On Sun, 18 Aug 2002 08:13:18 0400 Todd Miller wrote: Todd> Jochen Küpper wrote:
Looking at RandomArray2 I realized that the functions don't do any argument checking. Shouldn't uniform for example check at least whether ,  minimum != maximum ` or even make sure that maximum > minimum? (Although the result is probably "ok" if it isn't.) Something like ,  def uniform(minimum, maximum, shape=[]):  """Return array of random Floats in interval ]minimum, maximum[  with shape shape.  """  if maximum <= minimum:  raise ValueError  return minimum + (maximumminimum)*random(shape) `
Todd> I am +0 on this. The parameter order emulates "range".
Not exactly, currently: ,  >>> range(2, 4)  []  >>> ran.uniform(2, 4)  2.2346744537353516 ` That is, if max < min range returns an empty list, whereas uniform comes up with the same result as for (4, 2) (well, "mirrored"). Also note the "strange" docstring of range: ,  range(...)  range([start,] stop[, step]) > list of integers ` pointing straight toward its behavior. Todd> While it does look like it will compute the wrong answer if Todd> called incorrectly, that seems unlikely to me. Well, if max<min it "mirrors" the result inside the range. This is no problem as long as it is done "consistently". I don't have enough knowledge of RNG's to understand whether it is a problem (with respect to randomness) when calls with the right and wrong ordering of min and max are mixed. Thinking about the case min==max I must say it's a very wasted function call, but no actually big deal: ,  >>> import RandomArray2 as ran  >>> ran.uniform(1, 1)  1.0 ` So well, maybe someone with insight into RNG's can comment on the, mirroring issue?
Moreover there are some inconsistencies between functions, i.e.: ,  def randint(minimum, maximum=None, shape=[]): ` ,  def random_integers(maximum, minimum=1, shape=[]): `
Todd> It appears to me that the parameter order of randint again Todd> emulates "range". The fact that random_integers is not Todd> consistent with randint seem OK to me because random_integers Todd> appears to have been written expressly to tailor the calling Todd> sequence of randint. Hmm, v.s. Yes, initially I wondered why there are two functions at all. This explanation sounds like "we wanted some help in confusing the users" :)) Todd> Because randint redefines its parameters depending on whether 1 Todd> or 2 range values are used, as does range, I don't think there Todd> is a completely consistent way to do this. Either we're "wrong" Todd> for the 1 parameter case or the 2 parameter case. The way it is Todd> specified now seems simplest to me, with "minimum" preceding Todd> "maximum", even though it is not strictly the correct name for Todd> the 1 parameter case. What's about ,  uniform(limit1, limit2, shape=[]) ` and then rangelike behaviour? But then, what do we return on ,  uniform(2, 4) ` ??? To make it compatible with range, it should be an empty list, no? Yourevenmoreconfusedly's, Jochen  Einigkeit und Recht und Freiheit http://www.JochenKuepper.de Liberté, Égalité, Fraternité GnuPG key: 44BCCD8E Sex, drugs and rocknroll
Jochen Küpper wrote:
On Sun, 18 Aug 2002 08:13:18 0400 Todd Miller wrote:
Todd> Jochen Küpper wrote:
Looking at RandomArray2 I realized that the functions don't do any argument checking. Shouldn't uniform for example check at least whether ,  minimum != maximum ` or even make sure that maximum > minimum? (Although the result is probably "ok" if it isn't.) Something like ,  def uniform(minimum, maximum, shape=[]):  """Return array of random Floats in interval ]minimum, maximum[  with shape shape.  """  if maximum <= minimum:  raise ValueError  return minimum + (maximumminimum)*random(shape) `
Todd> I am +0 on this. The parameter order emulates "range".
Not exactly, currently: ,  >>> range(2, 4)  []  >>> ran.uniform(2, 4)  2.2346744537353516 ` That is, if max < min range returns an empty list, whereas uniform comes up with the same result as for (4, 2) (well, "mirrored").
Also note the "strange" docstring of range: ,  range(...)  range([start,] stop[, step]) > list of integers ` pointing straight toward its behavior.
Todd> While it does look like it will compute the wrong answer if Todd> called incorrectly, that seems unlikely to me.
Well, if max<min it "mirrors" the result inside the range. This is no problem as long as it is done "consistently". I don't have enough knowledge of RNG's to understand whether it is a problem (with respect to randomness) when calls with the right and wrong ordering of min and max are mixed.
Thinking about the case min==max I must say it's a very wasted function call, but no actually big deal: ,  >>> import RandomArray2 as ran  >>> ran.uniform(1, 1)  1.0 `
So well, maybe someone with insight into RNG's can comment on the, mirroring issue?
Moreover there are some inconsistencies between functions, i.e.: ,  def randint(minimum, maximum=None, shape=[]): ` ,  def random_integers(maximum, minimum=1, shape=[]): `
Todd> It appears to me that the parameter order of randint again Todd> emulates "range". The fact that random_integers is not Todd> consistent with randint seem OK to me because random_integers Todd> appears to have been written expressly to tailor the calling Todd> sequence of randint.
Hmm,
v.s.
Yes, initially I wondered why there are two functions at all. This explanation sounds like "we wanted some help in confusing the users" :))
I read it more like: someone wanted to make one particular user happy by giving them the interface they asked for. Since writing random_integers was easy, they did it even though it amounted to a small duplication of effort and interface functionality. But, I'm just speculating.
Todd> Because randint redefines its parameters depending on whether 1 Todd> or 2 range values are used, as does range, I don't think there Todd> is a completely consistent way to do this. Either we're "wrong" Todd> for the 1 parameter case or the 2 parameter case. The way it is Todd> specified now seems simplest to me, with "minimum" preceding Todd> "maximum", even though it is not strictly the correct name for Todd> the 1 parameter case.
What's about ,  uniform(limit1, limit2, shape=[]) ` and then rangelike behaviour?
But then, what do we return on ,  uniform(2, 4) ` ???
Perhaps my intuition about "range" was incorrect, or we're taking the analogy too far. It seems to me that randint is returning random numbers between two limits, and the order of the limits is irrelevant. randint(2,4) is identical to randint(4,2). As you have pointed out, this is distinctly different than range. At this point, I'm still unconvinced that the world would be made a better place either by raising an exception or by changing the semantics to return an "empty array". That small change seems just as likely to upset some user as to make another happy.
Yourevenmoreconfusedly's, Jochen
Todd  Todd Miller jmiller@stsci.edu STSCI / SSG
On Mon, 19 Aug 2002 09:27:35 0400 Todd Miller wrote: Todd> Jochen Küpper wrote:
Also note the "strange" docstring of range: ,  range(...)  range([start,] stop[, step]) > list of integers ` pointing straight toward its behavior.
Ok, reworked the docstrings of module RandomArray2 a bit in order to (hopefully) clarify these issues. I have attached a diff, if it is ok I'll check it in.
So well, maybe someone with insight into RNG's can comment on the, mirroring issue?
Anybody? Todd> It appears to me that the parameter order of randint again Todd> emulates "range". The fact that random_integers is not Todd> consistent with randint seem OK to me because random_integers Todd> appears to have been written expressly to tailor the calling Todd> sequence of randint. Put a comment about that in the docstring of random_integers. Greetings, Jochen  University of North Carolina phone: +19199624403 Department of Chemistry phone: +19199621579 Venable Hall CB#3290 (Kenan C148) fax: +19198436041 Chapel Hill, NC 27599, USA GnuPG key: 44BCCD8E
Jochen Küpper wrote:
On Mon, 19 Aug 2002 09:27:35 0400 Todd Miller wrote:
Todd> Jochen Küpper wrote:
Also note the "strange" docstring of range: ,  range(...)  range([start,] stop[, step]) > list of integers ` pointing straight toward its behavior.
Ok, reworked the docstrings of module RandomArray2 a bit in order to (hopefully) clarify these issues. I have attached a diff, if it is ok I'll check it in.
Please do. Todd
So well, maybe someone with insight into RNG's can comment on the, mirroring issue?
Anybody?
Todd> It appears to me that the parameter order of randint again Todd> emulates "range". The fact that random_integers is not Todd> consistent with randint seem OK to me because random_integers Todd> appears to have been written expressly to tailor the calling Todd> sequence of randint.
Put a comment about that in the docstring of random_integers.
Greetings, Jochen

? Packages/RandomArray2/build ? Packages/RandomArray2/Lib/ChangeLog Index: Packages/RandomArray2/Lib/RandomArray2.py =================================================================== RCS file: /cvsroot/numpy/numarray/Packages/RandomArray2/Lib/RandomArray2.py,v retrieving revision 1.3 diff u r1.3 RandomArray2.py  Packages/RandomArray2/Lib/RandomArray2.py 16 Aug 2002 10:44:21 0000 1.3 +++ Packages/RandomArray2/Lib/RandomArray2.py 22 Aug 2002 22:11:16 0000 @@ 5,6 +5,11 @@ import math from types import *
+__doc__ = """Random number array generators. + +This module provides functions to generate arrays of random numbers. +""" + # Extended RandomArray to provide more distributions: # normal, beta, chi square, F, multivariate normal, # exponential, binomial, multinomial @@ 13,8 +18,8 @@ ArgumentError = "ArgumentError"
def seed(x=0,y=0):  """seed(x, y), set the seed using the integers x, y;  Set a random one from clock if y == 0 + """Set the RNG seed using the integers x, y; + If y == 0 set a random one from clock. """ if type (x) != IntType or type (y) != IntType : raise ArgumentError, "seed requires integer arguments." @@ 30,14 +35,14 @@ seed()
def get_seed():  "Return the current seed pair" + """Return the current seed pair""" return ranlib.get_seeds()
def _build_random_array(fun, args, shape=[]): # Build an array by applying function fun to # the arguments in args, creating an array with # the specified shape. # Allows an integer shape n as a shorthand for (n,). + """Build an array by applying function fun to the arguments in + args, creating an array with the specified shape. + Allows an integer shape n as a shorthand for (n,). + """ if isinstance(shape, IntType): shape = [shape] if len(shape) != 0: @@ 51,20 +56,28 @@ return s[0]
def random(shape=[]):  "random(n) or random([n, m, ...]) returns array of random numbers" + """random(n) or random([n, m, ...]) + + Returns array of random numbers in the range 0.0 to 1.0. + """ return _build_random_array(ranlib.sample, (), shape)
def uniform(minimum, maximum, shape=[]):  """uniform(minimum, maximum, shape=[]) returns array of given shape of random reals  in given range""" + """uniform([minimum,], maximum[, shape]) + + Return array with shape shape of random Floats with all values + > minimum and < maximum. + """ return minimum + (maximumminimum)*random(shape)
def randint(minimum, maximum=None, shape=[]):  """randint(min, max, shape=[]) = random integers >=min, < max  If max not given, random integers >= 0, <min""" + """randint([minimum,] maximum[, shape]) + + Return random integers >= mininimum, < maximum, + if maximum not given, random integers >= 0, < minimum. + """ if maximum is None:  maximum = minimum  minimum = 0 + maximum, minimum = minimum, 0 a = Numeric.floor(uniform(minimum, maximum, shape)) if isinstance(a, Numeric.ArrayType): return a.astype(Numeric.Int32) @@ 72,79 +85,94 @@ return int(a)
def random_integers(maximum, minimum=1, shape=[]):  """random_integers(max, min=1, shape=[]) = random integers in range minmax inclusive""" + """Return array of random integers in interval [minimum, maximum] + + Note that this function has reversed arguments. It is simply a + redirection through randint, and use of that function (randint) is + suggested. + """ return randint(minimum, maximum+1, shape)
def permutation(n):  "permutation(n) = a permutation of indices range(n)" + """A permutation of indices range(n)""" return Numeric.argsort(random(n))
def standard_normal(shape=[]):  """standard_normal(n) or standard_normal([n, m, ...]) returns array of  random numbers normally distributed with mean 0 and standard  deviation 1""" + """standard_normal(n) or standard_normal([n, m, ...]) + + Returns array of random numbers normally distributed with mean 0 + and standard deviation 1. + """ return _build_random_array(ranlib.standard_normal, (), shape)
def normal(mean, std, shape=[]):  """normal(mean, std, n) or normal(mean, std, [n, m, ...]) returns  array of random numbers randomly distributed with specified mean and  standard deviation"""  s = standard_normal(shape)  return s * std + mean + """normal(mean, std, n) or normal(mean, std, [n, m, ...]) + + Returns array of random numbers randomly distributed with + specified mean and standard deviation + """ + s = standard_normal(shape) + return s * std + mean
def multivariate_normal(mean, cov, shape=[]):  """multivariate_normal(mean, cov) or multivariate_normal(mean, cov, [m, n, ...])  returns an array containing multivariate normally distributed random numbers  with specified mean and covariance.   mean must be a 1 dimensional array. cov must be a square two dimensional  array with the same number of rows and columns as mean has elements.   The first form returns a single 1D array containing a multivariate  normal.   The second form returns an array of shape (m, n, ..., cov.getshape()[0]).  In this case, output[i,j,...,:] is a 1D array containing a multivariate  normal."""  # Check preconditions on arguments  mean = Numeric.array(mean)  cov = Numeric.array(cov)  if len(mean.getshape()) != 1:  raise ArgumentError, "mean must be 1 dimensional."  if (len(cov.getshape()) != 2) or (cov.getshape()[0] != cov.getshape()[1]):  raise ArgumentError, "cov must be 2 dimensional and square."  if mean.getshape()[0] != cov.getshape()[0]:  raise ArgumentError, "mean and cov must have same length."  # Compute shape of output  if isinstance(shape, IntType): shape = [shape]  final_shape = list(shape[:])  final_shape.append(mean.getshape()[0])  # Create a matrix of independent standard normally distributed random  # numbers. The matrix has rows with the same length as mean and as  # many rows are necessary to form a matrix of shape final_shape.  x = ranlib.standard_normal(Numeric.multiply.reduce(final_shape))  x.setshape(Numeric.multiply.reduce(final_shape[0:len(final_shape)1]),  mean.getshape()[0])  # Transform matrix of standard normals into matrix where each row  # contains multivariate normals with the desired covariance.  # Compute A such that matrixmultiply(transpose(A),A) == cov.  # Then the matrix products of the rows of x and A has the desired  # covariance. Note that sqrt(s)*v where (u,s,v) is the singular value  # decomposition of cov is such an A.  (u,s,v) = LinearAlgebra2.singular_value_decomposition(cov)  x = Numeric.matrixmultiply(x*Numeric.sqrt(s),v)  # The rows of x now have the correct covariance but mean 0. Add  # mean to each row. Then each row will have mean mean.  Numeric.add(mean,x,x)  x.setshape(final_shape)  return x + """multivariate_normal(mean, cov) or multivariate_normal(mean, cov, [m, n, ...]) + + Returns an array containing multivariate normally distributed + random numbers with specified mean and covariance. + + mean must be a onedimensional array. cov must be a square + twodimensional array with the same number of rows and columns as + mean has elements. + + The first form returns a single 1D array containing a + multivariate normal. + + The second form returns an array of shape (m, n, ..., + cov.getshape()[0]). In this case, output[i,j,...,:] is a 1D array + containing a multivariate normal. + """ + # Check preconditions on arguments + mean = Numeric.array(mean) + cov = Numeric.array(cov) + if len(mean.getshape()) != 1: + raise ArgumentError, "mean must be 1 dimensional." + if (len(cov.getshape()) != 2) or (cov.getshape()[0] != cov.getshape()[1]): + raise ArgumentError, "cov must be 2 dimensional and square." + if mean.getshape()[0] != cov.getshape()[0]: + raise ArgumentError, "mean and cov must have same length." + # Compute shape of output + if isinstance(shape, IntType): shape = [shape] + final_shape = list(shape[:]) + final_shape.append(mean.getshape()[0]) + # Create a matrix of independent standard normally distributed random + # numbers. The matrix has rows with the same length as mean and as + # many rows are necessary to form a matrix of shape final_shape. + x = ranlib.standard_normal(Numeric.multiply.reduce(final_shape)) + x.setshape(Numeric.multiply.reduce(final_shape[0:len(final_shape)1]), + mean.getshape()[0]) + # Transform matrix of standard normals into matrix where each row + # contains multivariate normals with the desired covariance. + # Compute A such that matrixmultiply(transpose(A),A) == cov. + # Then the matrix products of the rows of x and A has the desired + # covariance. Note that sqrt(s)*v where (u,s,v) is the singular value + # decomposition of cov is such an A. + (u,s,v) = LinearAlgebra2.singular_value_decomposition(cov) + x = Numeric.matrixmultiply(x*Numeric.sqrt(s),v) + # The rows of x now have the correct covariance but mean 0. Add + # mean to each row. Then each row will have mean mean. + Numeric.add(mean,x,x) + x.setshape(final_shape) + return x
def exponential(mean, shape=[]):  """exponential(mean, n) or exponential(mean, [n, m, ...]) returns array  of random numbers exponentially distributed with specified mean"""  # If U is a random number uniformly distributed on [0,1], then  # ln(U) is exponentially distributed with mean 1, and so  # ln(U)*M is exponentially distributed with mean M. + """exponential(mean, n) or exponential(mean, [n, m, ...]) + + Returns array of random numbers exponentially distributed with + specified mean + """ + # If U is a random number uniformly distributed on [0,1], then + # ln(U) is exponentially distributed with mean 1, and so + # ln(U)*M is exponentially distributed with mean M. x = random(shape) Numeric.log(x, x) Numeric.subtract(0.0, x, x) @@ 160,52 +188,79 @@ return _build_random_array(ranlib.gamma, (a, r), shape)
def F(dfn, dfd, shape=[]):  """F(dfn, dfd) or F(dfn, dfd, [n, m, ...]) returns array of F distributed random numbers with dfn degrees of freedom in the numerator and dfd degrees of freedom in the denominator.""" + """F(dfn, dfd) or F(dfn, dfd, [n, m, ...]) + + Returns array of F distributed random numbers with dfn degrees of + freedom in the numerator and dfd degrees of freedom in the + denominator. + """ return ( chi_square(dfn, shape) / dfn) / ( chi_square(dfd, shape) / dfd)
def noncentral_F(dfn, dfd, nconc, shape=[]):  """noncentral_F(dfn, dfd, nonc) or noncentral_F(dfn, dfd, nonc, [n, m, ...]) returns array of noncentral F distributed random numbers with dfn degrees of freedom in the numerator and dfd degrees of freedom in the denominator, and noncentrality parameter nconc.""" + """noncentral_F(dfn, dfd, nonc) or noncentral_F(dfn, dfd, nonc, [n, m, ...]) + + Returns array of noncentral F distributed random numbers with dfn + degrees of freedom in the numerator and dfd degrees of freedom in + the denominator, and noncentrality parameter nconc. + """ return ( noncentral_chi_square(dfn, nconc, shape) / dfn ) / ( chi_square(dfd, shape) / dfd )
def chi_square(df, shape=[]):  """chi_square(df) or chi_square(df, [n, m, ...]) returns array of chi squared distributed random numbers with df degrees of freedom.""" + """chi_square(df) or chi_square(df, [n, m, ...]) + + Returns array of chi squared distributed random numbers with df + degrees of freedom. + """ return _build_random_array(ranlib.chisquare, (df,), shape)
def noncentral_chi_square(df, nconc, shape=[]):  """noncentral_chi_square(df, nconc) or chi_square(df, nconc, [n, m, ...]) returns array of noncentral chi squared distributed random numbers with df degrees of freedom and noncentrality parameter.""" + """noncentral_chi_square(df, nconc) or chi_square(df, nconc, [n, m, ...]) + + Returns array of noncentral chi squared distributed random numbers + with df degrees of freedom and noncentrality parameter. + """ return _build_random_array(ranlib.noncentral_chisquare, (df, nconc), shape)
def binomial(trials, p, shape=[]):  """binomial(trials, p) or binomial(trials, p, [n, m, ...]) returns array of binomially distributed random integers. + """binomial(trials, p) or binomial(trials, p, [n, m, ...]) + + Returns array of binomially distributed random integers.
 trials is the number of trials in the binomial distribution.  p is the probability of an event in each trial of the binomial distribution.""" + trials is the number of trials in the binomial distribution. + p is the probability of an event in each trial of the binomial + distribution. + """ return _build_random_array(ranlib.binomial, (trials, p), shape)
def negative_binomial(trials, p, shape=[]):  """negative_binomial(trials, p) or negative_binomial(trials, p, [n, m, ...]) returns  array of negative binomially distributed random integers. + """negative_binomial(trials, p) or negative_binomial(trials, p, [n, m, ...]) + + Returns array of negative binomially distributed random integers.
 trials is the number of trials in the negative binomial distribution.  p is the probability of an event in each trial of the negative binomial distribution.""" + trials is the number of trials in the negative binomial + distribution. p is the probability of an event in each trial of + the negative binomial distribution. + """ return _build_random_array(ranlib.negative_binomial, (trials, p), shape)
def multinomial(trials, probs, shape=[]):  """multinomial(trials, probs) or multinomial(trials, probs, [n, m, ...]) returns  array of multinomial distributed integer vectors. + """multinomial(trials, probs) or multinomial(trials, probs, [n, m, ...]) + + Returns array of multinomial distributed integer vectors. + + trials is the number of trials in each multinomial distribution. + probs is a one dimensional array. There are len(prob)+1 events. + prob[i] is the probability of the ith event, 0<=i<len(prob). The + probability of event len(prob) is 1.Numeric.sum(prob).
 trials is the number of trials in each multinomial distribution.  probs is a one dimensional array. There are len(prob)+1 events.  prob[i] is the probability of the ith event, 0<=i<len(prob).  The probability of event len(prob) is 1.Numeric.sum(prob).   The first form returns a single 1D array containing one multinomially  distributed vector.   The second form returns an array of shape (m, n, ..., len(probs)).  In this case, output[i,j,...,:] is a 1D array containing a multinomially  distributed integer 1D array."""  # Check preconditions on arguments + The first form returns a single 1D array containing one + multinomially distributed vector. + + The second form returns an array of shape (m, n, ..., len(probs)). + In this case, output[i,j,...,:] is a 1D array containing a + multinomially distributed integer 1D array. + """ + # Check preconditions on arguments probs = Numeric.array(probs) if len(probs.getshape()) != 1: raise ArgumentError, "probs must be 1 dimensional." @@ 215,14 +270,18 @@ final_shape.append(probs.getshape()[0]+1) x = ranlib.multinomial(trials, probs.astype(Numeric.Float32), Numeric.multiply.reduce(shape))  # Change its shape to the desire one + # Change its shape to the desire one x.setshape(final_shape) return x
def poisson(mean, shape=[]):  """poisson(mean) or poisson(mean, [n, m, ...]) returns array of poisson  distributed random integers with specifed mean.""" + """poisson(mean) or poisson(mean, [n, m, ...]) + + Returns array of poisson distributed random integers with specifed + mean. + """ return _build_random_array(ranlib.poisson, (mean,), shape) +
def test(): import test as _test Index: Packages/RandomArray2/Lib/__init__.py =================================================================== RCS file: /cvsroot/numpy/numarray/Packages/RandomArray2/Lib/__init__.py,v retrieving revision 1.1 diff u r1.1 __init__.py  Packages/RandomArray2/Lib/__init__.py 21 Jun 2002 18:25:29 0000 1.1 +++ Packages/RandomArray2/Lib/__init__.py 22 Aug 2002 22:11:16 0000 @@ 2,3 +2,6 @@
from RandomArray2 import *
+__doc__ = RandomArray2.__doc__ + """ +See RandomArray2.RandomArray2 for more information. +"""
 Todd Miller jmiller@stsci.edu STSCI / SSG
participants (3)

Jochen Küpper

Jochen Küpper

Todd Miller