {1.5, 2.5, 3.5, 4.5} pltcl> x 0 1.500000 pltcl> x 1 2.500000 pltcl> x 3 4.500000 pltcl> x : 1.500000 2.500000 3.500000 4.500000 pltcl> puts "x\[1\]=[x 1]" x[1]=2.500000 pltcl> puts "x\[:\] = [x :]" x[:] = 1.500000 2.500000 3.500000 4.500000 pltcl> foreach v [x *] { puts $v } 1.500000 2.500000 3.500000 4.500000 pltcl> for {set i 0} {$i < 4} {incr i} { if {[x $i] < 3} {puts [x $i]} } 1.500000 2.500000
Note from the above that the output of evaluating a matrix indexing operation is suitable for use in condition processing, list processing, etc.
You can assign to matrix locations in a similar way:
pltcl> x 2 = 7 pltcl> puts "[x :]" 1.500000 2.500000 7.000000 4.500000 pltcl> x : = 3 pltcl> puts "[x :]" 3.000000 3.000000 3.000000 3.000000
Note that the : provides a means of obtaining an index range,
and that it must be separated from the = by a space. This is a simple
example of matrix index slices, and a full index slice capability has
been implemented following what is available for Python (see Note 5 of
https://docs.python.org/2/library/stdtypes.html#sequence-types-str-unicode-list-tuple-bytearray-buffer-xrange
for Python 2 or Note 5 of https://docs.python.org/3/library/stdtypes.html#common-sequence-operations
for Python 3). Each index slice is represented by a colon-separated
list of three integers, i:j:k, which designate the index range and
increment. The default value of k is 1. For positive k the default
values of i and j are 0 and the number of elements in the dimension while for
negative k, the default values of i and j the number of elements in the dimension
and 0. Negative values of i and j have the number of elements in the dimension
added to them. After these rules have been applied to determine the
final i, j, and k values the slice from i to j with step k is defined
as the sequence of items with index x = i + n*k such that 0 ≤ n
< (j-i)/k. N.B. rational division is used to calculate the last
limit of this expression. As a result the indices in the slice are i,
i+k, i+2*k, i+3*k and so on, stopping when j is reached (but never
including j). Some examples (see
bindings/tcl/test_tclmatrix.tcl
) of using this
slice notation are given by the following Tcl code:
puts "Create one-dimensional x matrix using \"matrix x f 4 = {0., 1., 2., 3.}\"" matrix x f 4 = {0., 1., 2., 3.} puts "Various start:stop:step slice examples for this matrix" puts "Examples where start, stop, and step are default" puts "\[x :\] yields [x :]" puts "\"*\" (implemented for backwards compatibility) has exactly the same effect as \":\"" puts "\[x *\] yields [x *]" puts "\"::\" has exactly the same effect as \":\"" puts "\[x ::\] yields [x ::]" puts "Examples where start and stop are default" puts "\[x ::1\] yields [x ::1]" puts "\[x ::2\] yields [x ::2]" puts "\[x ::3\] yields [x ::3]" puts "\[x ::4\] yields [x ::4]" puts "\[x ::-1\] yields [x ::-1]" puts "\[x ::-2\] yields [x ::-2]" puts "\[x ::-3\] yields [x ::-3]" puts "\[x ::-4\] yields [x ::-4]" puts "Examples where start and step are default" puts "\[x :2:\] yields [x :2:]" puts "\[x :2\] yields [x :2]" puts "Examples where stop and step are default" puts "\[x 2::\] yields [x 2::]" puts "\[x 2:\] yields [x 2:]" puts "Examples where start is default" puts "\[x :3:2\] yields [x :3:2]" puts "\[x :-4:-2\] yields [x :-4:-2]" puts "Examples where stop is default" puts "\[x 1::2\] yields [x 1::2]" puts "\[x -2::-2\] yields [x -2::-2]" puts "Examples where step is default" puts "\[x 1:3:\] yields [x 1:3:]" puts "\[x 1:3\] yields [x 1:3]" puts "Examples where start, stop, and step are all explicitly specified" puts "\[x 1:0:2\] yields [x 1:0:2]" puts "\[x 1:1:2\] yields [x 1:1:2]" puts "\[x 1:2:2\] yields [x 1:2:2]" puts "\[x 1:3:2\] yields [x 1:3:2]" puts "\[x 1:4:2\] yields [x 1:4:2]" puts "\[x 1:5:2\] yields [x 1:5:2]" puts "\[x -2:-1:-2\] yields [x -2:-1:-2]" puts "\[x -2:-2:-2\] yields [x -2:-2:-2]" puts "\[x -2:-3:-2\] yields [x -2:-3:-2]" puts "\[x -2:-4:-2\] yields [x -2:-4:-2]" puts "\[x -2:-5:-2\] yields [x -2:-5:-2]" puts "\[x -2:-6:-2\] yields [x -2:-6:-2]"
which generates (see bindings/tcl/test_tclmatrix.out
)
the following results:
Create one-dimensional x matrix using "matrix x f 4 = {0., 1., 2., 3.}" Various start:stop:step slice examples for this matrix Examples where start, stop, and step are default [x :] yields 0.0 1.0 2.0 3.0 "*" (implemented for backwards compatibility) has exactly the same effect as ":" [x *] yields 0.0 1.0 2.0 3.0 "::" has exactly the same effect as ":" [x ::] yields 0.0 1.0 2.0 3.0 Examples where start and stop are default [x ::1] yields 0.0 1.0 2.0 3.0 [x ::2] yields 0.0 2.0 [x ::3] yields 0.0 3.0 [x ::4] yields 0.0 [x ::-1] yields 3.0 2.0 1.0 0.0 [x ::-2] yields 3.0 1.0 [x ::-3] yields 3.0 0.0 [x ::-4] yields 3.0 Examples where start and step are default [x :2:] yields 0.0 1.0 [x :2] yields 0.0 1.0 Examples where stop and step are default [x 2::] yields 2.0 3.0 [x 2:] yields 2.0 3.0 Examples where start is default [x :3:2] yields 0.0 2.0 [x :-4:-2] yields 3.0 1.0 Examples where stop is default [x 1::2] yields 1.0 3.0 [x -2::-2] yields 2.0 0.0 Examples where step is default [x 1:3:] yields 1.0 2.0 [x 1:3] yields 1.0 2.0 Examples where start, stop, and step are all explicitly specified [x 1:0:2] yields [x 1:1:2] yields [x 1:2:2] yields 1.0 [x 1:3:2] yields 1.0 [x 1:4:2] yields 1.0 3.0 [x 1:5:2] yields 1.0 3.0 [x -2:-1:-2] yields [x -2:-2:-2] yields [x -2:-3:-2] yields 2.0 [x -2:-4:-2] yields 2.0 [x -2:-5:-2] yields 2.0 0.0 [x -2:-6:-2] yields 2.0 0.0
We have already shown examples of matrix initialization above
where the RHS (right hand side) expression beyond the "=" sign was a
simple list of numbers and also an example of an matrix slice
assignment above where the RHS was a simple number, but much more
complex RHS expressions (arbitrary combinations of lists of lists and
matrix slices) are allowed for both matrix initialization and matrix
slice assignment. Furthermore, the RHS matrices are read from and the
LHS (left hand side) matrix or matrix slice are written to in row major order,
and excess elements on the RHS are ignored while excess
elements on the LHS of a matrix initialization or matrix slice
assignment are zeroed. Some examples (see
bindings/tcl/test_tclmatrix.tcl
) of using these
matrix initialization and matrix slice assignment capabilities are
given by the following Tcl code:
puts "Various matrix initializations and assignments" puts "Using a collection of space-separated numbers" matrix x f 4 = 1 2 3 4 puts "\[x :\] = [x :]" matrix y f 2 4 y : : = 1 2 3 4 5 6 7 8 puts "\[y : :\] = [y : :]" x delete y delete puts "Using a list of lists of numbers" matrix x f 4 = {{{1 2}} {3 4}} puts "\[x :\] = [x :]" matrix y f 2 4 y : : = {{1 2 3 4 5} {{6}} {7 8}} puts "\[y : :\] = [y : :]" puts "Using slices of a previously defined matrix" matrix z f 2 2 2 = [x ::] [x ::-1] puts "\[z : : :\] = [z : : :]" y : : = [x ::] [x ::-1] puts "\[y : :\] = [y : :]" puts "Combination of previously defined matrices, deep lists, and space-separated numbers" matrix a f 2 2 3 = [x ::] [x ::-1] {{{1.E-13} {2}}} 3 4 5 6 7 8 9 10 11 12 13 14 puts "\[a : : :\] = [a : : :]" matrix b f 2 2 3 b : : : = [x ::] [x ::-1] {{{1.E-13} {2}}} 3 4 5 6 7 8 9 10 11 12 13 14 puts "\[b : : :\] = [b : : :]"
which generates (see bindings/tcl/test_tclmatrix.out
)
the following results:
Various matrix initializations and assignments Using a collection of space-separated numbers [x :] = 1.0 2.0 3.0 4.0 [y : :] = 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 Using a list of lists of numbers [x :] = 1.0 2.0 3.0 4.0 [y : :] = 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 Using slices of a previously defined matrix [z : : :] = 1.0 2.0 3.0 4.0 4.0 3.0 2.0 1.0 [y : :] = 1.0 2.0 3.0 4.0 4.0 3.0 2.0 1.0 Combination of previously defined matrices, deep lists, and space-separated numbers [a : : :] = 1.0 2.0 3.0 4.0 4.0 3.0 2.0 1.0 1e-13 2.0 3.0 4.0 [b : : :] = 1.0 2.0 3.0 4.0 4.0 3.0 2.0 1.0 1e-13 2.0 3.0 4.0
A method of testing the matrix slice, initialization, and assignment capabilities using
bindings/tcl/test_tclmatrix.tcl
and
bindings/tcl/test_tclmatrix.out
has been given
in examples/tcl/README.tcldemos
.
Normally you will create a matrix in Tcl, and then want to pass it to
C in order to have the data filled in, or existing data to be used in
a computation, etc. To do this, pass the name of the matrix command
as an argument to your C Tcl command procedure. The C code should
include tclMatrix.h
, which has a definition for the
tclMatrix
structure. You fetch a pointer to the
tclMatrix
structure using the
Tcl_GetMatrixPtr
function.
For example, in Tcl:
matrix x f 100 wacky x
and in C:
int wackyCmd( ClientData clientData, Tcl_Interp *interp, int argc, char *argv[] ) { tclMatrix *w; w = Tcl_GetMatrixPtr( interp, argv[1] ); ...
To learn about what else you can do with the matrix once inside
compiled code, read tclMatrix.h
to learn the definition of the
tclMatrix
structure, and see the examples in files like
tclAPI.c
which show many various uses of the Tcl matrix.
Using a Tcl matrix from C++ is very much like using it from C, except
that tclMatrix.h
contains some C++ wrapper classes which are
somewhat more convenient than using the indexing macros which one has
to use in C. For example, here is a tiny snippet from one of the
authors codes in which Tcl matrices are passed in from Tcl to a C++
routine which is supposed to fill them in with values from some
matrices used in the compiled side of the code:
... if (item == "vertex_coords") { tclMatrix *matxg = Tcl_GetMatrixPtr( interp, argv[1] ); tclMatrix *matyg = Tcl_GetMatrixPtr( interp, argv[2] ); Mat2<float> xg(ncu, ncv), yg(ncu, ncv); cg->Get_Vertex_Coords( xg, yg ); TclMatFloat txg( matxg ), tyg( matyg ); for( i=0; i < ncu; i++ ) for( j=0; j < ncv; j++ ) { txg(i,j) = xg(i,j); tyg(i,j) = yg(i,j); }
There are other things you can do too, see the definitions of the
TclMatFloat
and TclMatInt
classes in
tclMatrix.h
.
The Tcl matrix facility provides creation, indexing, and information
gathering facilities. However, considering the scientifically
inclined PLplot user base, it is clear that some users will demand
more. Consequently there is a mechanism for augmenting the Tcl matrix
facility with your own, user defined, extension subcommands. Consider
xtk04.c
. In this extended wish, we want to be able to
determine the minimum and maximum values stored in a matrix. Doing
this in Tcl would involve nested loops, which in Tcl would be
prohibitively slow. We could register a Tcl extension command to do
it, but since the only sensible data for such a command would be a
Tcl matrix, it seems nice to provide this facility as an actual
subcommand of the matrix. However, the PLplot maintainers cannot
foresee every need, so a mechanism is provided to register subcommands
for use with matrix objects.
The way to register matrix extension subcommands is to call
Tcl_MatrixInstallXtnsn
:
typedef int (*tclMatrixXtnsnProc) ( tclMatrix *pm, Tcl_Interp *interp, int argc, char *argv[] ); int Tcl_MatrixInstallXtnsn( char *cmd, tclMatrixXtnsnProc proc );
In other words, make a function for handling the matrix extension
subcommand, with the same function signature (prototype) as
tclMatrixXtnsnProc
, and register the subcommand name along with
the function pointer. For example, xtk04.c has:
int mat_max( tclMatrix *pm, Tcl_Interp *interp, int argc, char *argv[] ) { float max = pm->fdata[0]; int i; for( i=1; i < pm->len; i++ ) if (pm->fdata[i] > max) max = pm->fdata[i]; sprintf( interp->result, "%f", max ); return TCL_OK; } int mat_min( tclMatrix *pm, Tcl_Interp *interp, int argc, char *argv[] ) { float min = pm->fdata[0]; int i; for( i=1; i < pm->len; i++ ) if (pm->fdata[i] < min) min = pm->fdata[i]; sprintf( interp->result, "%f", min ); return TCL_OK; }
Then, inside the application initialization function
(Tcl_AppInit()
to long time Tcl users):
Tcl_MatrixInstallXtnsn( "max", mat_max ); Tcl_MatrixInstallXtnsn( "min", mat_min );
Then we can do things like:
dino 65: xtk04 % matrix x f 4 = {1, 2, 3, 1.5} % x min 1.000000 % x max 3.000000
Your imagination is your only limit for what you can do with this. You could add an FFT subcommand, matrix math, BLAS, whatever.