def Utrsv_notranspose_nonunit(U, b):
UTL, UTR, \
UBL, UBR = flame.part_2x2(U, \
0, 0, 'BR')
bT, \
bB = flame.part_2x1(b, \
0, 'BOTTOM')
while UBR.shape[0] < U.shape[0]:
U00, u01, U02, \
u10t, upsilon11, u12t, \
U20, u21, U22 = flame.repart_2x2_to_3x3(UTL, UTR, \
UBL, UBR, \
1, 1, 'TL')
b0, \
beta1, \
b2 = flame.repart_2x1_to_3x1(bT, \
bB, \
1, 'TOP')
#------------------------------------------------------------#
dots(-u12t, b2, beta1)
scal(1 / upsilon11, beta1)
#------------------------------------------------------------#
UTL, UTR, \
UBL, UBR = flame.cont_with_3x3_to_2x2(U00, u01, U02, \
u10t, upsilon11, u12t, \
U20, u21, U22, \
'BR')
bT, \
bB = flame.cont_with_3x1_to_2x1(b0, \
beta1, \
b2, \
'BOTTOM')
flame.merge_2x1(bT, \
bB, b)
def trsv_unn(U, b):
UTL, UTR, \
UBL, UBR = flame.part_2x2(U, \
0, 0, 'BR')
bT, \
bB = flame.part_2x1(b, \
0, 'BOTTOM')
while UBR.shape[0] < U.shape[0]:
U00, u01, U02, \
u10t, upsilon11, u12t, \
U20, u21, U22 = flame.repart_2x2_to_3x3(UTL, UTR, \
UBL, UBR, \
1, 1, 'TL')
b0, \
beta1, \
b2 = flame.repart_2x1_to_3x1(bT, \
bB, \
1, 'TOP')
#------------------------------------------------------------#
dots( -u12t, b2, beta1 )
scal( 1/upsilon11, beta1 )
#------------------------------------------------------------#
UTL, UTR, \
UBL, UBR = flame.cont_with_3x3_to_2x2(U00, u01, U02, \
u10t, upsilon11, u12t, \
U20, u21, U22, \
'BR')
bT, \
bB = flame.cont_with_3x1_to_2x1(b0, \
beta1, \
b2, \
'BOTTOM')
flame.merge_2x1(bT, \
bB, b)
def trsv_ltu(L, B):
LTL, LTR, \
LBL, LBR = flame.part_2x2(L, \
0, 0, 'TL')
BT, \
BB = flame.part_2x1(B, \
0, 'TOP')
while LTL.shape[0] < L.shape[0]:
L00, l01, L02, \
l10t, lambda11, l12t, \
L20, l21, L22 = flame.repart_2x2_to_3x3(LTL, LTR, \
LBL, LBR, \
1, 1, 'BR')
B0, \
beta1, \
b2 = flame.repart_2x1_to_3x1(BT, \
BB, \
1, 'BOTTOM')
#------------------------------------------------------------#
dots( -l21, b2, beta1 )
scal( 1/lambda11, beta1 )
#------------------------------------------------------------#
LTL, LTR, \
LBL, LBR = flame.cont_with_3x3_to_2x2(L00, l01, L02, \
l10t, lambda11, l12t, \
L20, l21, L22, \
'TL')
BT, \
BB = flame.cont_with_3x1_to_2x1(B0, \
beta1, \
b2, \
'TOP')
flame.merge_2x1(BT, \
BB, B)
def chol_unb(A):
ATL, ATR, \
ABL, ABR = flame.part_2x2(A, \
0, 0, 'TL')
while ATL.shape[0] < A.shape[0]:
A00, a01, A02, \
a10t, alpha11, a12t, \
A20, a21, A22 = flame.repart_2x2_to_3x3(ATL, ATR, \
ABL, ABR, \
1, 1, 'BR')
#------------------------------------------------------------#
# alpha11[0,0] = np.sqrt( alpha11[0,0] )
# laff.invscal( alpha11, a21 )
# laff.ger( -1, a21, a21, A22 ) #Not tril
# laff.dots( a10t, a10t, alpha11 )
# alpha11[0,0] = np.sqrt( alpha11[0,0] )
# a21 -= A20 * np.transpose(a10t) #Not laff calls
# laff.invscal( alpha11, a21 )
trsv('Lower triangular', 'Nonunit diagonal', 'No transpose', A00, a10t)
dots(a10t, a10t, alpha11)
alpha11[0, 0] = np.sqrt(alpha11[0, 0])
#------------------------------------------------------------#
ATL, ATR, \
ABL, ABR = flame.cont_with_3x3_to_2x2(A00, a01, A02, \
a10t, alpha11, a12t, \
A20, a21, A22, \
'TL')
flame.merge_2x2(ATL, ATR, \
ABL, ABR, A)
def chol_unb(A):
ATL, ATR, \
ABL, ABR = flame.part_2x2(A, \
0, 0, 'TL')
while ATL.shape[0] < A.shape[0]:
A00, a01, A02, \
a10t, alpha11, a12t, \
A20, a21, A22 = flame.repart_2x2_to_3x3(ATL, ATR, \
ABL, ABR, \
1, 1, 'BR')
#------------------------------------------------------------#
# alpha11[0,0] = np.sqrt( alpha11[0,0] )
# laff.invscal( alpha11, a21 )
# laff.ger( -1, a21, a21, A22 ) #Not tril
# laff.dots( a10t, a10t, alpha11 )
# alpha11[0,0] = np.sqrt( alpha11[0,0] )
# a21 -= A20 * np.transpose(a10t) #Not laff calls
# laff.invscal( alpha11, a21 )
trsv( 'Lower triangular', 'Nonunit diagonal', 'No transpose', A00, a10t )
dots( a10t, a10t, alpha11 )
alpha11[0,0] = np.sqrt( alpha11[0,0] )
#------------------------------------------------------------#
ATL, ATR, \
ABL, ABR = flame.cont_with_3x3_to_2x2(A00, a01, A02, \
a10t, alpha11, a12t, \
A20, a21, A22, \
'TL')
flame.merge_2x2(ATL, ATR, \
ABL, ABR, A)