def Cmatrix(self):
'''
Calculate the C matrix
'''
self.C = []
self.gamma = []
self.f1001 = []
self.f1010 = []
S = getattr(self, "S")
R11 = getattr(self, "R11")
R12 = getattr(self, "R12")
R21 = getattr(self, "R21")
R22 = getattr(self, "R22")
BETX = getattr(self, "BETX")
BETY = getattr(self, "BETY")
ALFX = getattr(self, "ALFX")
ALFY = getattr(self, "ALFY")
J = numpy.reshape(numpy.array([0, 1, -1, 0]), (2, 2))
for j in range(0, len(S)):
R = numpy.array([[R11[j], R12[j]], [R21[j], R22[j]]])
C = matrixmultiply(-J, matrixmultiply(numpy.transpose(R), J))
C = (1 / numpy.sqrt(1 + determinant(R))) * C
g11 = 1 / numpy.sqrt(BETX[j])
g12 = 0
g21 = ALFX[j] / numpy.sqrt(BETX[j])
g22 = numpy.sqrt(BETX[j])
Ga = numpy.reshape(numpy.array([g11, g12, g21, g22]), (2, 2))
g11 = 1 / numpy.sqrt(BETY[j])
g12 = 0
g21 = ALFY[j] / numpy.sqrt(BETY[j])
g22 = numpy.sqrt(BETY[j])
Gb = numpy.reshape(numpy.array([g11, g12, g21, g22]), (2, 2))
C = matrixmultiply(Ga, matrixmultiply(C, inverse(Gb)))
gamma = 1 - determinant(C)
self.gamma.append(gamma)
C = numpy.ravel(C)
self.C.append(C)
self.f1001.append(((C[0] + C[3]) * 1j + (C[1] - C[2])) / 4 / gamma)
self.f1010.append(
((C[0] - C[3]) * 1j + (-C[1] - C[2])) / 4 / gamma)
self.F1001R = numpy.array(self.f1001).real
self.F1001I = numpy.array(self.f1001).imag
self.F1010R = numpy.array(self.f1010).real
self.F1010I = numpy.array(self.f1010).imag
self.F1001W = numpy.sqrt(self.F1001R**2 + self.F1001I**2)
self.F1010W = numpy.sqrt(self.F1010R**2 + self.F1010I**2)
self.GAMMAC = numpy.array(self.gamma)
def Cmatrix(self):
'''
Calculate the C matrix
'''
self.C = []
self.gamma = []
self.f1001 = []
self.f1010 = []
S = getattr(self, "S")
R11 = getattr(self, "R11")
R12 = getattr(self, "R12")
R21 = getattr(self, "R21")
R22 = getattr(self, "R22")
BETX = getattr(self, "BETX")
BETY = getattr(self, "BETY")
ALFX = getattr(self, "ALFX")
ALFY = getattr(self, "ALFY")
J = numpy.reshape(numpy.array([0, 1, -1, 0]), (2, 2))
for j in range(0, len(S)):
R = numpy.array([[R11[j], R12[j]], [R21[j], R22[j]]])
C = matrixmultiply(-J, matrixmultiply(numpy.transpose(R), J))
C = (1 / numpy.sqrt(1 + determinant(R))) * C
g11 = 1 / numpy.sqrt(BETX[j])
g12 = 0
g21 = ALFX[j] / numpy.sqrt(BETX[j])
g22 = numpy.sqrt(BETX[j])
Ga = numpy.reshape(numpy.array([g11, g12, g21, g22]), (2, 2))
g11 = 1 / numpy.sqrt(BETY[j])
g12 = 0
g21 = ALFY[j] / numpy.sqrt(BETY[j])
g22 = numpy.sqrt(BETY[j])
Gb = numpy.reshape(numpy.array([g11, g12, g21, g22]), (2, 2))
C = matrixmultiply(Ga, matrixmultiply(C, inverse(Gb)))
gamma = 1 - determinant(C)
self.gamma.append(gamma)
C = numpy.ravel(C)
self.C.append(C)
self.f1001.append(((C[0] + C[3]) * 1j + (C[1] - C[2])) / 4 / gamma)
self.f1010.append(((C[0] - C[3]) * 1j + (-C[1] - C[2])) / 4 / gamma)
self.F1001R = numpy.array(self.f1001).real
self.F1001I = numpy.array(self.f1001).imag
self.F1010R = numpy.array(self.f1010).real
self.F1010I = numpy.array(self.f1010).imag
self.F1001W = numpy.sqrt(self.F1001R ** 2 + self.F1001I ** 2)
self.F1010W = numpy.sqrt(self.F1010R ** 2 + self.F1010I ** 2)
def b_matrix(self, shg, shgbar=None, lcoords=None, coords=None, det=None,
disp=0, **kwargs):
"""Assemble and return the B matrix"""
B = zeros((self.ndi+self.nshr, self.num_node * self.num_dof_per_node))
B[0, 0::2] = shg[0, :]
B[1, 1::2] = shg[1, :]
B[3, 0::2] = shg[1, :]
B[3, 1::2] = shg[0, :]
if not disp:
return B
# Algorithm in
# The Finite Element Method: Its Basis and Fundamentals
# By Olek C Zienkiewicz, Robert L Taylor, J.Z. Zhu
# Jacobian at element centroid
dNdxi = self.shape.grad([0., 0.])
dxdxi = dot(dNdxi, coords)
J0 = inv(dxdxi)
dt0 = determinant(dxdxi)
xi, eta = lcoords
dNdxi = array([[-2. * xi, 0.], [0., -2. * eta]])
dNdx = dt0 / det * dot(J0, dNdxi)
G1 = array([[dNdx[0, 0], 0],
[0, dNdx[0, 1]],
[0, 0],
[dNdx[0, 1], dNdx[0, 0]]])
G2 = array([[dNdx[1, 0], 0],
[0, dNdx[1, 1]],
[0, 0],
[dNdx[1, 1], dNdx[1, 0]]])
G = concatenate((G1, G2), axis=1)
return B, G
# Algorithm in Taylor's original paper and
# The Finite Element Method: Linear Static and Dynamic
# Finite Element Analysis
# By Thomas J. R. Hughe
xi = self.gauss_coords
n = self.num_gauss
dxdxi = asum([coords[i, 0] * xi[i, 0] for i in range(n)])
dxdeta = asum([coords[i, 0] * xi[i, 1] for i in range(n)])
dydxi = asum([coords[i, 1] * xi[i, 0] for i in range(n)])
dydeta = asum([coords[i, 1] * xi[i, 1] for i in range(n)])
xi, eta = lcoords
G1 = array([[-xi * dydeta, 0],
[0, xi * dxdeta],
[0, 0],
[xi * dxdeta, -xi * dydeta]])
G2 = array([[-eta * dydxi, 0.],
[0, eta * dxdxi],
[0, 0],
[eta * dxdxi, -eta * dydxi]])
G = 2. / det * concatenate((G1, G2), axis=1)
return B, G
def __init__(self, *cords): """Solve linear equation system for polinom indices.""" main_mtrx = matrix( [[co[0]**p for p in xrange(len(cords)-1, -1, -1)] for co in cords] ) main_det = determinant(main_mtrx) matrices_dets = [] for i in xrange(len(cords)): m = main_mtrx.copy() for j in xrange(len(cords)): m[j, i] = cords[j][1] matrices_dets.append(determinant(m)) self.indices = tuple(m_det / main_det for m_det in matrices_dets) if main_det else None self.length = len(self.indices) if self.indices else 0
def F_value_wilks_lambda(ER, EF, dfnum, dfden, a, b):
"""
Calculation of Wilks lambda F-statistic for multivarite data, per
Maxwell & Delaney p.657.
Usage: F_value_wilks_lambda(ER,EF,dfnum,dfden,a,b)
"""
if type(ER) in [IntType, FloatType]:
ER = N.array([[ER]])
if type(EF) in [IntType, FloatType]:
EF = N.array([[EF]])
lmbda = LA.determinant(EF) / LA.determinant(ER)
if (a-1)**2 + (b-1)**2 == 5:
q = 1
else:
q = math.sqrt( ((a-1)**2*(b-1)**2 - 2) / ((a-1)**2 + (b-1)**2 -5) )
n_um = (1 - lmbda**(1.0/q))*(a-1)*(b-1)
d_en = lmbda**(1.0/q) / (m*q - 0.5*(a-1)*(b-1) + 1)
return n_um / d_en
def Cmatrix(self):
'''
Calculate the C matrix
'''
self.C = []
self.gamma = []
self.f1001 = []
self.f1010 = []
J = reshape(array([0,1,-1,0]),(2,2))
for j in range(0,len(self.S)):
R = array([[self.R11[j],self.R12[j]],[self.R21[j],self.R22[j]]])
#print R
C = matrixmultiply(-J,matrixmultiply(transpose(R),J))
C = (1/sqrt(1+determinant(R)))*C
g11 = 1/sqrt(self.BETX[j])
g12 = 0
g21 = self.ALFX[j]/sqrt(self.BETX[j])
g22 = sqrt(self.BETX[j])
Ga = reshape(array([g11,g12,g21,g22]),(2,2))
g11 = 1/sqrt(self.BETY[j])
g12 = 0
g21 = self.ALFY[j]/sqrt(self.BETY[j])
g22 = sqrt(self.BETY[j])
Gb = reshape(array([g11,g12,g21,g22]),(2,2))
C = matrixmultiply(Ga, matrixmultiply(C, inverse(Gb)))
gamma=1-determinant(C)
self.gamma.append(gamma)
C = ravel(C)
self.C.append(C)
self.f1001.append(((C[0]+C[3])*1j + (C[1]-C[2]))/4/gamma)
self.f1010.append(((C[0]-C[3])*1j +(-C[1]-C[2]))/4/gamma)
self.F1001R=array(self.f1001).real
self.F1001I=array(self.f1001).imag
self.F1010R=array(self.f1010).real
self.F1010I=array(self.f1010).imag
self.F1001W=sqrt(self.F1001R**2+self.F1001I**2)
self.F1010W=sqrt(self.F1010R**2+self.F1010I**2)
def multivariate_normal_prob(x, cov, mean=None):
"""Returns multivariate normal probability density of vector x.
Formula: http://www.riskglossary.com/link/joint_normal_distribution.htm
"""
if mean is None:
mean = zeros(len(x))
diff_row = x - mean
diff_col = diff_row[:, NewAxis]
numerator = exp(-0.5 * dot(dot(diff_row, inverse(cov)), diff_col))
denominator = sqrt((2 * pi)**(len(x)) * determinant(cov))
return numerator / denominator
def multivariate_normal_prob(x, cov, mean=None):
"""Returns multivariate normal probability density of vector x.
Formula: http://www.riskglossary.com/link/joint_normal_distribution.htm
"""
if mean is None:
mean = zeros(len(x))
diff_row = x-mean
diff_col = diff_row[:,NewAxis]
numerator = exp(-0.5 * dot(dot(diff_row, inverse(cov)), diff_col))
denominator = sqrt((2*pi)**(len(x)) * determinant(cov))
return numerator/denominator
def affine_transform(IMG, transform, offset=[0., 0.], shift=[0.0]):
''' transform(IMG,transform,offset=[0.,0.])
Transform an image using an affine transform transform about a fixed point offset
Unlike scipy.ndimage, offset is the *fixed point*. This is *a lot* more
sensible for computation!!!
Only works for rotations and linear scaling for now. Need to do a little extra lin
alg for non uniform scaling.
'''
itransform = inversemat(transform)
offset = (np.array(offset) -
np.array(offset).dot(itransform) / determinant(itransform))
#offset -= np.array(shift).dot(itransform)#/determinant(itransform)
img = scipy_affine_transform(IMG, transform,
offset=offset) #,offset=[-N/2,-N/2])
return img
def aanova(data,effects=['A','B','C','D','E','F','G','H','I','J','K']):
"""
Prints the results of single-variable between- and within-subject ANOVA
designs. The function can only handle univariate ANOVAs with a single
random factor. The random factor is coded in column 0 of the input
list/array (see below) and the measured variable is coded in the last
column of the input list/array. The following were used as references
when writing the code:
Maxwell, SE, Delaney HD (1990) Designing Experiments and Analyzing
Data, Wadsworth: Belmont, CA.
Lindman, HR (1992) Analysis of Variance in Experimental Design,
Springer-Verlag: New York.
TO DO: Increase Current Max Of 10 Levels Per W/I-Subject Factor
Consolidate Between-Subj Analyses For Between And Within/Between
Front-end for different input data-array shapes/organization
Axe mess of 'global' statements (particularly for Drestrict fcns)
Usage: anova(data, data = |Stat format
effects=['A','B','C','D','E','F','G','H','I','J','K'])
Note: |Stat format is as follows ... one datum per row, first element of
row is the subject identifier, followed by all within/between subject
variable designators, and the measured data point as the last element in the
row. Thus, [1, 'short', 'drugY', 2, 14.7] represents subject 1 when measured
in the short / drugY / 2 condition, and subject 1 gave a measured value of
14.7 in this combination of conditions. Thus, all input lists are '2D'
lists-of-lists.
"""
global alluniqueslist, Nlevels, Nfactors, Nsubjects, Nblevels, Nallsources
global Bscols, Bbetweens, SSlist, SSsources, DM, DN, Bwonly_sources, D
global Bwithins, alleffects, alleffsources
outputlist = []
SSbtw = []
SSbtwsources = []
SSwb = []
SSwbsources = []
alleffects = []
alleffsources = []
SSlist = []
SSsources = []
print
variables = 1 # this function only handles one measured variable
if type(data)!=type([]):
data = data.tolist()
## Create a list of all unique values in each column, and a list of these Ns
alluniqueslist = [0]*(len(data[0])-variables) # all cols but data cols
Nlevels = [0]*(len(data[0])-variables) # (as above)
for column in range(len(Nlevels)):
alluniqueslist[column] = pstat.unique(pstat.colex(data,column))
Nlevels[column] = len(alluniqueslist[column])
Ncells = N.multiply.reduce(Nlevels[1:]) # total num cells (w/i AND btw)
Nfactors = len(Nlevels[1:]) # total num factors
Nallsources = 2**(Nfactors+1) # total no. possible sources (factor-combos)
Nsubjects = len(alluniqueslist[0]) # total # subj in study (# of diff. subj numbers in column 0)
## Within-subj factors defined as those where there are fewer subj than
## scores in the first level of a factor (quick and dirty; findwithin() below)
Bwithins = findwithin(data) # binary w/i subj factors (excl. col 0)
Bbetweens = ~Bwithins & (Nallsources-1) - 1
Wcolumns = makelist(Bwithins,Nfactors+1) # get list of cols of w/i factors
Wscols = [0] + Wcolumns # w/i subj columns INCL col 0
Bscols = makelist(Bbetweens+1,Nfactors+1) #list of btw-subj cols,INCL col 0
Nwifactors = len(Wscols) - 1 # WAS len(Wcolumns)
Nwlevels = N.take(N.array(Nlevels),Wscols) # no.lvls for each w/i subj fact
Nbtwfactors = len(Bscols) - 1 # WASNfactors - Nwifactors + 1
Nblevels = N.take(N.array(Nlevels),Bscols)
Nwsources = 2**Nwifactors - 1 # num within-subject factor-combos
Nbsources = Nallsources - Nwsources
#
# CALC M-VARIABLE (LIST) and Marray/Narray VARIABLES (ARRAY OF CELL MNS/NS)
#
# Eliminate replications for the same subject in same condition as well as
# within-subject repetitions, keep as list
M = pstat.collapse(data,Bscols,-1,None,None,mean)
# Create an arrays of Nblevels shape (excl. subj dim)
Marray = N.zeros(Nblevels[1:],'f')
Narray = N.zeros(Nblevels[1:],'f')
# Fill arrays by looping through all scores in the (collapsed) M
for row in M:
idx = []
for i in range(len(row[:-1])):
idx.append(alluniqueslist[Bscols[i]].index(row[i]))
idx = idx[1:]
Marray[idx] = Marray[idx] + row[-1]
Narray[idx] = Narray[idx] + 1
Marray = Marray / Narray
#
# CREATE DATA ARRAY, DA, FROM ORIGINAL INPUT DATA
# (this is an unbelievably bad, wasteful data structure, but it makes lots
# of tasks much easier; should nevertheless be fixed someday)
# This limits the within-subject level count to 10!
coefflist =[[[1]],
[[-1,1]],
[[-1,0,1],[1,-2,1]],
[[-3,-1,1,3],[1,-1,-1,1],[-1,3,-3,1]],
[[-2,-1,0,1,2],[2,-1,-2,-1,2],[-1,2,0,-2,1],[1,-4,6,-4,1]],
[[-5,-3,-1,1,3,5],[5,-1,-4,-4,-1,5],[-5,7,4,-4,-7,5],
[1,-3,2,2,-3,1],[-1,5,-10,10,-5,1]],
[[-3,-2,-1,0,1,2,3],[5,0,-3,-4,-3,0,5],[-1,1,1,0,-1,-1,1],
[3,-7,1,6,1,-7,3],[-1,4,-5,0,5,-4,1],[1,-6,15,-20,15,-6,1]],
[[-7,-5,-3,-1,1,3,5,7],[7,1,-3,-5,-5,-3,1,7],
[-7,5,7,3,-3,-7,-5,7],[7,-13,-3,9,9,-3,-13,7],
[-7,23,-17,-15,15,17,-23,7],[1,-5,9,-5,-5,9,-5,1],
[-1,7,-21,35,-35,21,-7,1]],
[[-4,-3,-2,-1,0,1,2,3,4],[28,7,-8,-17,-20,-17,-8,7,28],
[-14,7,13,9,0,-9,-13,-7,14],[14,-21,-11,9,18,9,-11,-21,14],
[-4,11,-4,-9,0,9,4,-11,4],[4,-17,22,1,-20,1,22,-17,4],
[-1,6,-14,14,0,-14,14,-6,1],[1,-8,28,-56,70,-56,28,-8,1]],
[[-9,-7,-5,-3,-1,1,3,5,7,9],[6,2,-1,-3,-4,-4,-3,-1,2,6],
[-42,14,35,31,12,-12,-31,-35,-14,42],
[18,-22,-17,3,18,18,3,-17,-22,18],
[-6,14,-1,-11,-6,6,11,1,-14,6],[3,-11,10,6,-8,-8,6,10,-11,3],
[9,-47,86,-42,-56,56,42,-86,47,-9],
[1,-7,20,-28,14,14,-28,20,-7,1],
[-1,9,-36,84,-126,126,-84,36,-9,1]]]
dindex = 0
# Prepare a list to be filled with arrays of D-variables, array per within-
# subject combo (i.e., for 2 w/i subj factors E and F ... E, F, ExF)
NDs = [0]* Nwsources
for source in range(Nwsources):
if subset(source,Bwithins):
NDs[dindex] = numlevels(source,Nlevels)
dindex = dindex + 1
# Collapse multiple repetitions on the same subject and same condition
cdata = pstat.collapse(data,range(Nfactors+1),-1,None,None,mean)
# Find a value that's not a data score with which to fill the array DA
dummyval = -1
datavals = pstat.colex(data,-1)
while dummyval in datavals: # find a value that's not a data score
dummyval = dummyval - 1
DA = N.ones(Nlevels,'f')*dummyval # create plenty of data-slots to fill
if len(Bscols) == 1: # ie., if no btw-subj factors
# 1 (below) needed because we need 2D array even w/ only 1 group of subjects
subjslots = N.ones((Nsubjects,1))
else: # create array to hold 1s (subj present) and 0s (subj absent)
subjslots = N.zeros(Nblevels)
for i in range(len(data)): # for every datapoint given as input
idx = []
for j in range(Nfactors+1): # get n-D bin idx for this datapoint
new = alluniqueslist[j].index(data[i][j])
idx.append(new)
DA[idx] = data[i][-1] # put this data point in proper place in DA
btwidx = N.take(idx,N.array(Bscols))
subjslots[btwidx] = 1
# DONE CREATING DATA ARRAY, DA ... #dims = numfactors+1, dim 0=subjects
# dim -1=measured values, dummyval = values used to fill empty slots in DA
# PREPARE FOR MAIN LOOP
dcount = -1 # prepare for pre-increment of D-variable pointer
Bwsources = [] # binary #s, each=source containing w/i subj factors
Bwonly_sources = [] # binary #s, each=source of w/i-subj-ONLY factors
D = N.zeros(Nwsources,N.PyObject) # one slot for each Dx,2**Nwifactors
DM = [0] *Nwsources # Holds arrays of cell-means
DN = [0] *Nwsources # Holds arrays of cell-ns
# BEGIN MAIN LOOP!!!!!
# BEGIN MAIN LOOP!!!!!
# BEGIN MAIN LOOP!!!!!
for source in range(3,Nallsources,2): # all sources that incl. subjects
if ((source-1) & Bwithins) != 0: # 1 or more w/i subj sources?
Bwsources.append(source-1) # add it to a list
#
# WITHIN-SUBJECT-ONLY TERM? IF SO ... NEED TO CALCULATE NEW D-VARIABLE
# (per Maxwell & Delaney pp.622-4)
if subset((source-1),Bwithins):
# Keep track of which D-var set we're working with (De, Df, Def, etc.)
dcount = dcount + 1
Bwonly_sources.append(source-1) #add source, minus subj,to list
dwsc = 1.0 * DA # get COPY of w/i-subj data array
# Find all non-source columns, note ~source alone (below) -> negative number
Bnonsource = (Nallsources-1) & ~source
Bwscols = makebin(Wscols) # make a binary version of Wscols
# Figure out which cols from the ORIGINAL (input) data matrix are both non-
# source and also within-subj vars (excluding subjects col)
Bwithinnonsource = Bnonsource & Bwscols
# Next, make a list of the above. The list is a list of dimensions in DA
# because DA has the same number of dimensions as there are factors
# (including subjects), but with extra dummyval='-1' values the original
# data array (assuming between-subj vars exist)
Lwithinnonsource = makelist(Bwithinnonsource,Nfactors+1)
# Collapse all non-source, w/i subj dims, FROM THE END (otherwise the
# dim-numbers change as you collapse). THIS WORKS BECAUSE WE'RE
# COLLAPSING ACROSS W/I SUBJECT DIMENSIONS, WHICH WILL ALL HAVE THE
# SAME SUBJ IN THE SAME ARRAY LOCATIONS (i.e., dummyvals will still exist
# but should remain the same value through the amean() function
for i in range(len(Lwithinnonsource)-1,-1,-1):
dwsc = amean(dwsc,Lwithinnonsource[i])
mns = dwsc
# NOW, ACTUALLY COMPUTE THE D-VARIABLE ENTRIES FROM DA
# CREATE LIST OF COEFF-COMBINATIONS TO DO (len=e-1, f-1, (e-1)*(f-1), etc...)
#
# Figure out which cols are both source and within-subjects, including col 0
Bwithinsource = source & Bwscols
# Make a list of within-subj cols, incl subjects col (0)
Lwithinsourcecol = makelist(Bwithinsource, Nfactors+1)
# Make a list of cols that are source within-subj OR btw-subj
Lsourceandbtws = makelist(source | Bbetweens, Nfactors+1)
if Lwithinnonsource <> []:
Lwithinsourcecol = map(Lsourceandbtws.index,Lwithinsourcecol)
# Now indxlist should hold a list of indices into the list of possible
# coefficients, one row per combo of coefficient. Next line PRESERVES dummyval
dvarshape = N.array(N.take(mns.shape,Lwithinsourcecol[1:])) -1
idxarray = N.indices(dvarshape)
newshape = N.array([idxarray.shape[0],
N.multiply.reduce(idxarray.shape[1:])])
indxlist = N.swapaxes(N.reshape(idxarray,newshape),0,1)
# The following is what makes the D-vars 2D. It takes an n-dim array
# and retains the first (num of factors) dim while making the 2nd dim
# equal to the total number of source within-subject cells.
#
# CREATE ALL D-VARIABLES FOR THIS COMBINATION OF FACTORS
#
for i in range(len(indxlist)):
#
# FILL UP COEFFMATRIX (OF SHAPE = MNS) WITH CORRECT COEFFS FOR 1 D-VAR
#
coeffmatrix = N.ones(mns.shape,N.Float) # fewer dims than DA (!!)
# Make a list of dim #s that are both in source AND w/i subj fact, incl subj
Wsourcecol = makelist(Bwscols&source,Nfactors+1)
# Fill coeffmatrix with a complete set of coeffs (1 per w/i-source factor)
for wfactor in range(len(Lwithinsourcecol[1:])):
#put correct coeff. axis as first axis, or "swap it up"
coeffmatrix = N.swapaxes(coeffmatrix,0,
Lwithinsourcecol[wfactor+1])
# Find appropriate ROW of (static) coefflist we need
nlevels = coeffmatrix.shape[0]
# Get the next coeff in that row
try:
nextcoeff = coefflist[nlevels-1][indxlist[i,wfactor]]
except IndexError:
raise IndexError, "anova() can only handle up to 10 levels on a within-subject factors"
for j in range(nlevels):
coeffmatrix[j] = coeffmatrix[j] * nextcoeff[j]
# Swap it back to where it came from
coeffmatrix = N.swapaxes(coeffmatrix,0,
Lwithinsourcecol[wfactor+1])
# CALCULATE D VARIABLE
scratch = coeffmatrix * mns
# Collapse all dimensions EXCEPT subjects dim (dim 0)
for j in range(len(coeffmatrix.shape[1:])):
scratch = N.add.reduce(scratch,1)
if len(scratch.shape) == 1:
scratch.shape = list(scratch.shape)+[1]
try:
# Tack this column onto existing ones
tmp = D[dcount].shape
D[dcount] = pstat.aabut(D[dcount],scratch)
except AttributeError: # i.e., D[dcount]=integer/float
# If this is the first, plug it in
D[dcount] = scratch
# Big long thing to create DMarray (list of DM variables) for this source
variables = D[dcount].shape[1] # Num variables for this source
tidx = range(1,len(subjslots.shape)) + [0] # [0] = Ss dim
tsubjslots = N.transpose(subjslots,tidx) # put Ss in last dim
DMarray = N.zeros(list(tsubjslots.shape[0:-1]) +
[variables],'f') # btw-subj dims, then vars
DNarray = N.zeros(list(tsubjslots.shape[0:-1]) +
[variables],'f') # btw-subj dims, then vars
idx = [0] *len(tsubjslots.shape[0:-1])
idx[0] = -1
loopcap = N.array(tsubjslots.shape[0:-1]) -1
while incr(idx,loopcap) <> -1:
DNarray[idx] = float(asum(tsubjslots[idx]))
thismean = (N.add.reduce(tsubjslots[idx] * # 1=subj dim
N.transpose(D[dcount]),1) /
DNarray[idx])
thismean = N.array(thismean,N.PyObject)
DMarray[idx] = thismean
DM[dcount] = DMarray
DN[dcount] = DNarray
#
# DONE CREATING M AND D VARIABLES ... TIME FOR SOME SS WORK
# DONE CREATING M AND D VARIABLES ... TIME FOR SOME SS WORK
#
if Bscols[1:] <> []:
BNs = pstat.colex([Nlevels],Bscols[1:])
else:
BNs = [1]
#
# FIGURE OUT WHICH VARS TO RESTRICT, see p.680 (Maxwell&Delaney)
#
# BETWEEN-SUBJECTS VARIABLES ONLY, use M variable for analysis
#
if ((source-1) & Bwithins) == 0: # btw-subjects vars only?
sourcecols = makelist(source-1,Nfactors+1)
# Determine cols (from input list) required for n-way interaction
Lsource = makelist((Nallsources-1)&Bbetweens,Nfactors+1)
# NOW convert this list of between-subject column numbers to a list of
# DIMENSIONS in M, since M has fewer dims than the original data array
# (assuming within-subj vars exist); Bscols has list of between-subj cols
# from input list, the indices of which correspond to that var's loc'n in M
btwcols = map(Bscols.index,Lsource)
# Obviously-needed loop to get cell means is embedded in the collapse fcn, -1
# represents last (measured-variable) column, None=std, 1=retain Ns
hn = aharmonicmean(Narray,-1) # -1=unravel first
# CALCULATE SSw ... SUBTRACT APPROPRIATE CELL MEAN FROM EACH SUBJ SCORE
SSw = 0.0
idxlist = pstat.unique(pstat.colex(M,btwcols))
for row in M:
idx = []
for i in range(len(row[:-1])):
idx.append(alluniqueslist[Bscols[i]].index(row[i]))
idx = idx[1:] # Strop off Ss col/dim
newval = row[-1] - Marray[idx]
SSw = SSw + (newval)**2
# Determine which cols from input are required for this source
Lsource = makelist(source-1,Nfactors+1)
# NOW convert this list of between-subject column numbers to a list of
# DIMENSIONS in M, since M has fewer dims than the original data array
# (assuming within-subj vars exist); Bscols has list of between-subj cols
# from input list, the indices of which correspond to that var's loc'n in M
btwsourcecols = (N.array(map(Bscols.index,Lsource))-1).tolist()
# Average Marray and get harmonic means of Narray OVER NON-SOURCE DIMS
Bbtwnonsourcedims = ~source & Bbetweens
Lbtwnonsourcedims = makelist(Bbtwnonsourcedims,Nfactors+1)
btwnonsourcedims = (N.array(map(Bscols.index,Lbtwnonsourcedims))-1).tolist()
## Average Marray over non-source dimensions (1=keep squashed dims)
sourceMarray = amean(Marray,btwnonsourcedims,1)
## Calculate harmonic means for each level in source
sourceNarray = aharmonicmean(Narray,btwnonsourcedims,1)
## Calc grand average (ga), used for ALL effects
ga = asum((sourceMarray*sourceNarray)/
asum(sourceNarray))
ga = N.reshape(ga,N.ones(len(Marray.shape)))
## If GRAND interaction, use harmonic mean of ALL cell Ns
if source == Nallsources-1:
sourceNarray = aharmonicmean(Narray)
## Calc all SUBSOURCES to be subtracted from sourceMarray (M&D p.320)
sub_effects = 1.0 * ga # start with grand mean
for subsource in range(3,source,2):
## Make a list of the non-subsource dimensions
if subset(subsource-1,source-1):
sub_effects = (sub_effects +
alleffects[alleffsources.index(subsource)])
## Calc this effect (a(j)'s, b(k)'s, ab(j,k)'s, whatever)
effect = sourceMarray - sub_effects
## Save it so you don't have to calculate it again next time
alleffects.append(effect)
alleffsources.append(source)
## Calc and save sums of squares for this source
SS = asum((effect**2 *sourceNarray) *
N.multiply.reduce(N.take(Marray.shape,btwnonsourcedims)))
## Save it so you don't have to calculate it again next time
SSlist.append(SS)
SSsources.append(source)
collapsed = pstat.collapse(M,btwcols,-1,None,len,mean)
# Obviously needed for-loop to get source cell-means embedded in collapse fcns
contrastmns = pstat.collapse(collapsed,btwsourcecols,-2,sterr,len,mean)
# Collapse again, this time SUMMING instead of averaging (to get cell Ns)
contrastns = pstat.collapse(collapsed,btwsourcecols,-1,None,None,
N.sum)
# Collapse again, this time calculating harmonicmeans (for hns)
contrasthns = pstat.collapse(collapsed,btwsourcecols,-1,None,None,
harmonicmean)
# CALCULATE *BTW-SUBJ* dfnum, dfden
sourceNs = pstat.colex([Nlevels],makelist(source-1,Nfactors+1))
dfnum = N.multiply.reduce(N.ravel(N.array(sourceNs)-1))
dfden = Nsubjects - N.multiply.reduce(N.ravel(BNs))
# CALCULATE MS, MSw, F AND PROB FOR ALL-BETWEEN-SUBJ SOURCES ONLY
MS = SS / dfnum
MSw = SSw / dfden
if MSw <> 0:
f = MS / MSw
else:
f = 0 # i.e., absolutely NO error in the full model
if f >= 0:
prob = fprob(dfnum, dfden, f)
else:
prob = 1.0
# Now this falls thru to output stage
#
# SOME WITHIN-SUBJECTS FACTORS TO DEAL WITH ... use appropriate D variable
#
else: # Source has some w/i subj factors
# FIGURE OUT WHICH D-VAR TO USE BASED ON WHICH W/I-SUBJ FACTORS ARE IN SOURCE
# Determine which w/i-subj factors are in this source
sourcewithins = (source-1) & Bwithins
# Use D-var that was created for that w/i subj combo (the position of that
# source within Bwsources determines the index of that D-var in D)
workD = D[Bwonly_sources.index(sourcewithins)]
# CALCULATE Er, Ef
## Set up workD and subjslots for upcoming calcs
if len(workD.shape)==1:
workD = workD[:,N.NewAxis]
if len(subjslots.shape)==1:
subjslots = subjslots[:,N.NewAxis]
## Calculate full-model sums of squares
ef = Dfull_model(workD,subjslots) # Uses cell-means model
#
# **ONLY** WITHIN-SUBJECT VARIABLES TO CONSIDER
#
if subset((source-1),Bwithins):
# restrict grand mean, as per M&D p.680
er = Drestrict_mean(workD,subjslots)
#
# **BOTH** WITHIN- AND BETWEEN-SUBJECTS VARIABLES TO CONSIDER
#
else:
er = Drestrict_source(workD,subjslots,source) + ef
SSw = LA.determinant(ef)
SS = LA.determinant(er) - SSw
# CALCULATE *W/I-SUBJ* dfnum, dfden
sourceNs = pstat.colex([Nlevels],makelist(source,Nfactors+1))
# Calculation of dfnum is straightforward regardless
dfnum = N.multiply.reduce(N.ravel(N.array(sourceNs)-1)[1:])
# If only within-subject factors are involved, dfden is straightforward
if subset(source-1,Bwithins):
dfden = Nsubjects -N.multiply.reduce(N.ravel(BNs))-dfnum +1
MS = SS / dfnum
MSw = SSw / dfden
if MSw <> 0:
f = MS / MSw
else:
f = 0 # i.e., absolutely NO error in full model
if f >= 0:
prob = fprob(dfnum, dfden, f)
else:
prob = 1.0
# If combined within-between source, must use Rao's approximation for dfden
# from Tatsuoka, MM (1988) Multivariate Analysis (2nd Ed), MacMillan: NY p93
else: # it's a within-between combo source
try:
p = workD.shape[1]
except IndexError:
p = 1
k = N.multiply.reduce(N.ravel(BNs))
m = Nsubjects -1 -(p+k)/2.0
d_en = float(p**2 + (k-1)**2 - 5)
if d_en == 0.0:
s = 1.0
else:
s = math.sqrt(((p*(k-1))**2-4) / d_en)
dfden = m*s - dfnum/2.0 + 1
# Given a within-between combined source, Wilk's Lambda is appropriate
if LA.determinant(er) <> 0:
lmbda = LA.determinant(ef) / LA.determinant(er)
W = math.pow(lmbda,(1.0/s))
f = ((1.0-W)/W) * (dfden/dfnum)
else:
f = 0 # i.e., absolutely NO error in restricted model
if f >= 0:
prob = fprob(dfnum,dfden,f)
else:
prob = 1.0
#
# CREATE STRING-LIST FOR RESULTS FROM THIS PARTICULAR SOURCE
#
suffix = '' # for *s after the p-value
if prob < 0.001: suffix = '***'
elif prob < 0.01: suffix = '**'
elif prob < 0.05: suffix = '*'
adjsourcecols = N.array(makelist(source-1,Nfactors+1)) -1
thiseffect = ''
for col in adjsourcecols:
if len(adjsourcecols) > 1:
thiseffect = thiseffect + effects[col][0]
else:
thiseffect = thiseffect + (effects[col])
outputlist = (outputlist
# These terms are for the numerator of the current effect/source
+ [[thiseffect, round4(SS),dfnum,
round4(SS/float(dfnum)),round4(f),
round4(prob),suffix]]
# These terms are for the denominator for the current effect/source
+ [[thiseffect+'/w', round4(SSw),dfden,
round4(SSw/float(dfden)),'','','']]
+ [['\n']])
#
# PRINT OUT ALL MEANS AND Ns FOR THIS SOURCE (i.e., this combo of factors)
#
Lsource = makelist(source-1,Nfactors+1)
collapsed = pstat.collapse(cdata,Lsource,-1,sterr,len,mean)
# First, get the list of level-combos for source cells
prefixcols = range(len(collapsed[0][:-3]))
outlist = pstat.colex(collapsed,prefixcols)
# Start w/ factor names (A,B,C, or ones input to anova())
eff = []
for col in Lsource:
eff.append(effects[col-1])
# Add in the mean and N labels for printout
for item in ['MEAN','STERR','N']:
eff.append(item)
# To the list of level-combos, abut the corresp. means and Ns
outlist = pstat.abut(outlist,
map(round4,pstat.colex(collapsed,-3)),
map(round4,pstat.colex(collapsed,-2)),
map(round4,pstat.colex(collapsed,-1)))
outlist = [eff] + outlist # add titles to the top of the list
pstat.printcc(outlist) # print it in customized columns
print
###
### OUTPUT FINAL RESULTS (ALL SOURCES TOGETHER)
### Note: All 3 types of source-calcs fall through to here
###
print
title = [['FACTORS: ','RANDOM'] + effects[:Nfactors]]
title = title + [['LEVELS: ']+Nlevels]
facttypes = ['BETWEEN']*Nfactors
for i in range(len(Wscols[1:])):
facttypes[Wscols[i+1]-1] = 'WITHIN'
title = title + [['TYPE: ','RANDOM']+facttypes]
pstat.printcc(title)
print
title = [['Effect','SS','DF','MS','F','p','sig']] + ['dashes']
outputlist = title + outputlist
pstat.printcc(outputlist)
return
def DoMoleBalance(self, canUseEnth, calcStatus):
"""do a balance on the stream components.
If canUseEnth is true enthalpy balances may be used to try and
determine mole flows
"""
missing = [] # port missing port array (port, inletFlag)
sum = 0.0
nuPortsIn = len(self._matIn)
nuPortsOut = len(self._matOut)
totPorts = nuPortsIn + nuPortsOut
balanced = 0
if totPorts == 1:
balanced = 1
return balanced
if nuPortsIn: aPort = self._matIn[0]
elif nuPortsOut: aPort = self._matOut[0]
else:
balanced = 1
return balanced
scaleFactor = PropTypes[MOLEFLOW_VAR].scaleFactor
tolerance = aPort.GetParentOp().GetTolerance()
# do outlets
allMatOutAreZero = 1
for port in self._matOut:
flow = port.GetPropValue(MOLEFLOW_VAR)
if flow == None:
missing.append((port,0))
allMatOutAreZero = 0
else:
sum -= flow
if allMatOutAreZero:
if abs(flow)/scaleFactor >= tolerance:
allMatOutAreZero = 0
#This makes sure that aPort is not a zero flow
aPort = port
# do inlets
allMatInAreZero = 1
for port in self._matIn:
flow = port.GetPropValue(MOLEFLOW_VAR)
if flow == None:
missing.append((port,1))
allMatInAreZero = 0
else:
sum += flow
if allMatInAreZero:
if abs(flow)/scaleFactor >= tolerance:
allMatInAreZero = 0
#This makes sure that aPort is not a zero flow
aPort = port
#Mmmhh, Always check if H and composition can be shared
if totPorts == 2:
myPortLst = self._matIn + self._matOut
for i in range(len(myPortLst)-1):
myPortLst[i].ShareComposition(myPortLst[i+1])
if canUseEnth:
allEneAreZero = 1
eneScaleFactor = PropTypes[ENERGY_VAR].scaleFactor
for eneP in self._eneIn + self._eneOut:
eneFlow = eneP.GetPropValue(ENERGY_VAR)
if eneFlow == None or eneFlow != 0.0:
allEneAreZero = 0
break
if allEneAreZero:
for i in range(len(myPortLst)-1):
myPortLst[i].SharePropWith(myPortLst[i+1], H_VAR)
nuMissing = len(missing)
if nuMissing == 0:
# all flows known, but do consistency check
if aPort:
if scaleFactor:
if abs(sum)/scaleFactor > tolerance:
prop = aPort.GetProperty(MOLEFLOW_VAR)
aPort.GetParentOp().PushConsistencyError(prop, sum)
elif nuMissing == 1:
if missing[0][1]:
sum = -sum
missing[0][0].SetPropValue(MOLEFLOW_VAR, sum, calcStatus)
missing[0][0].CalcFlows()
else:
# more than 1 unknown
# see if we can find as many knowns as unknowns
# start with overall mole flow
row = []
a = [] # hold matrix
b = [] # hold rhs
for i in missing:
if i[1]: row.append(1.0)
else: row.append(-1.0)
a.append(row)
b.append(-sum)
if canUseEnth:
# see if all missing ports have enthalpies
row = []
for i in missing:
(port, isIn) = i
h = port.GetPropValue(H_VAR)
if h == None:
break # need them all
if isIn: row.append(h)
else: row.append(-h)
if len(row) == nuMissing:
# see if we can get the nonmissing total
sumq = 0.0
nuMissingQ = 0
for port in self._matIn:
q = port.GetPropValue(ENERGY_VAR)
if q == None:
nuMissingQ += 1
else:
sumq -= q
for port in self._matOut:
q = port.GetPropValue(ENERGY_VAR)
if q == None:
nuMissingQ += 1
else:
sumq += q
for port in self._eneIn:
q = port.GetPropValue(ENERGY_VAR)
if q == None:
nuMissingQ += 1
else:
sumq -= q
for port in self._eneOut:
q = port.GetPropValue(ENERGY_VAR)
if q == None:
nuMissingQ += 1
else:
sumq += q
if nuMissingQ == nuMissing:
# note conversion to W from KJ/hr and vice versa
b.append(sumq * 3.6)
a.append(row)
# look for mole fractions to use
for cmpNo in range(len(aPort.GetCompounds())):
if len(a) == nuMissing:
break # have enough equations
# see if all missing ports have mole fractions
row = []
for i in missing:
(port, isIn) = i
x = port.GetCompounds()[cmpNo].GetValue()
if x == None:
break # need them all
if isIn: row.append(x)
else: row.append(-x)
if len(row) != nuMissing:
continue
sumN = 0.0
nuMissingN = 0
for port in self._matIn:
flow = port.GetPropValue(MOLEFLOW_VAR)
x = port.GetCompounds()[cmpNo].GetValue()
if flow == None or x == None:
nuMissingN += 1
else:
sumN -= x * flow
for port in self._matOut:
flow = port.GetPropValue(MOLEFLOW_VAR)
x = port.GetCompounds()[cmpNo].GetValue()
if flow == None or x == None:
nuMissingN += 1
else:
sumN += x * flow
if nuMissingN == nuMissing:
b.append(sumN)
a.append(row)
if len(a) != nuMissing:
return balanced # not enough info
try:
if abs(determinant(array(a))) < 0.0001:
return balanced
flows = solve_linear_equations(array(a),array(b))
except:
return balanced
for i in range(nuMissing):
missing[i][0].SetPropValue(MOLEFLOW_VAR, flows[i], calcStatus)
missing[i][0].CalcFlows()
# flows are now known - do components
cmps = aPort.GetCompounds()
#iterate through components
missing = None
for cmpNo in range(len(cmps)):
sum = 0.0
# inlets
for port in self._matIn:
flow = port.GetPropValue(MOLEFLOW_VAR)
if flow == None:
return balanced # should not happen
if flow != 0.0:
x = port.GetCompounds()[cmpNo].GetValue()
if x != None:
if missing and missing is port:
return balanced # all components must be missing
sum += x * flow
elif missing and not port is missing:
return balanced # all missing compositions must be in same port
else:
missing = port
missingInlet = 1
# outlets
for port in self._matOut:
flow = port.GetPropValue(MOLEFLOW_VAR)
if flow == None:
return balanced # shouldn't happen
if flow != 0.0:
x = port.GetCompounds()[cmpNo].GetValue()
if x != None:
if missing and missing is port:
return balanced # all components must be missing
sum -= x * flow
elif missing and not port is missing:
return balanced # all missing compositions must be in same port
else:
missing = port
missingInlet = 0
#It balanced
if missing:
flow = missing.GetPropValue(MOLEFLOW_VAR)
if flow == 0:
return balanced
if missingInlet:
sum = -sum
missing.GetCompounds()[cmpNo].SetValue(sum/flow, calcStatus)
missing.CalcFlows()
else:
flow = aPort.GetPropValue(MOLEFLOW_VAR)
if flow == 0:
flow = 1000.0 # arbitrary scaling
x = abs(sum)/flow
scaleFactor = PropTypes[FRAC_VAR].scaleFactor
if scaleFactor:
tolerance = aPort.GetParentOp().GetTolerance()
if x/scaleFactor > tolerance:
prop = aPort.GetCompounds()[cmpNo]
aPort.GetParentOp().PushConsistencyError(prop, x)
#If it made it all the way here, then it must be balanced
balanced = 1
return balanced