def rank_by_w_correl(self):
''' find optimal rank by:
2) calculate summ of correlations for each row of self.w_correl
3) find index where those summ is minimal. This is a rank
@return pair of (calculated rank of SVD, w-correlation for that rank))
Note: rank >= 1
'''
# w-correlation matrix has simmetry about main diagonal.
# Coefficients at main diagonal always 1(self correlation).
# Coefficients at (i+1,j) where j=1(close to main diagonal) can
# be viewed as correlation of cos/sin of the same frequency
# when coefficient more 0.5 and as noise in other case.
# Assumptions:
# - calculation is made in one half of matrix,
# - main diagonal excluded from calculation.
# - for element (i,i) calculation made for elements (i+1, i+wd), where
# wd is a w-correlation depth.
# - No more than wlen elements analyzed. Assume rank of S no more
# than rank_max.
# - according to condition above, size of analized SVD is
# wd + rank_max.
# - correlations should be calculated at early step because
# the same value is used ofter more than one time.
if not self.ssa:
return 0, 0
# calc w-correl limit
rank_max = min(len(self.s_svd()) - 5, self.SSA_RANK_MAX)
if rank_max < 0:
self.log.error("Could not calc w-correl - S too short")
if rank_max + self.W_MIN_DEPTH > len(self.s_svd()):
m_size = len(self.s_svd())
else:
m_size = rank_max + self.W_MIN_DEPTH
if rank_max > len(self.s_svd()):
rank_max = len(self.s_svd())
if self.w_correl is None:
self.calc_w_unit_correl_matrix(rank_max, m_size)
weights = self.calc_w_unit_correl_weights(rank_max)
log_array(weights, "weights of w-correlation")
if self.USE_W_CORR_WEIGHTS:
self.log.info("correction weights by square")
for i in range(weights.size):
square = (i + 1) * (m_size - i)
weights[i] /= square
log_array(weights, "normalized by square weights of w-correlation")
w_min = 1e10
rank = -1
# first and second values excluded, because:
# 1) anyway, this value in most cases in small;
# 2) rank = 1 is not interested in most cases.
if weights.size < 3:
imin = 1
else:
imin = 3
for i in range(imin, weights.size):
if weights[i] < w_min:
rank = i
w_min = weights[i]
return (rank + 1, w_min)
def debug_array(self, m, title):
if self.loglevel <= logging.DEBUG:
log_array(m, title)