def Trmv_ln_unb_var1(L, x):
"""
Trmv_ln_unb_var1(matrix, vector)
Computes y = L * x using DOT products.
L is the lower triangular matrix.
Traverses matrix L from BOTTOM-RIGHT to TOP-LEFT,
vector x from BOTTOM to TOP.
"""
LTL, LTR, \
LBL, LBR = flame.part_2x2(L, \
0, 0, 'BR')
xT, \
xB = flame.part_2x1(x, \
0, 'BOTTOM')
while LBR.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, 'TL')
x0, \
chi1, \
x2 = flame.repart_2x1_to_3x1(xT, \
xB, \
1, 'TOP')
laff.scal( lambda11, chi1 )
laff.dots( l10t, x0, chi1 )
LTL, LTR, \
LBL, LBR = flame.cont_with_3x3_to_2x2(L00, l01, L02, \
l10t, lambda11, l12t, \
L20, l21, L22, \
'BR')
xT, \
xB = flame.cont_with_3x1_to_2x1(x0, \
chi1, \
x2, \
'BOTTOM')
flame.merge_2x1(xT, \
xB, x)
def Trmv_un_unb_var1(U, x):
"""
Trmv_un_unb_var1(matrix, vector)
Computes y = U * x using DOT products.
U is the upper triangular matrix.
Traverses matrix U from TOP-LEFT to BOTTOM-RIGHT,
vector x from TOP to BOTTOM.
"""
UTL, UTR, \
UBL, UBR = flame.part_2x2(U, \
0, 0, 'TL')
xT, \
xB = flame.part_2x1(x, \
0, 'TOP')
while UTL.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, 'BR')
x0, \
chi1, \
x2 = flame.repart_2x1_to_3x1(xT, \
xB, \
1, 'BOTTOM')
laff.scal(upsilon11, chi1)
laff.dots(u12t, x2, chi1)
UTL, UTR, \
UBL, UBR = flame.cont_with_3x3_to_2x2(U00, u01, U02, \
u10t, upsilon11, u12t, \
U20, u21, U22, \
'TL')
xT, \
xB = flame.cont_with_3x1_to_2x1(x0, \
chi1, \
x2, \
'TOP')
flame.merge_2x1(xT, \
xB, x)
def Trmv_un_unb_var1(U, x):
"""
Trmv_un_unb_var1(matrix, vector)
Computes y = U * x using DOT products.
U is the upper triangular matrix.
Traverses matrix U from TOP-LEFT to BOTTOM-RIGHT,
vector x from TOP to BOTTOM.
"""
UTL, UTR, \
UBL, UBR = flame.part_2x2(U, \
0, 0, 'TL')
xT, \
xB = flame.part_2x1(x, \
0, 'TOP')
while UTL.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, 'BR')
x0, \
chi1, \
x2 = flame.repart_2x1_to_3x1(xT, \
xB, \
1, 'BOTTOM')
laff.scal( upsilon11, chi1 )
laff.dots( u12t, x2, chi1 )
UTL, UTR, \
UBL, UBR = flame.cont_with_3x3_to_2x2(U00, u01, U02, \
u10t, upsilon11, u12t, \
U20, u21, U22, \
'TL')
xT, \
xB = flame.cont_with_3x1_to_2x1(x0, \
chi1, \
x2, \
'TOP')
flame.merge_2x1(xT, \
xB, x)
def Mvmult_n_unb_var1(A, x, y):
"""
Mvmult_n_unb_var1(matrix, vector, vector)
Compuyes y = A * x + y using DOT products.
Traverses matrix A from TOP to BOTTOM,
vector y from TOP to BOTTOM.
"""
AT, \
AB = flame.part_2x1(A, \
0, 'TOP')
yT, \
yB = flame.part_2x1(y, \
0, 'TOP')
while AT.shape[0] < A.shape[0]:
A0, \
a1t, \
A2 = flame.repart_2x1_to_3x1(AT, \
AB, \
1, 'BOTTOM')
y0, \
psi1, \
y2 = flame.repart_2x1_to_3x1(yT, \
yB, \
1, 'BOTTOM')
laff.dots( a1t, x, psi1 )
AT, \
AB = flame.cont_with_3x1_to_2x1(A0, \
a1t, \
A2, \
'TOP')
yT, \
yB = flame.cont_with_3x1_to_2x1(y0, \
psi1, \
y2, \
'TOP')
flame.merge_2x1(yT, \
yB, y)
def Mvmult_n_unb_var1(A, x, y):
"""
Mvmult_n_unb_var1(matrix, vector, vector)
Compuyes y = A * x + y using DOT products.
Traverses matrix A from TOP to BOTTOM,
vector y from TOP to BOTTOM.
"""
AT, \
AB = flame.part_2x1(A, \
0, 'TOP')
yT, \
yB = flame.part_2x1(y, \
0, 'TOP')
while AT.shape[0] < A.shape[0]:
A0, \
a1t, \
A2 = flame.repart_2x1_to_3x1(AT, \
AB, \
1, 'BOTTOM')
y0, \
psi1, \
y2 = flame.repart_2x1_to_3x1(yT, \
yB, \
1, 'BOTTOM')
laff.dots(a1t, x, psi1)
AT, \
AB = flame.cont_with_3x1_to_2x1(A0, \
a1t, \
A2, \
'TOP')
yT, \
yB = flame.cont_with_3x1_to_2x1(y0, \
psi1, \
y2, \
'TOP')
flame.merge_2x1(yT, \
yB, y)
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')
#------------------------------------------------------------#
laff.dots( -u12t, b2, beta1 )
laff.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 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')
#------------------------------------------------------------#
laff.dots(-u12t, b2, beta1)
laff.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, \
b1t, \
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, \
b1t, \
B2, \
'TOP')
flame.merge_2x1(BT, \
BB, B)
def Mvmult_t_unb_var1(A, x, y):
"""
Mvmult_t_unb_var1(matrix, vector, vector)
Computes y = A' * x + y using DOT products.
Traverses matrix A from LEFT to RIGHT,
vector y from TOP to BOTTOM.
"""
AL, AR = flame.part_1x2(A, \
0, 'LEFT')
yT, \
yB = flame.part_2x1(y, \
0, 'TOP')
while AL.shape[1] < A.shape[1]:
A0, a1, A2 = flame.repart_1x2_to_1x3(AL, AR, \
1, 'RIGHT')
y0, \
psi1, \
y2 = flame.repart_2x1_to_3x1(yT, \
yB, \
1, 'BOTTOM')
laff.dots( a1, x, psi1 )
AL, AR = flame.cont_with_1x3_to_1x2(A0, a1, A2, \
'LEFT')
yT, \
yB = flame.cont_with_3x1_to_2x1(y0, \
psi1, \
y2, \
'TOP')
flame.merge_2x1(yT, \
yB, y)
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 )
laff.trsv( 'Lower triangular', 'Nonunit diagonal', 'No transpose', A00, a10t )
laff.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 Tmvmult_ln_unb_var1(L, x, y):
"""
Tmvmult_ln_unb_var1(matrix, vector, vector)
Computes y = L * x + y using DOT products.
L is the lower triangular matrix.
Traverses matrix L from TOP-LEFT to BOTTOM-RIGHT,
vector x from TOP to BOTTOM,
vector y from TOP to BOTTOM.
"""
LTL, LTR, \
LBL, LBR = flame.part_2x2(L, \
0, 0, 'TL')
xT, \
xB = flame.part_2x1(x, \
0, 'TOP')
yT, \
yB = flame.part_2x1(y, \
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')
x0, \
chi1, \
x2 = flame.repart_2x1_to_3x1(xT, \
xB, \
1, 'BOTTOM')
y0, \
psi1, \
y2 = flame.repart_2x1_to_3x1(yT, \
yB, \
1, 'BOTTOM')
laff.dots(l10t, x0, psi1)
laff.dots(lambda11, chi1, psi1)
LTL, LTR, \
LBL, LBR = flame.cont_with_3x3_to_2x2(L00, l01, L02, \
l10t, lambda11, l12t, \
L20, l21, L22, \
'TL')
xT, \
xB = flame.cont_with_3x1_to_2x1(x0, \
chi1, \
x2, \
'TOP')
yT, \
yB = flame.cont_with_3x1_to_2x1(y0, \
psi1, \
y2, \
'TOP')
flame.merge_2x2(LTL, LTR, \
LBL, LBR, L)
flame.merge_2x1(xT, \
xB, x)
flame.merge_2x1(yT, \
yB, y)
def Tmvmult_lt_unb_var1(L, x, y):
"""
Tmvmult_lt_unb_var1(matrix, vector, vector)
Computes y = L' * x + y using DOT products.
L is the lower triangular matrix.
Traverses matrix L from TOP-LEFT to BOTTOM-RIGHT,
vector x from TOP to BOTTOM,
vector y from TOP to BOTTOM.
"""
LTL, LTR, \
LBL, LBR = flame.part_2x2(L, \
0, 0, 'TL')
xT, \
xB = flame.part_2x1(x, \
0, 'TOP')
yT, \
yB = flame.part_2x1(y, \
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')
x0, \
chi1, \
x2 = flame.repart_2x1_to_3x1(xT, \
xB, \
1, 'BOTTOM')
y0, \
psi1, \
y2 = flame.repart_2x1_to_3x1(yT, \
yB, \
1, 'BOTTOM')
laff.dots( l21, x2, psi1 )
laff.dots( lambda11, chi1, psi1 )
LTL, LTR, \
LBL, LBR = flame.cont_with_3x3_to_2x2(L00, l01, L02, \
l10t, lambda11, l12t, \
L20, l21, L22, \
'TL')
xT, \
xB = flame.cont_with_3x1_to_2x1(x0, \
chi1, \
x2, \
'TOP')
yT, \
yB = flame.cont_with_3x1_to_2x1(y0, \
psi1, \
y2, \
'TOP')
flame.merge_2x1(yT, \
yB, y)
def Symv_u_unb_var1(A, x, y):
"""
Symv_u_unb_var1(matrix, vector, vector)
Computes y = A * x + y using DOT products.
A is a symmetric matrix.
Traverses matrix A from TOP-LEFT to BOTTOM-RIGHT,
vector x from TOP to BOTTOM,
vector y from TOP to BOTTOM.
"""
ATL, ATR, \
ABL, ABR = flame.part_2x2(A, \
0, 0, 'TL')
xT, \
xB = flame.part_2x1(x, \
0, 'TOP')
yT, \
yB = flame.part_2x1(y, \
0, 'TOP')
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')
x0, \
chi1, \
x2 = flame.repart_2x1_to_3x1(xT, \
xB, \
1, 'BOTTOM')
y0, \
psi1, \
y2 = flame.repart_2x1_to_3x1(yT, \
yB, \
1, 'BOTTOM')
laff.dots( a01, x0, psi1 )
laff.dots( alpha11, chi1, psi1 )
laff.dots( a12t, x2, psi1 )
ATL, ATR, \
ABL, ABR = flame.cont_with_3x3_to_2x2(A00, a01, A02, \
a10t, alpha11, a12t, \
A20, a21, A22, \
'TL')
xT, \
xB = flame.cont_with_3x1_to_2x1(x0, \
chi1, \
x2, \
'TOP')
yT, \
yB = flame.cont_with_3x1_to_2x1(y0, \
psi1, \
y2, \
'TOP')
flame.merge_2x1(yT, \
yB, y)
def Tmvmult_ut_unb_var1(U, x, y):
"""
Tmvmult_ut_unb_var1(matrix, vector, vector)
Computes y = U' * x + y using DOT products.
Traverses matrix U from TOP-LEFT to BOTTOM-RIGHT,
vector x from TOP to BOTTOM,
vector y from TOP to BOTTOM.
"""
UTL, UTR, \
UBL, UBR = flame.part_2x2(U, \
0, 0, 'TL')
xT, \
xB = flame.part_2x1(x, \
0, 'TOP')
yT, \
yB = flame.part_2x1(y, \
0, 'TOP')
while UTL.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, 'BR')
x0, \
chi1, \
x2 = flame.repart_2x1_to_3x1(xT, \
xB, \
1, 'BOTTOM')
y0, \
psi1, \
y2 = flame.repart_2x1_to_3x1(yT, \
yB, \
1, 'BOTTOM')
laff.dots( upsilon11, chi1, psi1 )
laff.dots( u01, x0, psi1 )
UTL, UTR, \
UBL, UBR = flame.cont_with_3x3_to_2x2(U00, u01, U02, \
u10t, upsilon11, u12t, \
U20, u21, U22, \
'TL')
xT, \
xB = flame.cont_with_3x1_to_2x1(x0, \
chi1, \
x2, \
'TOP')
yT, \
yB = flame.cont_with_3x1_to_2x1(y0, \
psi1, \
y2, \
'TOP')
flame.merge_2x1(yT, \
yB, y)
def Symv_u_unb_var1(A, x, y):
"""
Symv_u_unb_var1(matrix, vector, vector)
Computes y = A * x + y using DOT products.
A is a symmetric matrix.
Traverses matrix A from TOP-LEFT to BOTTOM-RIGHT,
vector x from TOP to BOTTOM,
vector y from TOP to BOTTOM.
"""
ATL, ATR, \
ABL, ABR = flame.part_2x2(A, \
0, 0, 'TL')
xT, \
xB = flame.part_2x1(x, \
0, 'TOP')
yT, \
yB = flame.part_2x1(y, \
0, 'TOP')
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')
x0, \
chi1, \
x2 = flame.repart_2x1_to_3x1(xT, \
xB, \
1, 'BOTTOM')
y0, \
psi1, \
y2 = flame.repart_2x1_to_3x1(yT, \
yB, \
1, 'BOTTOM')
laff.dots(a01, x0, psi1)
laff.dots(alpha11, chi1, psi1)
laff.dots(a12t, x2, psi1)
ATL, ATR, \
ABL, ABR = flame.cont_with_3x3_to_2x2(A00, a01, A02, \
a10t, alpha11, a12t, \
A20, a21, A22, \
'TL')
xT, \
xB = flame.cont_with_3x1_to_2x1(x0, \
chi1, \
x2, \
'TOP')
yT, \
yB = flame.cont_with_3x1_to_2x1(y0, \
psi1, \
y2, \
'TOP')
flame.merge_2x1(yT, \
yB, y)