def computeG(rna,F,Z):
G = {}; n = len(rna); rna = '$'+rna
#-------------------------------------------
#Initialization to zero
for d in range(n): #d in [0,n-1]
for i in range(1,n+1-d): #i in [1,n-d]
j = i+d
for ch in NUCL:
for x in range(n+1):
G[(i,j,ch,x)] = 0
#-------------------------------------------
#Recursions
for d in range(4,n): #d in [4,n-1]
for i in range(1,n+1-d): #i in [1,n-d]
j = i+d #note that num elements in [i,j] is d+1
for ch in NUCL:
for x in range(d+1-4+1): #x in [0,d+1-4]
#Case 1: positions j-3,j-2,j-1,j are unpaired in S
G[(i,j,ch,x)] = F[(i,j-4,ch,x)]
#Case 2: j-4+u is paired, but j-4+u+1,...,j are unpaired in S
for u in range(1,5): #u in [1,4], consider 4-u unpaired in suffix
#Subcase A: (i,j-4+u) is base pair in S
if x==0 and j-4+u-i>THETA and basePair(rna[i],rna[j-4+u]):
G[(i,j,ch,x)] += Z[(i+1,j-4+u-1)]
#Subcase B: (k,j-4+u) is base pair in S, some k in [i+1,j-4+u-4]
for k in range(i+1,j-4+u-4+1): #k in [i+1,(j-4+u)-4]
if j-4+u-k>THETA and basePair(rna[k],rna[j-4+u]):
G[(i,j,ch,x)] += F[(i,k-1,ch,x)]*Z[(k+1,j-4+u-1)]
return G
def computeJ(rna,Z,FF):
#J(i,j,ch,x) is num str S on [i,j] having x visible occ of a nucl [i,j-4]
#which can basepair with rna[j] and in which j is unpaired in S.
#WARNING: J(i,j,ch,0) defined to be zero if i <= j <= i+3
J = {}; n = len(rna); rna = '$'+rna
#-------------------------------------------
#Initialization to zero
for d in range(n): #d in [0,n-1]
for i in range(1,n+1-d): #i in [1,n-d]
j = i+d
for ch in NUCL:
for x in range(n+1):
J[(i,j,ch,x)] = 0
#-------------------------------------------
#Recursions
for d in range(4,n): #d in [4,n-1]
for i in range(1,n+1-d): #i in [1,n-d]
j = i+d #note that num elements in [i,j] is d+1
for ch in NUCL:
for x in range(d+1-4+1): #x in [0,d+1-4]
#Case 1: positions j-3,j-2,j-1,j are unpaired in S
J[(i,j,ch,x)] = FF[(i,j-4,ch,x)]
#Case 2: j-4+u is paired, but j-4+u+1,...,j are unpaired in S
for u in range(1,4): #u in [1,3], consider 4-u unpaired in suffix
#Subcase A: (i,j-4+u) is base pair in S
if x==0 and j-4+u-i>THETA and basePair(rna[i],rna[j-4+u]):
J[(i,j,ch,x)] += Z[(i+1,j-4+u-1)]
#Subcase B: (k,j-4+u) is base pair in S, some k in [i+1,j-4+u-4]
for k in range(i+1,j-4+u-4+1): #k in [i+1,(j-4+u)-4]
if j-4+u-k>THETA and basePair(rna[k],rna[j-4+u]):
J[(i,j,ch,x)] += FF[(i,k-1,ch,x)]*Z[(k+1,j-4+u-1)]
return J
def computeEprime(rna,Z,E):
#Eprime(i,j) is sum over str on [i,j] sum over base pairs (x,y) in S
#I[(x,y) external in S and y <= j-4, AND j unpaired in S]
Eprime = {}; n = len(rna); rna = '$'+rna
#-------------------------------------------
#Initialization to zero
for d in range(n): #d in [0,n-1]
for i in range(1,n+1-d): #i in [1,n-d]
j = i+d
Eprime[(i,j)] = 0
#-------------------------------------------
#Recursions
for d in range(4,n): #d in [4,n-1]
for i in range(1,n+1-d): #i in [1,n-d]
j = i+d #note that num elements in [i,j] is d+1
#Case 1: positions j-3,j-2,j-1,j are unpaired in S
Eprime[(i,j)] = E[(i,j-4)]
#Case 2: j-4+u is paired, but j-4+u+1,...,j are unpaired in S
for u in range(1,4): #u in [1,3], consider 4-u unpaired in suffix
#Subcase A: (i,j-4+u) is base pair in S
if j-4+u-i>THETA and basePair(rna[i],rna[j-4+u]):
Eprime[(i,j)] += 0 #left here for clarity
#Subcase B: (k,j-4+u) is base pair in S, some k in [i+1,j-4+u-4]
for k in range(i+1,j-4+u-4+1): #k in [i+1,(j-4+u)-4]
if j-4+u-k>THETA and basePair(rna[k],rna[j-4+u]):
Eprime[(i,j)] += E[(i,k-1)]*Z[(k+1,j-4+u-1)]
return Eprime
def computeERprime(rna,Z,ER):
#ERprime(i,j,ch) is sum over str on [i,j] sum over base pairs (x,y) in S
#I[ S on [i,j], (x,y) external in S, y <= j-4, j unpaired in S and
# y basepairs with ch]
ERprime = {}; n = len(rna); rna = '$'+rna
#-------------------------------------------
#Initialization to zero
for d in range(n): #d in [0,n-1]
for i in range(1,n+1-d): #i in [1,n-d]
for ch in NUCL:
j = i+d
ERprime[(i,j,ch)] = 0
#-------------------------------------------
#Recursions
for ch in NUCL:
for d in range(4,n): #d in [4,n-1]
for i in range(1,n+1-d): #i in [1,n-d]
j = i+d #note that num elements in [i,j] is d+1
#Case 1: positions j-3,j-2,j-1,j are unpaired in S
ERprime[(i,j,ch)] = ER[(i,j-4,ch)]
#Case 2: j-4+u is paired, but j-4+u+1,...,j are unpaired in S
for u in range(1,4): #u in [1,3], consider 4-u unpaired in suffix
#Subcase A: (i,j-4+u) is base pair in S
if j-4+u-i>THETA and basePair(rna[i],rna[j-4+u]):
ERprime[(i,j,ch)] += 0 #left here for clarity
#Subcase B: (k,j-4+u) is base pair in S, some k in [i+1,j-4+u-4]
for k in range(i+1,j-4+u-4+1): #k in [i+1,(j-4+u)-4]
ok = j-4+u-k>THETA and basePair(rna[k],rna[j-4+u])
#WARNING: It is an ERROR to additionally require that
#basePair(ch,rna[j-4+u]), since j-4+u too close to j and so
#can't base pair with it.
if ok:
ERprime[(i,j,ch)] += ER[(i,k-1,ch)]*Z[(k+1,j-4+u-1)]
return ERprime
def numNborsNoShift(rna, Z):
#Q[(i,j)] = sum_x N(x), where x is sec str of rna[i:j+1] without shift
#Z[(i,j)] = number of sec str of rna[i:j+1]
Q = {}
n = len(rna)
rna = '$' + rna #add dummy character
#base case j-i in [0,1,2,3]
for i in range(1, n + 1):
for d in range(0, min(THETA, n - i) + 1):
j = i + d
Q[(i, j)] = 0.0
#inductive case j-i > 3, compute Q[(i,j)] all 1<=i<=j<=n
for d in range(THETA + 1, n + 1):
for i in range(1, n + 1):
j = i + d
if (j > n): break
q = Q[(i, j - 1)]
if basePair(rna[i], rna[j]):
q += 2 * Z[(i + 1, j - 1)] + Q[(i + 1, j - 1)]
for k in range(i + 1, j - THETA):
if basePair(rna[k], rna[j]):
q += 2 * Z[(i, k - 1)] * Z[(k + 1, j - 1)] + Z[
(i, k - 1)] * Q[(k + 1, j - 1)] + Q[(i, k - 1)] * Z[
(k + 1, j - 1)]
Q[(i, j)] = q
return Q[(1, n)]
def computeEright(rna,Z):
#ER(i,j,ch) = sum_S sum_{(x,y)}
# I[(x,y) external in S, y basepairs with ch]
ER = {}
n = len(rna)
rna = '$'+rna
#initialize
for i in range(1,n+1):
for j in range(i,n+1):
for ch in NUCL:
ER[(i,j,ch)] = 0
#fill
for ch in NUCL:
for d in range(THETA+1,n): #d in [4,n-1]
for i in range(1,n-d+1): #i in [1,n-d]
j = i+d
sum = ER[(i,j-1,ch)]
if basePair(rna[i],rna[j]) and basePair(rna[j],ch):
sum += Z[(i+1,j-1)]
for k in range(i+1,j-THETA):# k in [i+1..j-THETA-1]
if basePair(rna[k],rna[j]):
sum += ER[(i,k-1,ch)]*Z[(k+1,j-1)]
if basePair(rna[j],ch):
sum += Z[(i,k-1)]*Z[(k+1,j-1)]
# sum += (ER[(i,k-1,ch)]+Z[(i,k-1)])*Z[(k+1,j-1)]
ER[(i,j,ch)] = sum
return ER
def computeFF(rna,Z):
#Compute the function FF(i,j,ch,x) defined to be the
#num str on [i,j] having x visible occurrences of a nucleotide
#which can basepair with x. Note the difference with computeF(rna,Z)!!!
FF = {}
n = len(rna)
rna = '$'+rna
#initialization
#----------------------------------------------
#initialize all entries to 0
for i in range(1,n+1): #i in [1,n]
for j in range(i,n+1): #j in [i,n]
for ch in NUCL:
for x in range(n+1): #x in [0,n]
FF[(i,j,ch,x)] = 0
#----------------------------------------------
#Base case: define FF(i,j,ch,x) for i=j
for i in range(1,n+1): #i in [1,n]
for ch in NUCL:
if basePair(ch,rna[i]):
FF[(i,i,ch,1)] = 1
else:
FF[(i,i,ch,0)] = 1
#----------------------------------------------
#Base case: define FF(i,j,ch,x) for i<j<i+4
for i in range(1,n+1): #i in [1,n]
for j in range(i+1,min(n,i+3)+1): #j in [i+1,min(n,i+3)]
for ch in NUCL:
for x in range(j-i+2): #x in [0,j-i+1]
if basePair(ch,rna[j]):
if x>0:
FF[(i,j,ch,x)] = FF[(i,j-1,ch,x-1)]
else:
FF[(i,j,ch,x)] = FF[(i,j-1,ch,x)]
#----------------------------------------------
#Inductive case: define FF(i,j,ch,x) for j>=i+4
for d in range(4,n): #d in [4,n-1]
for i in range(1,n-d+1): #i in [1,n-d]
j = i+d #note that [i,j] contains d+1 elements
#Case 1: j unpaired in [i,j]
for ch in NUCL:
for x in range(d+2): #x in [0,d+1]
if basePair(ch,rna[j]):
if x>0:
FF[(i,j,ch,x)] = FF[(i,j-1,ch,x-1)]
else:
FF[(i,j,ch,x)] = FF[(i,j-1,ch,x)]
#Case 2: (i,j) is base pair in S
if basePair(rna[i],rna[j]):
for ch in NUCL:
FF[(i,j,ch,0)] += Z[(i+1,j-1)]
#Case 3: (k,j) is base pair in S for k in [i+1,j-4]
for k in range(i+1,j-3): #k in [i+1,j-4]
if basePair(rna[k],rna[j]):
for ch in NUCL:
for x in range(k-i+1): #x in [0,k-i], where k-i num elem in [i,k-1]
FF[(i,j,ch,x)] += FF[(i,k-1,ch,x)]*Z[(k+1,j-1)]
return FF
def numShifts(rna, secStr): #brute force computation of number shifts
#rna and secStr is 1-indexed
if VERBOSE_PRINT:
print "Sec str: %s" % secStr
n = len(rna)
rna0 = rna
secStr0 = secStr
rna = '$' + rna
secStr = '$' + secStr
SS = basePairList(secStr)
num = 0
tempSS = copy.deepcopy(SS)
for (i, j) in SS:
tempSS.remove((i, j))
if VERBOSE_PRINT:
print "Remove (%d,%d) from %s" % (i, j, secStr[1:])
for x in range(1, n + 1):
if abs(i - x) > THETA and x != j and basePair(rna[i], rna[x]):
if i < x:
tempSS.append((i, x))
if isSecStr(tempSS):
num += 1
if VERBOSE_PRINT:
ss = basePairList2dotBracketNotation(rna0, tempSS)
print '(%d,%d)\t%s' % (i, x, ss)
tempSS.remove((i, x))
else: #i>x
tempSS.append((x, i))
if isSecStr(tempSS):
num += 1
if VERBOSE_PRINT:
ss = basePairList2dotBracketNotation(rna0, tempSS)
print '(%d,%d)\t%s' % (x, i, ss)
tempSS.remove((x, i))
elif abs(j - x) > THETA and x != i and basePair(rna[j], rna[x]):
if j < x:
tempSS.append((j, x))
if isSecStr(tempSS):
num += 1
if VERBOSE_PRINT:
ss = basePairList2dotBracketNotation(rna0, tempSS)
print '(%d,%d)\t%s' % (j, x, ss)
tempSS.remove((j, x))
else: #j>x
tempSS.append((x, j))
if isSecStr(tempSS):
num += 1
if VERBOSE_PRINT:
ss = basePairList2dotBracketNotation(rna0, tempSS)
print '(%d,%d)\t%s' % (x, j, ss)
tempSS.remove((x, j))
tempSS.append((i, j)) #put back the base pair temporarily removed
if PRINT:
print "%s has %s shifts" % (secStr[1:], num
) #recall '$' prepended to secStr
return num
def numShifts(rna,secStr): #brute force computation of number shifts
#rna and secStr is 1-indexed
if VERBOSE_PRINT:
print "Sec str: %s" % secStr
n = len(rna)
rna0 = rna
secStr0= secStr
rna = '$'+rna
secStr = '$'+secStr
SS = basePairList(secStr)
num = 0; tempSS = copy.deepcopy(SS)
for (i,j) in SS:
tempSS.remove( (i,j) )
if VERBOSE_PRINT:
print "Remove (%d,%d) from %s" % (i,j,secStr[1:])
for x in range(1,n+1):
if abs(i-x)>THETA and x!=j and basePair(rna[i],rna[x]):
if i<x:
tempSS.append( (i,x) )
if isSecStr(tempSS):
num += 1
if VERBOSE_PRINT:
ss = basePairList2dotBracketNotation(rna0,tempSS)
print '(%d,%d)\t%s' % (i,x,ss)
tempSS.remove( (i,x) )
else: #i>x
tempSS.append( (x,i) )
if isSecStr(tempSS):
num += 1
if VERBOSE_PRINT:
ss = basePairList2dotBracketNotation(rna0,tempSS)
print '(%d,%d)\t%s' % (x,i,ss)
tempSS.remove( (x,i) )
elif abs(j-x)>THETA and x!= i and basePair(rna[j],rna[x]):
if j<x:
tempSS.append( (j,x) )
if isSecStr(tempSS):
num += 1
if VERBOSE_PRINT:
ss = basePairList2dotBracketNotation(rna0,tempSS)
print '(%d,%d)\t%s' % (j,x,ss)
tempSS.remove( (j,x) )
else: #j>x
tempSS.append( (x,j) )
if isSecStr(tempSS):
num += 1
if VERBOSE_PRINT:
ss = basePairList2dotBracketNotation(rna0,tempSS)
print '(%d,%d)\t%s' % (x,j,ss)
tempSS.remove( (x,j) )
tempSS.append( (i,j) ) #put back the base pair temporarily removed
if PRINT:
print "%s has %s shifts" % (secStr[1:],num) #recall '$' prepended to secStr
return num
def computeE(rna,Z):
#function E(i,j) = sum_S sum_{(x,y)} I[ (x,y) external in S]
E = {}
n = len(rna)
rna = '$'+rna
#initialize
for i in range(1,n+1):
for j in range(i,n+1):
E[(i,j)] = 0
#fill
for d in range(THETA+1,n): #d in [4,n-1]
for i in range(1,n-d+1): #i in [1,n-d]
j = i+d
sum = E[(i,j-1)]
if basePair(rna[i],rna[j]):
sum += Z[(i+1,j-1)]
for k in range(i+1,j-THETA):# k in [i+1..j-THETA-1]
if basePair(rna[k],rna[j]):
sum += (E[(i,k-1)]+Z[(i,k-1)])*Z[(k+1,j-1)]
E[(i,j)] = sum
return E
def partFunInner(rna):
#Z[(i,j)] is number of sec str of rna[i...j], using array n x n
Z = {}
n = len(rna)
rna = '$'+rna
#initialize
for i in range(1,n+1):
for j in range(1,n+1):
Z[(i,j)] = 1L
#fill
for d in range(THETA+1,n): #d in [4,n-1]
for i in range(1,n-THETA): #i in [1,n-THETA-1]
j = i+d
if j>n: break
sum = Z[(i,j-1)]
if (j-i>THETA):
if basePair(rna[i],rna[j]):
sum += Z[(i+1,j-1)]
for k in range(i+1,j-THETA):# k in [i+1..j-THETA-1]
if basePair(rna[k],rna[j]):
sum += Z[(i,k-1)]*Z[(k+1,j-1)]
Z[(i,j)] = sum
return Z
def partFunInner(rna):
#Z[(i,j)] is number of sec str of rna[i...j], using array n x n
Z = {}
n = len(rna)
rna = '$' + rna
#initialize
for i in range(1, n + 1):
for j in range(1, n + 1):
Z[(i, j)] = 1L
#fill
for d in range(THETA + 1, n): #d in [4,n-1]
for i in range(1, n - THETA): #i in [1,n-THETA-1]
j = i + d
if j > n: break
sum = Z[(i, j - 1)]
if (j - i > THETA):
if basePair(rna[i], rna[j]):
sum += Z[(i + 1, j - 1)]
for k in range(i + 1, j - THETA): # k in [i+1..j-THETA-1]
if basePair(rna[k], rna[j]):
sum += Z[(i, k - 1)] * Z[(k + 1, j - 1)]
Z[(i, j)] = sum
return Z
def numNborsNoShift(rna,Z):
#Q[(i,j)] = sum_x N(x), where x is sec str of rna[i:j+1] without shift
#Z[(i,j)] = number of sec str of rna[i:j+1]
Q = {};
n = len(rna)
rna = '$'+rna #add dummy character
#base case j-i in [0,1,2,3]
for i in range(1,n+1):
for d in range(0,min(THETA,n-i)+1):
j = i+d
Q[(i,j)]=0.0
#inductive case j-i > 3, compute Q[(i,j)] all 1<=i<=j<=n
for d in range(THETA+1,n+1):
for i in range(1,n+1):
j = i+d
if (j>n): break
q = Q[(i,j-1)]
if basePair(rna[i],rna[j]):
q += 2*Z[(i+1,j-1)]+Q[(i+1,j-1)]
for k in range(i+1,j-THETA):
if basePair(rna[k],rna[j]):
q += 2*Z[(i,k-1)]*Z[(k+1,j-1)]+Z[(i,k-1)]*Q[(k+1,j-1)]+Q[(i,k-1)]*Z[(k+1,j-1)]
Q[(i,j)] = q
return Q[(1,n)]
def computeEold(rna,Z):
#function E(i,j) = sum_S sum_{(x,y)} I[ (x,y) external in S]
E = {}
n = len(rna)
rna = '$'+rna
#initialize
for i in range(1,n+1):
for j in range(1,n+1):
E[(i,j)] = 0L
#fill
for d in range(THETA+1,n): #d in [4,n-1]
for i in range(1,n-THETA): #i in [1,n-THETA-1]
j = i+d
if j>n: break
sum = E[(i,j-1)]
if basePair(rna[i],rna[j]):
sum += Z[(i+1,j-1)]
#Tricky: contribution comes from 3rd term in derivation of E
#Contribution from 2nd term in derivation of E is ZERO
for k in range(i+1,j-THETA):# k in [i+1..j-THETA-1]
if basePair(rna[k],rna[j]):
sum += (E[(i,k-1)]+Z[(i,k-1)])*Z[(k+1,j-1)]
E[(i,j)] = sum
return E
def computeEold(rna, Z):
#function E(i,j) = sum_S sum_{(x,y)} I[ (x,y) external in S]
E = {}
n = len(rna)
rna = '$' + rna
#initialize
for i in range(1, n + 1):
for j in range(1, n + 1):
E[(i, j)] = 0L
#fill
for d in range(THETA + 1, n): #d in [4,n-1]
for i in range(1, n - THETA): #i in [1,n-THETA-1]
j = i + d
if j > n: break
sum = E[(i, j - 1)]
if basePair(rna[i], rna[j]):
sum += Z[(i + 1, j - 1)]
#Tricky: contribution comes from 3rd term in derivation of E
#Contribution from 2nd term in derivation of E is ZERO
for k in range(i + 1, j - THETA): # k in [i+1..j-THETA-1]
if basePair(rna[k], rna[j]):
sum += (E[(i, k - 1)] + Z[(i, k - 1)]) * Z[(k + 1, j - 1)]
E[(i, j)] = sum
return E
def numBasePairAdditionsRemovals(rna,secStr): #brute force
#rna and secStr is 1-indexed
if PRINTbasepairadditionsremovals:
print "Sec str: %s" % secStr
n = len(rna)
rna0 = rna
rna = '$'+rna
secStr = '$'+secStr
SS = basePairList(secStr)
num = len(SS); tempSS = copy.deepcopy(SS)
for x in range(1,n-THETA):
for y in range(x+THETA+1,n+1):
if basePair(rna[x],rna[y]):
if (x,y) not in tempSS:
tempSS.append( (x,y) )
if isSecStr(tempSS):
num += 1
if PRINTbasepairadditionsremovals:
ss = basePairList2dotBracketNotation(rna0,tempSS)
print '(%d,%d)\t%s' % (x,y,ss)
tempSS.remove( (x,y) )
return num
def numBasePairAdditionsRemovals(rna, secStr): #brute force
#rna and secStr is 1-indexed
if PRINTbasepairadditionsremovals:
print "Sec str: %s" % secStr
n = len(rna)
rna0 = rna
rna = '$' + rna
secStr = '$' + secStr
SS = basePairList(secStr)
num = len(SS)
tempSS = copy.deepcopy(SS)
for x in range(1, n - THETA):
for y in range(x + THETA + 1, n + 1):
if basePair(rna[x], rna[y]):
if (x, y) not in tempSS:
tempSS.append((x, y))
if isSecStr(tempSS):
num += 1
if PRINTbasepairadditionsremovals:
ss = basePairList2dotBracketNotation(rna0, tempSS)
print '(%d,%d)\t%s' % (x, y, ss)
tempSS.remove((x, y))
return num
def computeQ(rna, Z):
FF = computeFF(rna, Z)
J = computeJ(rna, Z, FF)
EL = computeEleft(rna, Z)
ER = computeEright(rna, Z)
ERprime = computeERprime(rna, Z, ER)
#--------------------------------------------
#E[(i,j) = sum_S sum_{(x,y)} I[(x,y) external in S]
#
#Ebis[(i,j) = sum_S sum_{(x,y)} I[(x,y) external in S, y<n]
#
#Eprime[(i,j) = sum_S sum_{(x,y)}
# I[(x,y) external in S, y <= j-4, j unpaired]
#EL[(i,j) = sum_S sum_{(x,y)}
# I[(x,y) external in S, x basepairs with rna[n]]
#ER[(i,j) = sum_S sum_{(x,y)}
# I[(x,y) external in S, y basepairs with rna[n]]
#ERprime[(i,j) = sum_S sum_{(x,y)}
# I[(x,y) external in S, y basepairs with rna[n], y<=j-4, n unpaired in S]
Q = {}
n = len(rna)
rna = '$' + rna
#-------------------------------------------
#Initialization to zero
for d in range(n): #d in [0,n-1]
for i in range(1, n + 1 - d): #i in [1,n-d]
j = i + d
Q[(i, j)] = 0
#-------------------------------------------
#Recursions
for d in range(THETA + 1, n): #d in [4,n-1]
for i in range(1, n + 1 - d): #i in [1,n-d]
j = i + d
#Case 1: first term Q(i,j-1)
Q[(i, j)] = Q[(i, j - 1)]
if PRINT:
print "\n\n", Q[(i, j - 1)], "\tQ(%d,%d)" % (i, j - 1)
#Case 2: second term 2 * sum_k z(i,k-1)*z(k+1,j-1)
sum = 0
if basePair(rna[i], rna[j]):
sum += Z[(i + 1, j - 1)]
for k in range(i + 1, j - 3): #k in [i+1,j-4]
if basePair(rna[k], rna[j]):
sum += Z[(i, k - 1)] * Z[(k + 1, j - 1)]
Q[(i, j)] += 2 * sum
if PRINT:
text = "\t2 sum_{k=%s}^{%s-4} z(%s,k-1)*z(k+1,%s-1)"
print(2 * sum), text % (i, j, i, j)
#Case 3: 2*EL[(i,j-1)]+2*ERprime[(i,j)]
sum = 2 * EL[(i, j - 1, rna[j])] + 2 * ERprime[(i, j, rna[j])]
Q[(i, j)] += sum
if PRINT:
text1 = "%s\t" % sum
text2 = "2*EL[(%s,%s-1,%s)]+2*ERprime[(%s,%s,%s)]"
text2 = text2 % (i, j, rna[j], i, j, rna[j])
print text1, text2
text1 = " %s\t" % 2 * EL[(i, j - 1, rna[j])]
text2 = "2*EL[(%s,%s-1,%s)]" % (i, j, rna[j])
print text1, text2
text1 = " %s\t" % 2 * ERprime[(i, j, rna[j])]
text2 = "2*ERprime[(%s,%s,%s)]" % (i, j, rna[j])
print text1, text2
#Case 4: fourth term is sum_{x=2}^{n-4} x*(x-1)*H(1,n,ch,x)
sum = 0
for x in range(2, j - i + 1 - 3): #x in [2,j-i+1-4]
sum += x * (x - 1) * J[(i, j, rna[j], x)]
Q[(i, j)] += sum
newsum = 0
if PRINT:
text = "\tch\tx\tx-1\tJ(%s,%s,ch,x)\tsum_ch sum_x x(x-1)J(%s,%s,ch,x)"
print sum, "\tch\tx\tx-1\tJ(1,n,ch,x)\tsum_ch sum_x x(x-1)J(1,n,ch,x)"
ch = rna[j]
for x in range(2, j - i + 1 - 3): #x in [2,j-i+1-4]
print "\t%s\t%s\t%s\t%s = \t%s" % (ch, x, x - 1, J[
(1, n, ch, x)], x * (x - 1) * J[(1, n, ch, x)])
#Case 5: fifth term
#sum_{k=1}^{n-\theta-1} \left( z(k-1) \cdot Q(n-k-1) \right) +
#\left( Q(k-1) \cdot z(n-k-1) \right)
#Case 5a: (i,j) paired
sum = 0
if basePair(rna[i], rna[j]):
sum += Q[(i + 1, j - 1)]
for k in range(i + 1, j - 3): #k in [i+1,j-4]
if basePair(rna[k], rna[j]):
sum += (Z[(i, k - 1)] * Q[(k + 1, j - 1)]) + (Q[
(i, k - 1)] * Z[(k + 1, j - 1)])
Q[(i, j)] += sum
if PRINT:
text = "sum_k (Z[(%s,k-1)]*Q[(k+1,%s-1)])+(Q[(%s,k-1)]*Z[(k+1,%s-1)])"
text = text % (i, j, i, j)
print "%s\t%s" % (sum, text)
return Q
def computeQ(rna,Z):
FF = computeFF(rna,Z)
J = computeJ(rna,Z,FF)
EL = computeEleft(rna,Z)
ER = computeEright(rna,Z)
ERprime = computeERprime(rna,Z,ER)
#--------------------------------------------
#E[(i,j) = sum_S sum_{(x,y)} I[(x,y) external in S]
#
#Ebis[(i,j) = sum_S sum_{(x,y)} I[(x,y) external in S, y<n]
#
#Eprime[(i,j) = sum_S sum_{(x,y)}
# I[(x,y) external in S, y <= j-4, j unpaired]
#EL[(i,j) = sum_S sum_{(x,y)}
# I[(x,y) external in S, x basepairs with rna[n]]
#ER[(i,j) = sum_S sum_{(x,y)}
# I[(x,y) external in S, y basepairs with rna[n]]
#ERprime[(i,j) = sum_S sum_{(x,y)}
# I[(x,y) external in S, y basepairs with rna[n], y<=j-4, n unpaired in S]
Q = {}
n = len(rna)
rna = '$'+rna
#-------------------------------------------
#Initialization to zero
for d in range(n): #d in [0,n-1]
for i in range(1,n+1-d): #i in [1,n-d]
j = i+d
Q[(i,j)]=0
#-------------------------------------------
#Recursions
for d in range(THETA+1,n): #d in [4,n-1]
for i in range(1,n+1-d): #i in [1,n-d]
j = i+d
#Case 1: first term Q(i,j-1)
Q[(i,j)] = Q[(i,j-1)]
if PRINT:
print "\n\n",Q[(i,j-1)], "\tQ(%d,%d)" % (i,j-1)
#Case 2: second term 2 * sum_k z(i,k-1)*z(k+1,j-1)
sum = 0
if basePair(rna[i],rna[j]):
sum += Z[(i+1,j-1)]
for k in range(i+1,j-3): #k in [i+1,j-4]
if basePair(rna[k],rna[j]):
sum += Z[(i,k-1)]*Z[(k+1,j-1)]
Q[(i,j)] += 2*sum
if PRINT:
text = "\t2 sum_{k=%s}^{%s-4} z(%s,k-1)*z(k+1,%s-1)"
print (2*sum),text % (i,j,i,j)
#Case 3: 2*EL[(i,j-1)]+2*ERprime[(i,j)]
sum = 2*EL[(i,j-1,rna[j])]+2*ERprime[(i,j,rna[j])]
Q[(i,j)] += sum
if PRINT:
text1 = "%s\t" % sum
text2 = "2*EL[(%s,%s-1,%s)]+2*ERprime[(%s,%s,%s)]"
text2 = text2 % (i,j,rna[j],i,j,rna[j])
print text1,text2
text1 = " %s\t" % 2*EL[(i,j-1,rna[j])]
text2 = "2*EL[(%s,%s-1,%s)]" % (i,j,rna[j])
print text1,text2
text1 = " %s\t" % 2*ERprime[(i,j,rna[j])]
text2 = "2*ERprime[(%s,%s,%s)]" % (i,j,rna[j])
print text1,text2
#Case 4: fourth term is sum_{x=2}^{n-4} x*(x-1)*H(1,n,ch,x)
sum = 0
for x in range(2,j-i+1-3): #x in [2,j-i+1-4]
sum += x*(x-1)*J[(i,j,rna[j],x)]
Q[(i,j)] += sum
newsum = 0
if PRINT:
text = "\tch\tx\tx-1\tJ(%s,%s,ch,x)\tsum_ch sum_x x(x-1)J(%s,%s,ch,x)"
print sum,"\tch\tx\tx-1\tJ(1,n,ch,x)\tsum_ch sum_x x(x-1)J(1,n,ch,x)"
ch = rna[j]
for x in range(2,j-i+1-3): #x in [2,j-i+1-4]
print "\t%s\t%s\t%s\t%s = \t%s"%(ch,x,x-1,J[(1,n,ch,x)],x*(x-1)*J[(1,n,ch,x)])
#Case 5: fifth term
#sum_{k=1}^{n-\theta-1} \left( z(k-1) \cdot Q(n-k-1) \right) +
#\left( Q(k-1) \cdot z(n-k-1) \right)
#Case 5a: (i,j) paired
sum = 0
if basePair(rna[i],rna[j]):
sum += Q[(i+1,j-1)]
for k in range(i+1,j-3): #k in [i+1,j-4]
if basePair(rna[k],rna[j]):
sum += (Z[(i,k-1)]*Q[(k+1,j-1)])+(Q[(i,k-1)]*Z[(k+1,j-1)])
Q[(i,j)] += sum
if PRINT:
text = "sum_k (Z[(%s,k-1)]*Q[(k+1,%s-1)])+(Q[(%s,k-1)]*Z[(k+1,%s-1)])"
text = text % (i,j,i,j)
print "%s\t%s" % (sum,text)
return Q
