def Trmv_ln_unb_var2(L, x):
"""
Trmv_ln_unb_var2(matrix, vector)
Computes y = L * x using AXPY operations.
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.axpy( chi1, l21, x2 )
laff.scal( lambda11, 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 ForwardSubstitution_unb(A, b):
"""
ForwardSubstitution_unb(matrix, vector)
Computes coefficients using Forward Substituion.
Traverses matrix A from TOP-LEFT to BOTTOM-RIGHT,
vector b from TOP to BOTTOM.
"""
ATL, ATR, \
ABL, ABR = flame.part_2x2(A, \
0, 0, 'TL')
bT, \
bB = flame.part_2x1(b, \
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')
b0, \
beta1, \
b2 = flame.repart_2x1_to_3x1(bT, \
bB, \
1, 'BOTTOM')
laff.axpy( -beta1, a21, b2 )
ATL, ATR, \
ABL, ABR = flame.cont_with_3x3_to_2x2(A00, a01, A02, \
a10t, alpha11, a12t, \
A20, a21, A22, \
'TL')
bT, \
bB = flame.cont_with_3x1_to_2x1(b0, \
beta1, \
b2, \
'TOP')
flame.merge_2x1(bT, \
bB, b)
def Trmv_un_unb_var2(U, x):
"""
Trmv_un_unb_var2(matrix, vector)
Computes y = U * x using AXPY operations.
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.axpy(chi1, u01, x0)
laff.scal(upsilon11, 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_var2(U, x):
"""
Trmv_un_unb_var2(matrix, vector)
Computes y = U * x using AXPY operations.
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.axpy( chi1, u01, x0 )
laff.scal( upsilon11, 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 trsv_lnn(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')
#------------------------------------------------------------#
scal( 1./lambda11, beta1 )
axpy( -beta1, l21, b2 )
#------------------------------------------------------------#
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 trsv_lnn(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')
#------------------------------------------------------------#
scal(1. / lambda11, beta1)
axpy(-beta1, l21, b2)
#------------------------------------------------------------#
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 trsv_utn( U, b ):
UTL, UTR, \
UBL, UBR = flame.part_2x2(U, \
0, 0, 'TL')
bT, \
bB = flame.part_2x1(b, \
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')
b0, \
beta1, \
b2 = flame.repart_2x1_to_3x1(bT, \
bB, \
1, 'BOTTOM')
#------------------------------------------------------------#
invscal( upsilon11, beta1 )
axpy( -beta1, u12t, b2 )
#------------------------------------------------------------#
UTL, UTR, \
UBL, UBR = flame.cont_with_3x3_to_2x2(U00, u01, U02, \
u10t, upsilon11, u12t, \
U20, u21, U22, \
'TL')
bT, \
bB = flame.cont_with_3x1_to_2x1(b0, \
beta1, \
b2, \
'TOP')
flame.merge_2x1(bT, \
bB, b)
def Mvmult_t_unb_var2(A, x, y):
"""
Mvmult_t_unb_var2(matrix, vector, vector)
Computes y = A' * x + y using AXPY operations.
Traverses matrix A from TOP to BOTTOM,
vector x from TOP to BOTTOM.
"""
AT, \
AB = flame.part_2x1(A, \
0, 'TOP')
xT, \
xB = flame.part_2x1(x, \
0, 'TOP')
while AT.shape[0] < A.shape[0]:
A0, \
a1t, \
A2 = flame.repart_2x1_to_3x1(AT, \
AB, \
1, 'BOTTOM')
x0, \
chi1, \
x2 = flame.repart_2x1_to_3x1(xT, \
xB, \
1, 'BOTTOM')
laff.axpy( chi1, a1t, y )
AT, \
AB = flame.cont_with_3x1_to_2x1(A0, \
a1t, \
A2, \
'TOP')
xT, \
xB = flame.cont_with_3x1_to_2x1(x0, \
chi1, \
x2, \
'TOP')
def Mvmult_n_unb_var2(A, x, y):
"""
Mvmult_n_unb_var2(matrix, vector, vector)
Compuyes y = A * x + y using AXPY operations.
Traverses matrix A from LEFT to RIGHT,
vector x from TOP to BOTTOM.
"""
AL, AR = flame.part_1x2(A, \
0, 'LEFT')
xT, \
xB = flame.part_2x1(x, \
0, 'TOP')
while AL.shape[1] < A.shape[1]:
A0, a1, A2 = flame.repart_1x2_to_1x3(AL, AR, \
1, 'RIGHT')
x0, \
chi1, \
x2 = flame.repart_2x1_to_3x1(xT, \
xB, \
1, 'BOTTOM')
laff.axpy( chi1, a1, y )
AL, AR = flame.cont_with_1x3_to_1x2(A0, a1, A2, \
'LEFT')
xT, \
xB = flame.cont_with_3x1_to_2x1(x0, \
chi1, \
x2, \
'TOP')
def Mvmult_n_unb_var2(A, x, y):
"""
Mvmult_n_unb_var2(matrix, vector, vector)
Compuyes y = A * x + y using AXPY operations.
Traverses matrix A from LEFT to RIGHT,
vector x from TOP to BOTTOM.
"""
AL, AR = flame.part_1x2(A, \
0, 'LEFT')
xT, \
xB = flame.part_2x1(x, \
0, 'TOP')
while AL.shape[1] < A.shape[1]:
A0, a1, A2 = flame.repart_1x2_to_1x3(AL, AR, \
1, 'RIGHT')
x0, \
chi1, \
x2 = flame.repart_2x1_to_3x1(xT, \
xB, \
1, 'BOTTOM')
laff.axpy(chi1, a1, y)
AL, AR = flame.cont_with_1x3_to_1x2(A0, a1, A2, \
'LEFT')
xT, \
xB = flame.cont_with_3x1_to_2x1(x0, \
chi1, \
x2, \
'TOP')
def Tmvmult_ln_unb_var2(L, x, y):
"""
Tmvmult_ln_unb_var2(matrix, vector, vector)
Computes y = L * x + y using AXPY operations.
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.axpy(chi1, lambda11, psi1)
laff.axpy(chi1, l21, y2)
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 Tmvmult_lt_unb_var2(L, x, y):
"""
Tmvmult_lt_unb_var2(matrix, vector, vector)
Computes y = L' * x + y using AXPY operations.
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.axpy( chi1, lambda11, psi1 )
laff.axpy( chi1, l10t, y0 )
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_var2(A, x, y):
"""
Symv_u_unb_var2(matrix, vector, vector)
Computes y = A * x + y using AXPY operations.
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.axpy( chi1, a01, y0 )
laff.axpy( chi1, alpha11, psi1 )
laff.axpy( chi1, a12t, y2 )
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_var2(U, x, y):
"""
Tmvmult_ut_unb_var2(matrix, vector, vector)
Computes y = U' * x + y using AXPY operations.
Traverses matrix A 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.axpy( chi1, u12t, y2 )
laff.axpy( chi1, upsilon11, 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_var2(A, x, y):
"""
Symv_u_unb_var2(matrix, vector, vector)
Computes y = A * x + y using AXPY operations.
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.axpy(chi1, a01, y0)
laff.axpy(chi1, alpha11, psi1)
laff.axpy(chi1, a12t, y2)
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)
