- Vector
- abs · add · addrand · append · apply · as_numpy · at · buffer_size · c · cl · contains · convlv · copy · correl · deriv · div · dot · eq · fft · fill · filter · fit · floor · fread · from_double · from_python · fwrite · get · hist · histogram · ind · index · indgen · indvwhere · indwhere · inf · insrt · integral · label · line · log · log10 · mag · mark · max · max_ind · mean · meansqerr · medfltr · median · min · min_ind · mul · play · play_remove · plot · ploterr · pow · printf · psth · rebin · record · reduce · remove · resample · resize · reverse · rotate · scale · scanf · scantil · set · setrand · sin · size · smhist · sort · sortindex · spctrm · spikebin · sqrt · stderr · stdev · sub · sum · sumgauss · sumsq · tanh · to_python · trigavg · var · vread · vwrite · where · x
Vector
- class Vector
This class was implemented by
----------------------------- Zach Mainen and Michael Hines -----------------------------
- Syntax:
obj = h.Vector()
obj = h.Vector(size)
obj = h.Vector(size, init)
obj = h.Vector(python_iterable)
Description:
NEURON’s Vector class provides functionality that is similar (and partly interchangeable) with a numpy one-dimensional array of doubles. The reason for the continued use of Vector is both due to back-compatibility and due to the many faster C-level extensions that have been written as NMOD programs that make use of this class.
A Vector is itself an iterable and can be used in any context that takes an iterable, e.g.,
for x in vec: print(x) [x for x in vec] numpy.array(vec)
A Vector object created with this class can be thought of as containing a one dimensional x array with elements of type float. The
objref[index]
notation can be used to read and set Vector elements (setting requires NEURON 7.7+). An older syntaxobjref.x[index]
works on all Python-supporting versions of NEURON.Beginning with NEURON 9.0 Vectors support slicing; e.g.:
vec = h.Vector([0, 1, 2, 3, 4, 5, 6, 7, 8]) new_vec = v[2:6]
will assign new_vec as a vector containing the values [2, 3, 4, 5]
vec[5:7] = [1, 2]
will update the values at indices 5,6 resulting in
vec = [0, 1, 2, 3, 4, 1, 2, 7, 8]
A vector can be created with length size and with each element set to the value of init or can be created using a Python iterable.
Vector methods that modify the elements are generally of the form
obj = vsrcdest.method(...)
in which the values of vsrcdest on entry to the method are used as source values by the method to compute values which replace the old values in vsrcdest. The return value is simply an additional reference to the same Vector.
Beginning with NEURON 7.7, Vectors support arithmetic operations; e.g. one can write
v1 = v2*s2 + v3*s3 + v4*s4
.Note
In older code, you may see the use of the arithmetic functions add, mul, etc. Those functions changed the vectors they operated on, so to avoid this, the .c() method was used to create a new copy of a vector. The expression that can now be written
v1 = v2*s2 + v3*s3 + v4*s4
using the older form would be written asv1 = v2.c().mul(s2).add(v3.c().mul(s3)).add(v4.c().mul(s4))
Examples:
vec = h.Vector(20,5)
will create a vector with 20 indices, each having the value of 5.
vec1 = h.Vector()
will create a vector with 0 size. It is seldom necessary to specify a size for a Vector since most operations, if necessary, increase or decrease the number of elements as needed.
v = h.Vector([1, 2, 3])
will create a vector of length 3 whose entries are: 1, 2, and 3. The constructor takes any Python iterable. In particular, it also works with numpy arrays:
import numpy x = numpy.linspace(0, 2 * numpy.pi, 50) y = h.Vector(numpy.sin(x))
produces a vector
y
of length 50 corresponding to the sine of evenly spaced points between 0 and 2 pi, inclusive.See also
- Vector.x
- Syntax:
vec.x[index]
- Description:
Elements of a vector can be accessed with
vec.x[index]
notation for either access or assignment. Vector indices range from 0 to len(Vector)-1 Vector contents can also be accessed withvec.get(index)
or set withvec.set(index, value)
This is not recommended for new code; use vec[index] instead.
- Example:
print(vec.x[0], vec[0])
prints the value of the 0th (first) element twice.vec.x[i] = 3
sets the i’th element to 3. Beginning with NEURON 7.7, it suffices to writevec[i] = 3
instead.h.xpanel("show a field editor") h.xpvalue("last element", vec._ref_x[len(vec)-1]) h.xpanel()
Note, however, that there is a potential difficulty with the
xpvalue()
field editor since, if vec is resized to be larger than vec.buffer_size() a reallocation of the memory will cause the pointer to be invalid. In this case, the field editor will display the string, “Free’d”.
Warning
vec.x[-1]
orvec[-1]
return or set the value of the last element of the vector butvec._ref_x
cannot be accessed in this way.
- Vector.size()
- Syntax:
size = vec.size()
- Description:
Deprecated in favor of len(vec); note that
len(vec) == vec.size()
Return the number of elements in the vector. The last element has the index:vec.size() - 1
which can be abbreviated using -1 as above.for i in range(vec.size()): print(vec[i])
Note
for
loops can also use Vector as an iterablefor item in vec: print(item)
Note
There is a distinction between the size of a vector and the amount of memory allocated to hold the vector. Generally, memory is only freed and reallocated if the size needed is greater than the memory storage previously allocated to the vector. Thus the memory used by vectors tends to grow but not shrink. To reduce the memory used by a vector, one can explicitly call
buffer_size()
.See also
- Vector.resize()
- Syntax:
obj = vsrcdest.resize(new_size)
- Description:
Resize the vector. If the vector is made smaller, then trailing elements will be zeroed. If it is expanded, the new elements will be initialized to 0.0; original elements will remain unchanged.
Warning: Any function that resizes the vector to a larger size than its available space will reallocate and thereby make existing pointers to the elements invalid (see note in
Vector.size()
). For example, resizing vectors that have been plotted will remove that vector from the plot list. Other functions may not be so forgiving and result in a memory error (segmentation violation or unhandled exception).
Example:
vec = h.Vector(20,5) vec.resize(30) # Appends 10 elements, each having a value of 0 vec.printf() vec.resize(10) # removes the last 20 elements; values of the first 10 elements are unchanged
See also
- Vector.buffer_size()
- Syntax:
space = vsrc.buffer_size()
space = vsrc.buffer_size(request)
- Description:
Returns the length of the double precision array memory allocated to hold the vector. This is NOT the size of the vector. The vector size can efficiently grow up to this value without reallocating memory.
With an argument, frees the old memory space and allocates new memory space for the vector, copying old element values to the new elements. If the request is less than the size, the size is truncated to the request. For vectors that grow continuously, it may be more efficient to allocate enough space at the outset, or else occasionally change the buffer_size by larger chunks. It is not necessary to worry about the efficiency of growth during a Vector.record since the space available automatically increases by doubling.
Example:
y = h.Vector(10) print(len(y)) print(y.buffer_size()) y.resize(5) print(len(y)) print(y.buffer_size()) print(y.buffer_size(100)) print(len(y))
- Vector.get()
- Syntax:
x = vec.get(index)
- Description:
Return the value of a vector element index.
- Vector.set()
- Syntax:
obj = vsrcdest.set(index,value)
- Description:
Set vector element index to value. Equivalent to
vec[i] = expr
notation.
- Vector.fill()
- Syntax:
obj = vsrcdest.fill(value)
obj = vsrcdest.fill(value, start, end)
- Description:
The first form assigns value to every element in vsrcdest.
If start and end arguments are present, they specify the index range for the assignment.
Example:
vec = h.Vector(20,5) vec.fill(9,2,7)
assigns 9 to vec[2] through vec[7] (a total of 6 elements)
See also
- Vector.label()
- Syntax:
s = vec.label()
s = vec.label(str_type)
- Description:
Label the vector with a string. The return value is the label, which is an empty string if no label has been set. Labels are printed on a Graph when the
Graph.plot()
method is called.
Example:
from neuron import h vec = h.Vector() print(vec.label()) vec.label("hello") print(vec.label())
See also
- Vector.record()
- Syntax:
vdest = vdest.record(var_reference)
vdest = vdest.record(var_reference, Dt)
vdest = vdest.record(var_reference, tvec)
vdest = vdest.record(point_process_object, var_reference, ...)
- Description:
Save the stream of values of “var” during a simulation into the vdest vector. Previous record and play specifications of this Vector (if any) are destroyed.
Details: NEURON pointers in python are handled using the _ref_ syntax. e.g., soma(0.5)._ref_v
To save a scalar from NEURON that scalar must exist in NEURON’s scope.
Transfers take place on exit from
finitialize()
and on exit fromfadvance()
. At the end offinitialize()
,v[0] = var
. At the end offadvance
, var will be saved ift
(after being incremented byfadvance
) is equal or greater than the associated time of the next index. The system maintains a set of record vectors and the vector will be removed from the list if the vector or var is destroyed. The vector is automatically increased in size by 100 elements at a time if more space is required, so efficiency will be slightly improved if one creates vectors with sufficient size to hold the entire stream, and plots will be more persistent (recall that resizing may cause reallocation of memory to hold elements and this will make pointers invalid).The record semantics can be thought of as:
var(t) -> v[index]
The default relationship between
index
andt
ist = index*dt
.In the second form,
t = index*Dt
.In the third form,
t = tvec[index]
.For the local variable timestep method,
CVode.use_local_dt()
and/or multiple threads,ParallelContext.nthread()
, it is often helpful to provide specific information about which cell the var pointer is associated with by inserting as the first arg some POINT_PROCESS object which is located on the cell. This is necessary if the pointer is not a RANGE variable and is much more efficient if it is. The fixed step and global variable time step method do not need or use this information for the local step method but will use it for multiple threads. It is therefore a good idea to supply it if possible.Prior to version 7.7, the record methode returned 1.0 .
Warning
record/play behavior is reasonable but surprising if
dt
is greater thanDt
. Things work best ifDt
happens to be a multiple ofdt
. All combinations of record ; play ;Dt =>< dt
; and tvec sequences have not been tested.Example:
If NEURON has loaded its standard run library, the time course of membrane potential in the
middle of a section called “terminal” can be captured to a vector called dv by
dv = h.Vector().record(terminal(0.5)._ref_v) h.run()
Note that the next “run” will overwrite the previous time course stored in the vector as it automatically performs an “init” before running a simulation.
- Thus dv should be copied to another vector ( see
copy()
). To remove dv from the list of record vectors, the easiest method is to destroy the instance with
dv = h.Vector()
Any of the following makes NEURON load its standard run library:
starting NEURON by executing nrngui -python
executing any of the following statements: - from neuron import gui # also brings up the NEURON Main Menu - h.load_file(“noload.hoc”) # does not bring up the NEURON Main Menu - h.load_file(“stdrun.hoc”) # does not bring up the NEURON Main Menu
See also
- Vector.play()
- Syntax:
vdest = vsrc.play(var_reference, Dt)
vdest = vsrc.play(var_reference, tvec)
vdest = vsrc.play(index)
vdest = vsrc.play(var_reference or stmt, tvec, continuous)
vdest = vsrc.play(var_reference or stmt, tvec, indices_of_discontinuities_vector)
vdest = vsrc.play(point_process_object, var_reference, ...)
- Description:
The
vsrc
vector values are assigned to the “var” variable during a simulation.The same vector can be played into different variables.
The index form immediately sets the var (or executes the stmt) with the value of vsrc[index]
The play semantics can be thought of as
v[index] -> var(t)
where t(index) is Dt*index or tvec[index] The discrete event delivery system is used to determine the precise time at which values are copied from vsrc to var. Note that for variable step methods, unless continuity is specifically requested, the function is a step function. Also, for the local variable dt method, var MUST be associated with the cell that contains the section accessed via sec=sec in the arg list (but see the paragraph below about the use of a point_process_object inserted as the first arg).For the fixed step method, transfers take place on entry to
finitialize()
and on entry tofadvance()
. At the beginning offinitialize()
,var = v[0]
. Onfadvance()
a transfer will take place if t will be equal or greater than the associated time of the next index after thefadvance
increment.- For the variable step methods, transfers take place exactly at the times specified by the Dt
or tvec arguments.
The system maintains a set of play vectors and the vector will be removed from the list if the vector or var is destroyed. If the end of the vector is reached, no further transfers are made (
var
becomes constant)Note well: for the fixed step method, if
fadvance
exits with time equal tot
(ie enters at time t-dt), then on entry tofadvance
, var is set equal to the value of the vector at the index appropriate to time t. Execute tests/nrniv/vrecord.py to see what this implies during a simulation. ie the value of var fromt-dt
to t played into by a vector is equal to the value of the vector atindex(t)
. If the vector was meant to serve as a continuous stimulus function, this results in a first order correct simulation with respect to dt. If a second order correct simulation is desired, it is necessary (though perhaps not sufficient since all other equations in the system must also be solved using methods at least second order correct) to fill the vector with function values at f((i-.5)*dt).When continuous is 1 then linear interpolation is used to define the values between time points. However, events at each Dt or tvec are still used and that has beneficial performance implications for variable step methods since vsrc is equivalent to a piecewise linear function and variable step methods can excessively reduce dt as one approaches a discontinuity in the first derivative. Note that if there are discontinuities in the function itself, then tvec should have adjacent elements with the same time value. When a value is greater than the range of the t vector, linear extrapolation of the last two points is used instead of a constant last value. If a constant outside the range is desired, make sure the last two points have the same y value and have different t values (if the last two values are at the same time, the constant average will be returned).
The indices_of_discontinuities_vector argument is used to specifying the indices in tvec of the times at which discrete events should be used to notify that a discontinuity in the function, or any derivative of the function, occurs. Presently, linear interpolation is used to determine var(t) in the interval between these discontinuities (instead of cubic spline) so the length of steps used by variable step methods near the breakpoints depends on the details of how the parameter being played into affects the states.
For the local variable timestep method,
CVode.use_local_dt()
and/or multiple threads,ParallelContext.nthread()
, it is often helpful to provide specific information about which cell the var pointer is associated with by inserting as the first arg some POINT_PROCESS object which is located on the cell. This is necessary if the pointer is not a RANGE variable and is much more efficient if it is. The fixed step and global variable time step method do not need or use this information for the local step method but will use it for multiple threads. It is therefore a good idea to supply it if possible.Prior to version 7.7, the play method returned 1.0 .
See also
Example of playing into an Iclamp for varying current:
from neuron import h import pylab as plt, numpy as np h.load_file('stdrun.hoc') sec = h.Section(name='sec') sec.insert(h.pas) inp = np.zeros(500) inp[50:250] = 1 pvec = h.Vector().from_python(inp) stim = h.IClamp(sec(0.5)) stim.dur = 1e9 pvec.play(stim, stim._ref_amp, True) rd = {k:h.Vector().record(v) for k,v in zip(['t', 'v', 'stim_i', 'amp'], [h._ref_t, sec(0.5)._ref_v, stim._ref_i, stim._ref_amp])} h.v_init, h.tstop= -70, 500 h.run() plt.plot(rd['t'], rd['v']) plt.show()
Example of playing into a segment’s ina:
from neuron import h, gui import numpy # create a geometry soma = h.Section(name='soma') # insert variables for sodium ions soma.insert('na_ion') # driving stimulus t = h.Vector(numpy.linspace(0, 2 * numpy.pi, 50)) y = h.Vector(numpy.sin(t)) # play the stimulus into soma(0.5)'s ina # the last True means to interpolate; it's not the default, but unless # you know what you're doing, you probably want to pass True there y.play(soma(0.5)._ref_ina, t, True) # setup a graph g = h.Graph() g.addvar("ina", soma(0.5)._ref_ina) g.size(0, 6.28, -1, 1) h.graphList[0].append(g) # run the simulation h.finitialize(-65) h.continuerun(6.28)
A runnable example of using this method for a time-varying current clamp is available here.
- Vector.play_remove()
- Syntax:
v.play_remove()
- Description:
Removes the vector from BOTH record and play lists. Note that the vector is automatically removed if the variable which is recorded or played is destroyed or if the vector is destroyed. This function is used in those cases where one wishes to keep the vector data even under subsequent runs.
See also
- Vector.indgen()
- Syntax:
obj = vsrcdest.indgen()
obj = vsrcdest.indgen(stepsize)
obj = vsrcdest.indgen(start,stepsize)
obj = vsrcdest.indgen(start,stop,stepsize)
- Description:
Fill the elements of a vector with a sequence of values. With no arguments, the sequence is integers from 0 to (size-1).
With only stepsize passed, the sequence goes from 0 to stepsize**(size-1) in steps of *stepsize. Stepsize does not have to be an integer.
With start, stop and stepsize, the vector is resized to be 1 + (stop - $varstart)/stepsize long and the sequence goes from start up to and including stop in increments of stepsize.
Example:
vec = h.Vector(100) vec.indgen(5)
creates a vector with 100 elements going from 0 to 495 in increments of 5.
vec.indgen(50, 100, 10)
reduces the vector to 6 elements going from 50 to 100 in increments of 10.
vec.indgen(90, 1000, 30)
expands the vector to 31 elements going from 90 to 990 in increments of 30.
See also
- Vector.append()
- Syntax:
obj = vsrcdest.append(vec1, vec2, ...)
- Description:
Concatenate values onto the end of a vector. The arguments may be either scalars or vectors. The values are appended to the end of the
vsrcdest
vector.
Example:
vec = h.Vector(10,4) vec1 = h.Vector(10,5) vec2 = h.Vector(10,6) vec.append(vec1, vec2, 7, 8, 9) vec.append(h.Vector([4,1,2,7]))
turns
vec
into a 37 element vector, whose first ten elements = 4, whose second ten elements = 5, whose third ten elements = 6, and whose 31st, 32nd, and 33rd elements = 7, 8, and 9, and 34-37 are 4,1,2,7. Note that the Vector created to pass the Python listinto append is immediately discarded. Remember, index 32 refers to the 33rd element.
- Vector.insrt()
- Syntax:
obj = vsrcdest.insrt(index, vec1, vec2, ...)
- Description:
Inserts values before the index element. The arguments may be either scalars or vectors.
obj.insrt(obj.size, ...)
is equivalent toobj.append(...)
- Vector.remove()
- Syntax:
obj = vsrcdest.remove(index)
obj = vsrcdest.remove(start, end)
- Description:
Remove the indexed element (or inclusive range) from the vector. The vector is resized.
- Vector.contains()
- Syntax:
numerical_truth_value = vsrc.contains(value)
- Description:
Return whether or not the vector contains value as at least one of its elements (to within
float_epsilon
). It returns True if the value is found; otherwise
it returns False. (In NEURON 7.5 and before, this method returned 1 or 0 instead of True or False, respectively.)
Example:
vec = h.Vector(range(0, 49, 5)) vec.contains(30)
returns True, meaning the vector does contain an element whose value is 30.
vec.contains(50)
returns False. The vector does not contain an element whose value is 50.
Note
An h.Vector is a Python iterable, so you can also use Python’s
in
keyword:5 in h.Vector([1, 5])
returns True.
- Vector.copy()
- Syntax:
obj = vdest.copy(vsrc)
obj = vdest.copy(vsrc, dest_start)
obj = vdest.copy(vsrc, src_start, src_end)
obj = vdest.copy(vsrc, dest_start, src_start, src_end)
obj = vdest.copy(vsrc, dest_start, src_start, src_end, dest_inc, src_inc)
obj = vdest.copy(vsrc, vsrcdestindex)
obj = vdest.copy(vsrc, vsrcindex, vdestindex)
- Description:
Copies some or all of vsrc into vdest. If the dest_start argument is present (an integer index), source elements (beginning at src*``[0]``) are copied to *vdest beginning at dest*``[dest_start]``, *Src_start and src_end here refer to indices of vsrcx, not vdest. If vdest is too small for the size required by vsrc and the arguments, then it is resized to hold the data. If the dest is larger than required AND there is more than one argument the dest is NOT resized. One may use -1 for the src_end argument to specify the entire size (instead of the tedious
len(src)-1
)If the second (and third) argument is a vector, the elements of that vector are the indices of the vsrc to be copied to the same indices of the vdest. In this case the vdest is not resized and any indices that are out of range of either vsrc or vdest are ignored. This function allows mapping of a subset of a source vector into the subset of a destination vector.
This function can be slightly more efficient than
c()
since if vdest contains enough space, memory will not have to be allocated for it. Also it is convenient for those cases in which vdest is being plotted and therefore reallocation of memory (with consequent removal of vdest from the Graph) is to be explicitly avoided.- Example:
To copy the odd elements use:
v1 = h.Vector(range(30)) v1.printf() v2 = h.Vector() v2.copy(v1, 0, 1, -1, 1, 2) v2.printf()
To merge or shuffle two vectors into a third, use:
v1 = h.Vector(15) v1.indgen() v1.printf() v2 = h.Vector(15) v2.indgen(10) v2.printf() v3 = h.Vector() v3.copy(v1, 0, 0, -1, 2, 1) v3.copy(v2, 1, 0, -1, 2, 1) v3.printf()
Example:
vec = h.Vector(100,10) vec1 = h.Vector() vec1.indgen(5,105,10) vec.copy(vec1, 50, 3, 6)
turns
vec
from a 100 element into a 54 element vector. The first 50 elements will each have the value 10 and the last four will have the values 35, 45, 55, and 65 respectively.Warning
Vectors copied to themselves are not usually what is expected. eg.
vec = h.Vector(range(20)) vec.copy(vec, 10)
produces a 30 element vector cycling three times from 0 to 9. However the self copy may work if the src index is always greater than or equal to the destination index.
- Vector.c()
- Syntax:
newvec = vsrc.c()
newvec = vsrc.c(srcstart)
newvec = vsrc.c(srcstart, srcend)
- Description:
Return a h.Vector which is a copy of the vsrc Vector, but does not copy the label. For a complete copy including the label use
Vector.cl()
. (Identical to theVector.at()
function but has a short name that suggests copy or clone). Useful in the construction of filter chains.In versions of NEURON before 7.7, this was often used in building Vectors from other Vectors, e.g.
vec2 = vec1.c().add(1)
; in new code, it is recommended to use the shorter equivalentvec2 = vec1 + 1
.
- Vector.cl()
- Syntax:
newvec = vsrc.cl()
newvec = vsrc.cl(srcstart)
newvec = vsrc.cl(srcstart, srcend)
- Description:
Return a h.Vector which is a copy, including the label, of the vsrc vector. (Similar to the
Vector.c()
function which does not copy the label) Useful in the construction of filter chains. Note that with no arguments, it is not necessary to type the parentheses.
- Vector.at()
- Syntax:
newvec = vsrc.at()
newvec = vsrc.at(start)
newvec = vsrc.at(start,end)
- Description:
Return a h.Vector consisting of all or part of another.
This function predates the introduction of the vsrc.c, “clone”, function which is synonymous but is retained for backward compatibility.
It merely avoids the necessity of a
vdest = h.Vector()
command and is equivalent tovdest = h.Vector() vdest.copy(vsrc, start, end)
Example:
vec = h.Vector() vec.indgen(10,50,2) vec1 = vec.at(2, 10)
creates
vec1
with 9 elements which correspond to the values at indices 2 - 10 invec
. The contents ofvec1
would then be, in order: 14, 16, 18, 20, 22, 24, 26, 28, 30.
- Vector.from_double()
- Syntax:
obj = vdest.from_double(n, pointer)
- Description:
Resizes the vector to size n and copies the values from the double array to the vector.
Examples:
Interacting with a HOC array:
from neuron import h # create and populate a HOC array h('double px[5]') h.px[0] = 5 h.px[3] = 2 # transfer the data v.from_double(5, h._ref_px[0]) # print out the vector v.printf()
Copying from a numpy array into an existing vector:
from neuron import h import neuron import numpy a = numpy.array([5, 1, 6], 'd') v = h.Vector() v.from_double(3, neuron.numpy_element_ref(a, 0)) v.printf()
Note
To create a new vector from a numpy array just use
v = h.Vector(python_iterable)
.
- Vector.where()
- Syntax:
obj = vdest.where(vsource, opstring, value1)
obj = vdest.where(vsource, op2string, value1, value2)
obj = vsrcdest.where(opstring, value1)
obj = vsrcdest.where(op2string, value1, value2)
- Description:
vdest
is vector consisting of those elements of the given vector,vsource
that match the condition opstring.Opstring is a string matching one of these (all comparisons are with respect to
float_epsilon
):"=="
,"!="
,">"
,"<"
,">="
,"<="
Op2string requires two numbers defining open/closed ranges and matches one of these:
"[]"
,"[)"
,"(]"
,"()"
Example:
vec = h.Vector(range(0, 245, 10)) vec1 = h.Vector() vec1.where(vec, ">=", 50)
creates
vec1
with 20 elements ranging in value from 50 to 240 in increments of 10.r = h.Random() vec = h.Vector(25) vec1 = h.Vector() r.uniform(10,20) vec.fill(r) vec1.where(vec, ">", 15)
creates
vec1
with random elements gotten fromvec
which have values greater than 15. The h.elements in vec1 will be ordered according to the order of their appearance invec
.See also
- Vector.indwhere()
See also
- Vector.indvwhere()
- Syntax:
i = vsrc.indwhere(opstring, value)
i = vsrc.indwhere(op2string, low, high)
obj = vsrcdest.indvwhere(opstring,value)
obj = vsrcdest.indvwhere(opstring,value)
obj = vdest.indvwhere(vsource,op2string,low, high)
obj = vdest.indvwhere(vsource,op2string,low, high)
- Description:
The i = vsrc form returns the index of the first element of v matching the criterion given by the opstring. If there is no match, the return value is -1.
vdest
is a vector consisting of the indices of those elements of the source vector that match the condition opstring.Opstring is a string matching one of these:
"=="
,"!="
,">"
,"<"
,">="
,"<="
Op2string is a string matching one of these:
"[]"
,"[)"
,"(]"
,"()"
Comparisons are relative to the
float_epsilon
global variable.
Example:
vs = h.Vector() vs.indgen(0, .9, .1) vs.printf() print(vs.indwhere(">", .3)) print(f"note roundoff error, vs[3] - 0.3 = {vs[3] - 0.3}") print(vs.indwhere("==", .5)) vd = vs.c().indvwhere(vs, "[)", .3, .7) vd.printf()
See also
- Vector.fwrite()
- Syntax:
n = vsrc.fwrite(fileobj)
n = vsrc.fwrite(fileobj, start, end)
- Description:
Write the vector
vec
to an open fileobj of typeFile
in machine dependent binary format. You must keep track of the vector’s size for later reading, so it is recommended that you store the size of the vector as the first element of the file.It is almost always better to use
vwrite()
since it stores the size of the vector automatically and is more portable since the corresponding vread will take care of machine dependent binary byte ordering differences.Return value is the number of items. (0 if error)
fread()
is used to read a file containing numbers stored byfwrite
but must have the same size.
- Vector.fread()
- Syntax:
n = vdest.fread(fileobj)
n = vdest.fread(fileobj, n)
n = vdest.fread(fileobj, n, precision)
- Description:
Read the elements of a vector from the file in binary as written by
fwrite.
If n is present, the vector is resized before reading. Note that files created with fwrite cannot be fread on a machine with different byte ordering. E.g. spark and intel cpus have different byte ordering.It is almost always better to use
vwrite
in combination withvread
. See vwrite for the meaning of the precision argment.Return value is 1 (no error checking).
- Vector.vwrite()
- Syntax:
n = vec.vwrite(fileobj)
n = vec.vwrite(fileobj, precision)
- Description:
Write the vector in binary format to an already opened for writing * fileobj* of type
File
.vwrite()
is easier to use thanfwrite()
since it stores the size of the vector and type information for a more automated read/write. The file data can also be vread on a machine with different byte ordering. e.g. you can vwrite with an intel cpu and vread on a sparc. Precision formats 1 and 2 employ a simple automatic compression which is uncompressed automatically by vread. Formats 3 and 4 remain uncompressed.Default precision is 4 (double) because this is the usual type used for numbers in oc and therefore requires no conversion or compression
* 1 : char shortest 8 bits * 2 : short 16 bits 3 : float 32 bits 4 : double longest 64 bits 5 : int sizeof(int) bytes
Warning
These are useful primarily for storage of data: exact values will not necessarily be maintained due to the conversion process.
Return value is 1. Only if the type field is invalid will the return value be 0.
- Vector.vread()
- Syntax:
n = vec.vread(fileobj)
- Description:
Read vector from binary format file written with
vwrite()
. Size and data type have been stored byvwrite()
to allow correct retrieval syntax, byte ordering, and decompression (where necessary). The vector is automatically resized.Return value is 1. (No error checking.)
Example:
v1 = h.Vector(range(20, 31, 2)) v1.printf() f = h.File() f.wopen("temp.tmp") v1.vwrite(f) v2 = h.Vector() f.ropen("temp.tmp") v2.vread(f) v2.printf()
- Vector.printf()
- Syntax:
n = vec.printf()
n = vec.printf(format_string)
n = vec.printf(format_string, start, end)
n = vec.printf(fileobj)
n = vec.printf(fileobj, format_string)
n = vec.printf(fileobj, format_string, start, end)
- Description:
Print the values of the vector in ascii either to the screen or a File instance (if
fileobj
is present). Start and end enable you to specify which particular set of indexed values to print. Useformat_string
for formatting the output of each element. This string must contain exactly one%f
,%g
, or%e
, but can also contain additional formatting instructions.Return value is number of items printed.
Example:
vec = h.Vector() vec.indgen(0, 1, 0.1) vec.printf("%8.4f\n")
prints the numbers 0.0000 through 0.9000 in increments of 0.1. Each number will take up a total of eight spaces, will have four decimal places and will be printed on a h.line.
Warning
No error checking is done on the format string and invalid formats can cause segmentation violations.
- Vector.scanf()
- Syntax:
n = vec.scanf(fileobj)
n = vec.scanf(fileobj, n)
n = vec.scanf(fileobj, c, nc)
n = vec.scanf(fileobj, n, c, nc)
- Description:
Read ascii values from a
File
instance (must already be opened for reading) into vector. If present, scanning takes place til n items are read or until EOF. Otherwise,vec.scanf
reads until end of file. If reading til eof, a number followed by a newline must be the last string in the file. (no trailing spaces after the number and no extra newlines). When reading til EOF, the vector grows approximately by doubling when its currently allocated space is filled. To avoid the overhead of memory reallocation when scanning very long vectors (e.g. > 50000 elements) it is a good idea to presize the vector to a larger value than the expected number of elements to be scanned. Note that although the vector is resized to the actual number of elements scanned, the space allocated to the vector remains available for growth. SeeVector.buffer_size()
.Read from column c of nc columns when data is in column format. It numbers the columns beginning from 1.
The scan takes place at the current position of the file.
Return value is number of items read.
See also
- Vector.scantil()
- Syntax:
n = vec.scantil(fileobj, sentinel)
n = vec.scantil(fileobj, sentinel, c, nc)
- Description:
Like
Vector.scanf()
but scans til it reads a value equal to the sentinel. e.g. -1e15 is a possible sentinel value in many situations. The vector does not include the sentinel value. The file pointer is left at the character following the sentinel.Read from column c of nc columns when data is in column format. It numbers the columns beginning from 1. The scan stops when the sentinel is found in any position prior to column c+1 but it is recommended that the sentinel appear by itself on its own line. The file pointer is left at the character following the sentinel.
The scan takes place at the current position of the file.
Return value is number of items read.
- Vector.plot()
- Syntax:
obj = vec.plot(graphobj)
obj = vec.plot(graphobj, color, brush)
obj = vec.plot(graphobj, x_vec)
obj = vec.plot(graphobj, x_vec, color, brush)
obj = vec.plot(graphobj, x_increment)
obj = vec.plot(graphobj, x_increment, color, brush)
- Description:
Plot vector in a
Graph
object. The default is to plot the elements of the vector as y values with their indices as x values. An optional argument can be used to specify the x-axis. Such an argument can be either a vector, x_vec, in which case its values are used for x values, or a scalar, x_increment, in which case x is incremented according to this number.This function plots the
vec
values that exist in the vector at the time of graph flushing or window resizing. The alternative isvec.line()
which plots the vector values that exist at the time of the call toplot
. It is therefore possible withvec.line()
to produce multiple plots on the same graph.Once a vector is plotted, it is only necessary to call
graphobj.flush()
in order to display further changes to the vector. In this way it is possible to produce rather rapid line animation.If the vector
Graph.label()
is not empty it will be used as the label for the line on the Graph.Resizing a vector that has been plotted will remove it from the Graph.
The number of points plotted is the minimum of vec.size and x_vec.size at the time vec.plot is called. x_vec is assumed to be an unchanging Vector.
Example:
from neuron import h, gui import time g = h.Graph() g.size(0,10,-1,1) vec = h.Vector() vec.indgen(0,10, .1) vec.apply("sin") vec.plot(g, .1) def do_run(): for i in range(len(vec)): vec.rotate(1) g.flush() h.doNotify() time.sleep(0.01) h.xpanel("") h.xbutton("run", do_run) h.xpanel()
See also
Graph.Vector()
- Vector.line()
- Syntax:
obj = vec.line(graphobj)
obj = vec.line(graphobj, color, brush)
obj = vec.line(graphobj, x_vec)
obj = vec.line(graphobj, x_vec, color, brush)
obj = vec.line(graphobj, x_increment)
obj = vec.line(graphobj, x_increment, color, brush)
- Description:
Plot vector on a
Graph
. Exactly like.plot()
except the vector is not plotted by reference so that the values may be changed subsequently w/o disturbing the plot. It is therefore possible to produce a number of plots of the same function on the same graph, without erasing any previous plot.The line on a graph is given the
Graph.label()
if the label is not empty.The number of point plotted is the minimum of vec.size and x_vec.size .
Example:
from neuron import h, gui g = h.Graph() g.size(0,10,-1,1) vec = h.Vector() vec.indgen(0,10, .1) vec.apply("sin") for i in range(4): vec.line(g, 0.1) vec.rotate(10)
See also
- Vector.ploterr()
- Syntax:
obj = vec.ploterr(graphobj, x_vec, err_vec)
obj = vec.ploterr(graphobj, x_vec, err_vec, size)
obj = vec.ploterr(graphobj, x_vec, err_vec, size, color, brush)
- Description:
Similar to
vec.line()
, but plots error bars with size +/- the elements of vector err_vec.size sets the width of the seraphs on the error bars to a number of printer dots.
brush sets the width of the plot line. 0=invisible, 1=minimum width, 2=1point, etc.
Example:
g = h.Graph() g.size(0,100, 0,250) vec = h.Vector() xvec = h.Vector() errvec = h.Vector() vec.indgen(0,200,20) xvec.indgen(0,100,10) errvec.copy(xvec) errvec.apply("sqrt") vec.ploterr(g, xvec, errvec, 10) vec.mark(g, xvec, "O", 5)
creates a graph which has x values of 0 through 100 in increments of 10 and y values of 0 through 200 in increments of 20. At each point graphed, vertical error bars are also drawn which are the +/- the length of the square root of the values 0 through 100 in increments of 10. Each error bar has seraphs which are ten printer points wide. The graph is also marked with filled circles 5 printers points in diameter.
- Vector.mark()
- Syntax:
obj = vec.mark(graphobj, x_vector)
obj = vec.mark(graphobj, x_vector, "style")
obj = vec.mark(graphobj, x_vector, "style", size)
obj = vec.mark(graphobj, x_vector, "style", size, color, brush)
obj = vec.mark(graphobj, x_increment)
obj = vec.mark(graphobj, x_increment, "style", size, color, brush)
- Description:
Similar to
vec.line
, but instead of connecting by lines, it make marks, centered at the indicated position, which do not change size when window is zoomed or resized. The style is a single character|,-,+,o,O,t,T,s,S
whereo,t,s
stand for circle, triangle, square and capitalized means filled. Default size is 12 points.
- Vector.histogram()
- Syntax:
newvect = vsrc.histogram(low, high, width)
- Description:
Create a histogram constructed by binning the values in
vsrc
.Bins run from low to high in divisions of width. Data outside the range is not binned.
This function returns a vector that contains the counts in each bin, so while it is to execute
newvect = h.Vector()
.The first element of
newvect
is 0 (newvect[0] = 0
). Forii > 0
,newvect[ii]
equals the number of items invsrc
whose values lie in the half open interval[a,b)
whereb = low + ii*width
anda = b - width
. In other words,newvect[ii]
is the number of items invsrc
that fall in the bin just below the boundaryb
.
Example:
rand = h.Random() rand.negexp(1) interval = h.Vector(100) interval.setrand(rand) # random intervals hist = interval.histogram(0, 10, .1) # and for a manhattan style plot ... g = h.Graph() g.size(0,10,0,30) # create an index vector with 0,0, 1,1, 2,2, 3,3, ... v2 = h.Vector(2*len(hist)) v2.indgen(.5) v2.apply("int") # v3 = h.Vector(1) v3.index(hist, v2) v3.rotate(-1) # so different y's within each pair v3[0] = 0 v3.plot(g, v2)
creates a histogram of the occurrences of random numbers ranging from 0 to 10 in divisions of 0.1.
- Vector.hist()
- Syntax:
obj = vdest.hist(vsrc, low, size, width)
- Description:
Similar to
histogram()
(but notice the different argument meanings. Put a histogram in vdest by binning the data in vsrc. Bins run from low tolow + size * width
in divisions of width. Data outside the range is not binned.
- Vector.sumgauss()
- Syntax:
newvect = vsrc.sumgauss(low, high, width, var)
newvect = vsrc.sumgauss(low, high, width, var, weight_vec)
- Description:
Create a vector which is a curve calculated by summing gaussians of area 1 centered on all the points in the vector. This has the advantage over
histogram
of not imposing arbitrary bins. low and high set the range of the curve. width determines the granularity of the curve. var sets the variance of the gaussians.The optional argument
weight_vec
is a vector which should be the same size asvec
and is used to scale or weight the gaussians (default is for them all to have areas of 1 unit).This function returns a vector, so while it is to declare vectobj as a
h.Vector()
.To plot, use
v.indgen(low,high,width)
for the x-vector argument.
Example:
r = h.Random() r.normal(1, 2) data = h.Vector(100) data.setrand(r) hist = data.sumgauss(-4, 6, .5, 1) x = h.Vector(len(hist)) x.indgen(-4, 6, .5) g = h.Graph() g.size(-4, 6, 0, 30) hist.plot(g, x)
- Vector.smhist()
- Syntax:
obj = vdest.smhist(vsrc, start, size, step, var)
obj = vdest.smhist(vsrc, start, size, step, var, weight_vec)
- Description:
Very similar to
sumgauss()
. Calculate a smooth histogram by convolving the raw data set with a gaussian kernel. The histogram begins atvarstart
and hasvarsize
values in increments of sizevarstep
.varvar
sets the variance of the gaussians. The optional argumentweight_vec
is a vector which should be the same size asvsrc
and is used to scale or weight the number of data points at a particular value.
- Vector.ind()
- Syntax:
newvect = vsrc.ind(vindex)
- Description:
Return a h.Vector consisting of the elements of
vsrc
whose indices are given by the elements ofvindex
.
Example:
vec = h.Vector(100) vec2 = h.Vector() vec.indgen(5) vec2.indgen(49, 59, 1) vec1 = vec.ind(vec2)
creates
vec1
to contain the fiftieth through the sixtieth elements ofvec2
which would have the values 245 through 295 in increments of 5.
- Vector.addrand()
- Syntax:
obj = vsrcdest.addrand(randobj)
obj = vsrcdest.addrand(randobj, start, end)
- Description:
Adds random values to the elements of the vector by sampling from the same distribution as last picked in the Random object randobj.
Example:
from neuron import h, gui vec = h.Vector(50) g = h.Graph() g.size(0,50,0,100) r = h.Random() r.poisson(.2) vec.plot(g) def race(): vec.fill(0) for i in range(300): vec.addrand(r) g.flush() h.doNotify() race()
- Vector.setrand()
- Syntax:
obj = vdest.setrand(randobj)
obj = vdest.setrand(randobj, start, end)
- Description:
Sets random values for the elements of the vector by sampling from the same distribution as last picked in randobj.
- Vector.sin()
- Syntax:
obj = vdest.sin(freq, phase)
obj = vdest.sin(freq, phase, dt)
- Description:
Generate a sin function in vector
vec
with frequency freq hz, phase phase in radians. dt is assumed to be 1 msec unless specified.
- Vector.apply()
- Syntax:
obj = vsrcdest.apply("func")
obj = vsrcdest.apply("func", start, end)
- Description:
Apply a hoc function to each of the elements in the vector. The function can be any function that is accessible in oc. It must take only one scalar argument and return a scalar. Note that the function name must be in quotes and that the parentheses are omitted.
Example:
vec.apply("sin", 0, 9)
applies the sin function to the first ten elements of the vector
vec
.
- Vector.reduce()
- Syntax:
x = vsrc.reduce("func")
x = vsrc.reduce("func", base)
x = vsrc.reduce("func", base, start, end)
- Description:
Pass all elements of a vector through a HOC function and return the sum of the results. Use base to initialize the value x. Note that the function name must be in quotes and that the parentheses are omitted.
Example:
from neuron import h vec = h.Vector(range(0, 10, 2)) h("func sq(){return $1*$1}") print(vec.reduce("sq", 100))
displays the value 320.
100 + 0*0 + 2*2 + 4*4 + 6*6 + 8*8 + 10*10 = 320
Although reduce only works with HOC functions, it can be emulated in Python using generators and the
sum
function. For example, the last two lines of the above example are equivalent to:def sq(x): return x * x print(sum((sq(x) for x in vec), 100))
- Vector.floor()
- Syntax:
vec.floor()
- Description:
Rounds toward negative infinity. Note that
float_epsilon
is not used in this calculation.
- Vector.to_python()
- Syntax:
pythonlist = vec.to_python()
pythonlist = vec.to_python(pythonlist)
numpyarray = vec.to_python(numpyarray)
- Description:
Copy the vector elements from the hoc vector to a pythonlist or 1-d numpyarray. If the arg exists the pythonobject must have the same size as the hoc vector.
- Vector.from_python()
- Syntax:
vec = vec.from_python(pythonlist)
vec = vec.from_python(numpyarray)
- Description:
Copy the python list elements into the hoc vector. The elements must be numbers that are convertable to doubles. Copy the numpy 1-d array elements into the hoc vector. The hoc vector is resized.
- Vector.as_numpy()
- Syntax:
numpyarray = vec.as_numpy()
Description:
The numpyarray points into the data of the Hoc Vector, i.e. does not copy the data. Do not use the numpyarray if the Vector is destroyed.
Example:
from neuron import h v = h.Vector(range(5)) n = v.as_numpy() print(n) #[0. 1. 2. 3. 4.] v[1] += 10 n[2] += 20 print(n) #[ 0. 11. 22. 3. 4.] v.printf() #0 11 22 3 4
- Vector.fit()
- Syntax:
error = data_vec.fit(fit_vec,"fcn",indep_vec, pointer1, [pointer2], ... [pointerN])
- Description:
Use a simplex algorithm to find parameters p1 through pN such to minimize the mean squared error between the “data” contained in
data_vec
and the approximation generated by the user-supplied “fcn” applied to the elements ofindep_vec
.fcn must take one argument which is the main independent variable followed by one or more arguments which are tunable parameters which will be optimized. Thus the arguments to .fit following “fcn” should be completely analogous to the arguments to fcn itself. The difference is that the args to fcn must all be scalars while the corresponding args to .fit will be a vector object (for the independent variable) and pointers to scalars (for the remaining parameters).
The results of a call to .fit are three-fold. First, the parameters of best fit are returned by setting the values of the variables p1 to pN (possible because they are passed as pointers). Second, the values of the vector fit_vec are set to the fitted function. If
fit_vec
is not passed with the same size asindep_vec
anddata_vec
, it is resized accordingly. Third, the mean squared error between the fitted function and the data is returned by.fit
. The.fit()
call may be reiterated several times until the error has reached an acceptable level.Care must be taken in selecting an initial set of parameter values. Although you need not be too close, wild discrepancies will cause the simplex algorithm to give up. Values of 0 are to be avoided. Trial and error is sometimes necessary.
Because calls to hoc have a high overhead, this procedure can be rather slow. Several commonly-used functions are provided directly in c code and will work much faster. In each case, if the name below is used, the builtin function will be used and the user is expected to provide the correct number of arguments (here denoted
a,b,c
…)."exp1": y = a * exp(-x/b) "exp2": y = a * exp(-x/b) + c * exp (-x/d) "charging": y = a * (1-exp(-x/b)) + c * (1-exp(-x/d)) "line": y = a * x + b "quad": y = a * x^2 + b*x + c
Warning
This function is not very useful for fitting the results of simulation runs due to its argument organization. For that purpose the
fit_praxis()
syntax is more suitable. This function should become a top-level function which merely takes a user error function name and a parameter list.An alternative implementation of the simplex fitting algorithm is in the scopmath library.
See also
- Example:
The
widget uses this function and is implemented innrn/lib/hoc/funfit.hoc
The following example demonstrates the strategy used by the simplex fitting algorithm to search for a minimum. The location of the parameter values is plotted on each call to the function. The sample function has a minimum at the point (1, .5)
from neuron import h, gui g = h.Graph() g.size(0, 3, 0, 3) def fun(a, x, y): if a == 0: g.line(x, y) g.flush() print(a, x, y) return (x - 1) ** 2 + (y - 0.5) ** 2 dvec = h.Vector(2) fvec = h.Vector([1, 1]) ivec = h.Vector(range(2)) a = h.ref(2) b = h.ref(1) g.beginline() error = dvec.fit(fvec, fun, ivec, a, b) print(a[0], b[0], error)
Warning
Does not currently work with Python functions. It requires a string whose value is the name of a HOC function instead.
- Vector.interpolate()
- Syntax:
obj = ysrcdest.interpolate(xdest, xsrc)
obj = ydest.interpolate(xdest, xsrc, ysrc)
- Description:
Linearly interpolate points from (xsrc,ysrc) to (xdest,ydest) In the second form, xsrc and ysrc remain unchanged. Destination points outside the domain of xsrc are set to
ysrc[0]
orysrc[ysrc.size-1]
Example:
g = h.Graph() g.size(0,10,0,100) #... xs = h.Vector(range(10)) ys = xs * xs ys.line(g, xs, 1, 0) # black reference line xd = h.Vector() xd.indgen(-.5, 10.5, .1) yd = ys.c().interpolate(xd, xs) yd.line(g, xd, 3, 0) # blue more points than reference xd.indgen(-.5, 13, 3) yd = ys.c().interpolate(xd, xs) yd.line(g, xd, 2, 0) # red fewer points than reference
- Vector.deriv()
- Syntax:
obj = vdest.deriv(vsrc)
obj = vdest.deriv(vsrc, dx)
obj = vdest.deriv(vsrc, dx, method)
obj = vsrcdest.deriv()
obj = vsrcdest.deriv(dx)
obj = vsrcdest.deriv(dx, method)
- Description:
The numerical Euler derivative or the central difference derivative of
vec
is placed invdest
. The variable dx gives the increment of the independent variable between successive elements ofvec
.- method = 1 = Euler derivative:
vec1[i] = (vec[i+1] - vec[i])/dx
Each time this method is used, the first element of
vec
is lost since i cannot equal -1. Therefore, since theintegral
function performs an Euler integration, the integral ofvec1
will reproducevec
minus the first element.- method = 2 = Central difference derivative:
vec1[i] = ((vec[i+1]-vec[i-1])/2)/dx
This method produces an Euler derivative for the first and last elements of
vec1
. The central difference method maintains the same number of elements invec1
as were invec
and is a more accurate method than the Euler method. A vector differentiated by this method cannot, however, be integrated to reproduce the originalvec
.
Example:
from neuron import h vec = h.Vector(range(6)) vec = vec * vec vec1 = h.Vector() vec1.deriv(vec, 0.1)
creates
vec1
with elements:10 20 40 60 80 90
Since dx=0.1, and there are eleven elements including 0, the entire function exists between the values of 0 and 1, and the derivative values are large compared to the function values. With dx=1,the vector
vec1
would consist of the following elements:1 2 4 6 8 9
The Euler method vs. the Central difference method:
Beginning with the vector
vec
:0 1 4 9 16 25
vec1.deriv(vec, 1, 1)
(Euler) would go about producingvec1
by the following method:1-0 = 1 4-1 = 3 9-4 = 5 16-9 = 7 25-16 = 9
whereas
vec1.deriv(vec, 1, 2)
(Central difference) would go about producingvec1
as such:1-0 = 1 (4-0)/2 = 2 (9-1)/2 = 4 (16-4)/2 = 6 (25-9)/2 = 8 25-16 = 9
- Vector.integral()
- Syntax:
obj = vdest.integral(vsrc)
obj = vdest.integral(vsrc, dx)
obj = vsrcdest.integral()
obj = vsrcdest.integral(dx)
- Description:
Places a numerical Euler integral of the vsrc elements in vdest. dx sets the size of the discretization.
vdest[i+1] = vdest[i] + vsrc[i+1]
and the first element ofvdest
is always equal to the first element ofvsrc
.
Example:
from neuron import h vec = h.Vector([0, 1, 4, 9, 16, 25]) vec1 = h.Vector() vec1.integral(vec, 1) # Euler integral of vec elements approximating # an x-squared function, dx = 0.1 vec1.printf()
will print the following elements in
vec1
to the screen:0 1 5 14 30 55
In order to make the integral values more accurate, it is necessary to increase the size of the vector and to decrease the size of dx.
from neuron import h import numpy # set vec to the squares of 51 values from 0 to 5 vec = h.Vector(numpy.linspace(0, 5, 51)) vec.pow(2) vec1 = h.Vector() vec1.integral(vec, 0.1) # Euler integral of vec elements approximating # an x-squared function, dx = 0.1 # print every 10th index for i in range(0, len(vec1), 10): print(vec1[i])
will print the following elements of
vec1
corresponding to the integers 0-5 to the screen:0 0.385 2.87 9.455 22.14 42.925
The integration naturally becomes more accurate as dx is reduced and the size of the vector is increased. If the vector is taken to 501 elements from 0-5 and dx is made to equal 0.01, the integrals of the integers 0-5 yield the following (compared to their continuous values on their right).
0.00000 -- 0.00000 0.33835 -- 0.33333 2.6867 -- 2.6666 9.04505 -- 9.00000 21.4134 -- 21.3333 41.7917 -- 41.6666
- Vector.median()
- Syntax:
median = vsrc.median()
- Description:
Find the median value of
vec
.
- Vector.medfltr()
- Syntax:
obj = vdest.medfltr(vsrc)
obj = vdest.medfltr(vsrc, points)
obj = vsrcdest.medfltr()
obj = vsrcdest.medfltr( points)
- Description:
Apply a median filter to vsrc, producing a smoothed version in vdest. Each point is replaced with the median value of the points on either side. This is typically used for eliminating spikes from data.
- Vector.sort()
- Syntax:
obj = vsrcdest.sort()
- Description:
Sort the elements of
vec1
in place, putting them in numerical order.
- Vector.sortindex()
- Syntax:
vdest = vsrc.sortindex()
vdest = vsrc.sortindex(vdest)
- Description:
Return a h.Vector of indices which sort the vsrc elements in numerical order. That is vsrc.index(vsrc.sortindex) is equivalent to vsrc.sort(). If vdest is present, use that as the destination vector for the indices. This, if it is large enough, avoids the destruct/construct of vdest.
Example:
from neuron import h r = h.Random() r.uniform(0, 100) a = h.Vector(10) a.setrand(r) a.printf() si = a.sortindex() si.printf() a.index(si).printf()
- Vector.reverse()
- Syntax:
obj = vsrcdest.reverse()
- Description:
Reverses the elements of
vec
in place.
- Vector.rotate()
- Syntax:
obj = vsrcdest.rotate(value)
obj = vsrcdest.rotate(value, 0)
- Description:
A negative value will move elements to the left. A positive argument will move elements to the right. In both cases, the elements shifted off one end of the vector will reappear at the other end. If a 2nd arg is present, 0 values get shifted in and elements shifted off one end are lost.
Example:
vec.indgen(1, 10, 1) vec.rotate(3)
orders the elements of
vec
as follows:8 9 10 1 2 3 4 5 6 7
whereas,
vec.indgen(1, 10, 1) vec.rotate(-3)
orders the elements of
vec
as follows:4 5 6 7 8 9 10 1 2 3
vec = h.Vector(range(1, 6)) vec.printf() vec.c().rotate(2).printf() vec.c().rotate(2, 0).printf() vec.c().rotate(-2).printf() vec.c().rotate(-2, 0).printf()
- Vector.rebin()
- Syntax:
obj = vdest.rebin(vsrc,factor)
obj = vsrcdest.rebin(factor)
- Description:
Compresses length of vector
vsrc
by an integer factor. The sum of elements is conserved, unless the factor produces a remainder, in which case the remainder values are truncated fromvdest
.
Example:
vec.indgen(1, 10, 1) vec1.rebin(vec, 2)
produces
vec1
:3 7 11 15 19
where each pair of
vec
elements is added together into one element.But,
vec.indgen(1, 10, 1) vec1.rebin(vec, 3)
adds trios
vec
elements and gets rid of the value 10, producingvec1
:6 15 24
- Vector.pow()
- Syntax:
obj = vdest.pow(vsrc, power)
obj = vsrcdest.pow(power)
- Description:
Raise each element to some power. A power of -1, 0, .5, 1, or 2 are efficient.
- Vector.sqrt()
- Syntax:
obj = vdest.sqrt(vsrc)
obj = vsrcdest.sqrt()
- Description:
Take the square root of each element. No domain checking.
- Vector.log()
- Syntax:
obj = vdest.log(vsrc)
obj = vsrcdest.log()
- Description:
Take the natural log of each element. No domain checking.
- Vector.log10()
- Syntax:
obj = vdest.log10(vsrc)
obj = vsrcdest.log10()
- Description:
Take the logarithm to the base 10 of each element. No domain checking.
- Vector.tanh()
- Syntax:
obj = vdest.tanh(vsrc)
obj = vsrcdest.tanh()
- Description:
Take the hyperbolic tangent of each element.
- Vector.abs()
- Syntax:
obj = vdest.abs(vsrc)
obj = vsrcdest.abs()
- Description:
Take the absolute value of each element.
Example:
v1 = h.Vector() v1.indgen(-.5, .5, .1) v1.printf() v1.abs().printf()
See also
- Vector.index()
- Syntax:
obj = vdest.index(vsrc, indices)
- Description:
The values of the vector
vsrc
indexed by the vector indices are collected intovdest
.
Example:
from neuron import h vec = h.Vector() vec1 = h.Vector() vec2 = h.Vector() vec3 = h.Vector(6) vec.indgen(0, 5.1, 0.1) # vec will have 51 values from 0 to 5, with increment=0.1 vec1.integral(vec, 0.1) # Euler integral of vec elements approximating # an x-squared function, dx = 0.1 vec2.indgen(0, 50, 10) vec3.index(vec1, vec2) # put the value of every 10th index in vec2
makes
vec3
with six elements corresponding to the integrated integers fromvec
.
- Vector.min()
- Syntax:
x = vec.min()
x = vec.min(start, end)
- Description:
Return the minimum value.
- Vector.min_ind()
- Syntax:
i = vec.min_ind()
i = vec.min_ind(start, end)
- Description:
Return the index of the minimum value.
- Vector.max()
- Syntax:
x = vec.max()
x = vec.max(start, end)
- Description:
Return the maximum value.
- Vector.max_ind()
- Syntax:
i = vec.max_ind()
i = vec.max_ind(start, end)
- Description:
Return the index of the maximum value.
Examples:
v = h.Vector([4, 2, 61, 17, 13]) print(v.max_ind()) # 2 print(v.max_ind(1, 2)) # 2 print(v.max_ind(3, 4)) # 3
Warning
Some older versions of NEURON reported erroneous values for max_ind when start and end are specified. Test for this with the example above. All released versions _newer_ than 8.2.2 work correctly, as does the current develoopment version.
- Vector.sum()
- Syntax:
x = vec.sum()
x = vec.sum(start, end)
- Description:
Return the sum of element values.
- Vector.sumsq()
- Syntax:
x = vec.sumsq()
x = vec.sumsq(start, end)
- Description:
Return the sum of squared element values.
- Vector.mean()
- Syntax:
x = vec.mean()
x = vec.mean(start, end)
- Description:
Return the mean of element values.
- Vector.var()
- Syntax:
x = vec.var()
x = vec.var(start, end)
- Description:
Return the variance of element values.
- Vector.stdev()
- Syntax:
vec.stdev()
vec.stdev(start,end)
- Description:
Return the standard deviation of the element values.
- Vector.stderr()
- Syntax:
x = vec.stderr()
x = vec.stderr(start, end)
- Description:
Return the standard error of the mean (SEM) of the element values.
- Vector.dot()
- Syntax:
x = vec.dot(vec1)
- Description:
Return the dot (inner) product of
vec
and vec1.
- Vector.mag()
- Syntax:
x = vec.mag()
- Description:
Return the vector length or magnitude.
- Vector.add()
- Syntax:
obj = vsrcdest.add(scalar)
obj = vsrcdest.add(vec1)
- Description:
Add either a scalar to each element of the vector or add the corresponding elements of vec1 to the elements of
vsrcdest
.vsrcdest
and vec1 must have the same size.
- Vector.sub()
- Syntax:
obj = vsrcdest.sub(scalar)
obj = vsrcdest.sub(vec1)
- Description:
Subtract either a scalar from each element of the vector or subtract the corresponding elements of vec1 from the elements of
vsrcdest
.vsrcdest
and vec1 must have the same size.
- Vector.mul()
- Syntax:
obj = vsrcdest.mul(scalar)
obj = vsrcdest.mul(vec1)
- Description:
Multiply each element of
vsrcdest
either by either a scalar or the corresponding elements of vec1.vsrcdest
and vec1 must have the same size.
- Vector.div()
- Syntax:
obj = vsrcdest.div(scalar)
obj = vsrcdest.div(vec1)
- Description:
Divide each element of
vsrcdest
either by a scalar or by the corresponding elements of vec1.vsrcdest
and vec1 must have the same size.
- Vector.scale()
- Syntax:
scale = vsrcdest.scale(low, high)
- Description:
Scale values of the elements of a vector to lie within the given range. Return the scale factor used.
- Vector.eq()
- Syntax:
numerical_truth_value = vec.eq(vec1)
- Description:
Test equality of vectors. Returns 1 if all elements of vec == corresponding elements of vec1 (to within
float_epsilon
). Otherwise it returns 0. This can be made into a boolean truth value with Python function bool()
- Vector.meansqerr()
- Syntax:
x = vec.meansqerr(vec1)
x = vec.meansqerr(vec1, weight_vec)
- Description:
Return the mean squared error between values of the elements of
vec
and the corresponding elements of vec1.vec
and vec1 must have the same size.If the second vector arg is present, it also must have the same size and the return value is sum of
w[i]*(v1[i] - v2[i])^2 / size
Fourier Analysis
The following routines are based on the fast fourier transform (FFT) and are implemented using code from Numerical Recipes in C (2nd ed.) Refer to this source for further information.
- Vector.correl()
- Syntax:
obj = vdest.correl(src)
obj = vdest.correl(src, vec2)
- Description:
Compute the cross-correlation function of src and vec2 (or the autocorrelation of src if vec2 is not present).
- Vector.convlv()
- Syntax:
obj = vdest.convlv(src,filter)
obj = vdest.convlv(src,filter, sign)
- Description:
Compute the convolution of src with filter. If <sign>=-1 then compute the deconvolution. Assumes filter is given in “wrap-around” order, with countup
t=0..t=n/2
followed by countdownt=n..t=n/2
. The size of filter should be an odd <= the size of v1>.
Example:
v1 = h.Vector(16) v2 = h.Vector(16) v3 = h.Vector() v1[5] = v1[6] = 1 v2[3] = v2[4] = 3 v3.convlv(v1, v2) v1.printf() v2.printf() v3.printf()
- Vector.spctrm()
- Syntax:
obj = vdest.spctrm(vsrc)
- Description:
Return the power spectral density function of vsrc.
- Vector.filter()
- Syntax:
obj = vdest.filter(src,filter)
obj = vsrcdest.filter(filter)
- Description:
Digital filter implemented by taking the inverse fft of filter and convolving it with vec1. vec and vec1 are in the time domain and filter is in the frequency domain.
- Vector.fft()
- Syntax:
obj = vdest.fft(vsrc, sign)
obj = vsrcdest.fft(sign)
- Description:
Compute the fast fourier transform of the source data vector. If sign=-1 then compute the inverse fft.
If vsrc.
size()
is not an integral power of 2, it is padded with 0’s to the next power of 2 size.The complex frequency domain is represented in the vector as pairs of numbers — except for the first two numbers. vec[0] is the amplitude of the 0 frequency cosine (constant) and vec[1] is the amplitude of the highest (N/2) frequency cosine (ie. alternating 1,-1’s in the time domain) vec[2, 3] is the amplitude of the cos(2*PI*i/n), sin(2*PI*i/n) components (ie. one whole wave in the time domain) vec[n-2, n-1] is the amplitude of the cos(PI*(n-1)*i/n), sin(PI*(n-1)*i/n) components. The following example of a pure time domain sine wave sampled at 16 points should be played with to see where the specified frequency appears in the frequency domain vector (note that if the frequency is greater than 8, aliasing will occur, ie sampling makes it appear as a lower frequency) Also note that the forward transform does not produce the amplitudes of the frequency components that goes up to make the time domain function but instead each element is the integral of the product of the time domain function and a specific pure frequency. Thus the 0 and highest frequency cosine are N times the amplitudes and all others are N/2 times the amplitudes.
from neuron import h, gui N = 16 # should be a power of 2 class MyGUI: def __init__(self): self.c = 1 self.f = 1 # waves per domain, max is N/2 self.box = h.VBox() self.box.intercept(1) h.xpanel('', 1) h.xradiobutton('sin ', lambda: self.p(0)) h.xradiobutton('cos ', lambda: self.p(1), 1) h.xvalue('freq (waves/domain)', (self, 'f'), 1, lambda: self.p(self.c)) h.xpanel() self.g1 = h.Graph() self.g2 = h.Graph() self.g3 = h.Graph() self.box.intercept(0) self.box.map() self.g1.size(0, N, -1, 1) self.g2.size(0, N, -N, N) self.g3.size(0, N, -N, N) self.p(self.c) def p(self, c): self.v1 = h.Vector(N) self.v1.sin(self.f, c * h.PI / 2, 1000. / N) self.v1.plot(self.g1) self.v2 = h.Vector() self.v2.fft(self.v1, 1) # forward self.v2.plot(self.g2) self.v3 = h.Vector() self.v3.fft(self.v2, -1) # inverse self.v3.plot(self.g3) # amplitude N/2 times the original gui = MyGUI()
The inverse fft is mathematically almost identical to the forward transform but often has a different operational interpretation. In this case the result is a time domain function which is merely the sum of all the pure sinusoids weighted by the (complex) frequency function (although, remember, points 0 and 1 in the frequency domain are special, being the constant and the highest alternating cosine, respectively). The example below shows the index of a particular frequency and phase as well as the time domain pattern. Note that index 1 is for the higest frequency cosine instead of the 0 frequency sin.
Because the frequency domain representation is something only a programmer could love, and because one might wish to plot the real and imaginary frequency spectra, one might wish to encapsulate the fft in a function which uses a more convenient representation.
Below is an alternative FFT function where the frequency values are spectrum amplitudes (no need to divide anything by N) and the real and complex frequency components are stored in separate vectors (of length N/2 + 1).
Consider the functions
FFT(1, vt_src, vfr_dest, vfi_dest) FFT(-1, vt_dest, vfr_src, vfi_src)
The forward transform (first arg = 1) requires a time domain source vector with a length of N = 2^n where n is some positive integer. The resultant real (cosine amplitudes) and imaginary (sine amplitudes) frequency components are stored in the N/2 + 1 locations of the vfr_dest and vfi_dest vectors respectively (Note: vfi_dest[0] and vfi_dest[N/2] are always set to 0. The index i in the frequency domain is the number of full pure sinusoid waves in the time domain. ie. if the time domain has length T then the frequency of the i’th component is i/T.
The inverse transform (first arg = -1) requires two freqency domain source vectors for the cosine and sine amplitudes. The size of these vectors must be N/2+1 where N is a power of 2. The resultant time domain vector will have a size of N.
If the source vectors are not a power of 2, then the vectors are padded with 0’s til vtsrc is 2^n or vfr_src is 2^n + 1. The destination vectors are resized if necessary.
This function has the property that the sequence
FFT(1, vt, vfr, vfi) FFT(-1, vt, vfr, vfi)
leaves vt unchanged. Reversal of the order would leave vfr and vfi unchanged.
The implementation is:
def FFT(direction, vt, vfr, vfi): if direction == 1: # forward vfr.fft(vt, 1) n = len(vfr) vfr.div(n/2) vfr[0] /= 2 # makes the spectrum appear discontinuous vfr[1] /= 2 # but the amplitudes are intuitive vfi.copy(vfr, 0, 1, -1, 1, 2) # odd elements vfr.copy(vfr, 0, 0, -1, 1, 2) # even elements vfr.resize(n/2+1) vfi.resize(n/2+1) vfr[n/2] = vfi[0] #highest cos started in vfr[1] vfi[0] = vfi[n/2] = 0 # weights for sin(0*i)and sin(PI*i) else: # inverse # shuffle vfr and vfi into vt n = len(vfr) vt.copy(vfr, 0, 0, n-2, 2, 1) vt[1] = vfr[n-1] vt.copy(vfi, 3, 1, n-2, 2, 1) vt[0] *= 2 vt[1] *= 2 vt.fft(vt, -1)
If you load the previous example so that FFT is defined, the following example shows the cosine and sine spectra of a pulse.
from neuron import h, gui N = 128 class MyGUI: def __init__(self): self.delay = 0 self.duration = N / 2 self.box = h.VBox() self.box.intercept(1) h.xpanel('') h.xvalue('delay (points)', (self, 'delay'), 1, self.p) h.xvalue('duration (points)', (self, 'duration'), 1, self.p) h.xpanel() self.g1 = h.Graph() self.b1 = h.HBox() self.b1.intercept(1) self.g2 = h.Graph() self.g3 = h.Graph() self.b1.intercept(0) self.b1.map() self.g4 = h.Graph() self.box.intercept(0) self.box.map() self.g1.size(0, N, -1, 1) self.g2.size(0, N / 2, -1, 1) self.g3.size(0, N / 2, -1, 1) self.g4.size(0, N, -1, 1) self.p() def p(self): self.v1 = h.Vector(N) self.v1.fill(1, self.delay, self.delay + self.duration - 1) self.v1.plot(self.g1) self.v2 = h.Vector() self.v3 = h.Vector() FFT(1, self.v1, self.v2, self.v3) self.v2.plot(self.g2) self.v3.plot(self.g3) self.v4 = h.Vector() FFT(-1, self.v4, self.v2, self.v3) self.v4.plot(self.g4) mygui = MyGUI()
- Vector.trigavg()
- Syntax:
v1.trigavg(data,trigger,pre,post)
- Description:
Perform an event-triggered average of <data> using times given by <trigger>. The duration of the average is from -<pre> to <post>. This is useful, for example, in calculating a spike triggered stimulus average.
- Vector.spikebin()
- Syntax:
v.spikebin(data,thresh)
- Description:
Used to make a binary version of a spike train. <data> is a vector of membrane potential. <thresh> is the voltage threshold for spike detection. <v> is set to all zeros except at the onset of spikes (the first dt which the spike crosses threshold)
- Vector.psth()
- Syntax:
vmeanfreq = vdest.psth(vsrchist,dt,trials,size)
- Description:
The name of this function is somewhat misleading, since its input, vsrchist, is a finely-binned post-stimulus time histogram, and its output, vdest, is an array whose elements are the mean frequencies f_mean[i] that correspond to each bin of vsrchist.
For bin i, the corresponding mean frequency f_mean[i] is determined by centering an adaptive square window on i and widening the window until the number of spikes under the window equals size. Then f_mean[i] is calculated as
f_mean[i] = N[i] / (m dt trials)
where
f_mean[i] is in spikes per _second_ (Hz). N[i] = total number of events in the window centered on bin i m = total number of bins in the window centered on bin i dt = binwidth of vsrchist in _milliseconds_ (so m dt is the width of the window in milliseconds) trials = an integer scale factor
trials is used to adjust for the number of traces that were superimposed to compute the elements of vsrchist. In other words, suppose the elements of vsrchist were computed by adding up the number of spikes in n traces
\[v1[i] = \sum_{j=1}^n {\text{number of spikes in bin i of trace j}}\]Then trials would be assigned the value n. Of course, if the elements of vsrchist are divided by n before calling psth(), then trials should be set to 1.
Acknowledgment: The documentation and example for psth was prepared by Ted Carnevale.
Warning
The total number of spikes in vsrchist must be greater than size.
Example:
from neuron import h, gui b = h.VBox() b.intercept(1) g1 = h.Graph() g1.size(0,200,0,10) g2 = h.Graph() g2.size(0,200,0,10) b.intercept(0) b.map("psth and mean freq") VECSIZE = 200 MINSUM = 50 DT = 1000 # ms per bin of v1 (vsrchist) TRIALS = 1 v1 = h.Vector(VECSIZE) r = h.Random() for ii in range(VECSIZE): v1[ii] = int(r.uniform(0, 10)) v1.plot(g1) v2 = h.Vector() v2.psth(v1, DT, TRIALS, MINSUM) v2.plot(g2)
- Vector.inf()
- Syntax:
v.inf(i,dt,gl,el,cm,th,res,[ref])
- Description:
Simulate a leaky integrate and fire neuron. <i> is a vector containing the input. <dt> is the timestep. <gl> and <el> are the conductance and reversal potential of the leak term <cm> is capacitance. <th> is the threshold voltage and <res> is the reset voltage. <ref>, if present sets the duration of ab absolute refractory period.
N.b. Currently working with forward Euler integration, which may give spurious results.