def Scale_a_matrix_unb_var2(beta, A):
"""
Scale_a_matrix_unb_var2(scalar, matrix)
Scales matrix A by a factor of beta.
Traverses matrix A from TOP to BOTTOM.
"""
AT, \
AB = flame.part_2x1(A, \
0, 'TOP')
while AT.shape[0] < A.shape[0]:
A0, \
a1t, \
A2 = flame.repart_2x1_to_3x1(AT, \
AB, \
1, 'BOTTOM')
laff.scal(beta,a1t)
AT, \
AB = flame.cont_with_3x1_to_2x1(A0, \
a1t, \
A2, \
'TOP')
flame.merge_2x1(AT, \
AB, A)
def trsm_utn(U, B):
BT, \
BB = flame.part_2x1(B, \
0, 'TOP')
while BT.shape[0] < B.shape[0]:
B0, \
b1t, \
B2 = flame.repart_2x1_to_3x1(BT, \
BB, \
1, 'BOTTOM')
#------------------------------------------------------------#
#TODO: Fix trsv.py to handle rows properly
#Sorry for the hackiness in the fix here, I got pressed for time
laff.trsv('Upper triangular', 'Transpose', 'Nonunit diagonal', U,
transpose(b1t))
#------------------------------------------------------------#
BT, \
BB = flame.cont_with_3x1_to_2x1(B0, \
b1t, \
B2, \
'TOP')
flame.merge_2x1(BT, \
BB, B)
def trsm_ltu(L, B):
BT, \
BB = flame.part_2x1(B, \
0, 'TOP')
while BT.shape[0] < B.shape[0]:
B0, \
b1t, \
B2 = flame.repart_2x1_to_3x1(BT, \
BB, \
1, 'BOTTOM')
#------------------------------------------------------------#
#TODO: Fix trsv.py to handle rows properly
#Sorry for the hackiness in the fix here, I got pressed for time
laff.trsv( 'Lower triangular', 'Transpose', 'Unit diagonal', L, transpose( b1t ) )
#------------------------------------------------------------#
BT, \
BB = flame.cont_with_3x1_to_2x1(B0, \
b1t, \
B2, \
'TOP')
flame.merge_2x1(BT, \
BB, B)
def Set_to_zero_unb_var2(A):
"""
Set_to_zero_unb_var2(matrix)
Sets the input matrix to zeros.
Traverses input matrix from TOP to BOTTOM
and sets results column-wise.
"""
AT, \
AB = flame.part_2x1(A, \
0, 'TOP')
while AT.shape[0] < A.shape[0]:
A0, \
a1t, \
A2 = flame.repart_2x1_to_3x1(AT, \
AB, \
1, 'BOTTOM')
laff.zerov(a1t)
AT, \
AB = flame.cont_with_3x1_to_2x1(A0, \
a1t, \
A2, \
'TOP')
flame.merge_2x1(AT, \
AB, A)
def Set_to_zero_unb_var2(A):
"""
Set_to_zero_unb_var2(matrix)
Sets the input matrix to zeros.
Traverses input matrix from TOP to BOTTOM
and sets results column-wise.
"""
AT, \
AB = flame.part_2x1(A, \
0, 'TOP')
while AT.shape[0] < A.shape[0]:
A0, \
a1t, \
A2 = flame.repart_2x1_to_3x1(AT, \
AB, \
1, 'BOTTOM')
laff.zerov(a1t)
AT, \
AB = flame.cont_with_3x1_to_2x1(A0, \
a1t, \
A2, \
'TOP')
flame.merge_2x1(AT, \
AB, A)
def Set_to_diagonal_matrix_unb_var2(d, A):
"""
Set_to_diagonal_matrix_unb_var2(vector, matrix)
Sets the diagonal elements of A to the components of vector d.
Traverses matrix A from TOP-LEFT to BOTTOM-RIGHT,
traverses vector d from TOP to BOTTOM
and sets results row-wise.
"""
dT, \
dB = flame.part_2x1(d, \
0, 'TOP')
ATL, ATR, \
ABL, ABR = flame.part_2x2(A, \
0, 0, 'TL')
while dT.shape[0] < d.shape[0]:
d0, \
delta1, \
d2 = flame.repart_2x1_to_3x1(dT, \
dB, \
1, 'BOTTOM')
A00, a01, A02, \
a10t, alpha11, a12t, \
A20, a21, A22 = flame.repart_2x2_to_3x3(ATL, ATR, \
ABL, ABR, \
1, 1, 'BR')
laff.zerov(a10t)
laff.copy(delta1, alpha11)
laff.zerov(a12t)
dT, \
dB = flame.cont_with_3x1_to_2x1(d0, \
delta1, \
d2, \
'TOP')
ATL, ATR, \
ABL, ABR = flame.cont_with_3x3_to_2x2(A00, a01, A02, \
a10t, alpha11, a12t, \
A20, a21, A22, \
'TL')
flame.merge_2x1(dT, \
dB, d)
flame.merge_2x2(ATL, ATR, \
ABL, ABR, A)
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_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_lt_unb_var1(L, x):
"""
Trmv_lt_unb_var1(matrix, vector)
Computes x = L' * x using DOT products.
Traverses matrix L from TOP-LEFT to BOTTOM-RIGHT,
vector x from TOP to BOTTOM.
"""
LTL, LTR, \
LBL, LBR = flame.part_2x2(L, \
0, 0, 'TL')
xT, \
xB = flame.part_2x1(x, \
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')
laff.scal(lambda11, chi1)
laff.dots(l21, x2, chi1)
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')
flame.merge_2x1(xT, \
xB, x)
def Trmv_ut_unb_var1(U, x):
"""
Trmv_ut_unb_var1(matrix, vector)
Computes x = U' * x using DOT products.
Traverses matrix U from BOTTOM-RIGHT to TOP-LEFT,
vector x from BOTTOM to TOP.
"""
UTL, UTR, \
UBL, UBR = flame.part_2x2(U, \
0, 0, 'BR')
xT, \
xB = flame.part_2x1(x, \
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')
x0, \
chi1, \
x2 = flame.repart_2x1_to_3x1(xT, \
xB, \
1, 'TOP')
laff.scal( upsilon11, chi1 )
laff.dots( u01, x0, chi1 )
UTL, UTR, \
UBL, UBR = flame.cont_with_3x3_to_2x2(U00, u01, U02, \
u10t, upsilon11, u12t, \
U20, u21, U22, \
'BR')
xT, \
xB = flame.cont_with_3x1_to_2x1(x0, \
chi1, \
x2, \
'BOTTOM')
flame.merge_2x1(xT, \
xB, x)
def Trmv_ut_unb_var2(U, x):
"""
Trmv_ut_unb_var2(matrix, vector)
Computes x = U' * x using AXPY operations.
Traverses matrix U from BOTTOM-RIGHT to TOP-LEFT,
vector x from BOTTOM to TOP.
"""
UTL, UTR, \
UBL, UBR = flame.part_2x2(U, \
0, 0, 'BR')
xT, \
xB = flame.part_2x1(x, \
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')
x0, \
chi1, \
x2 = flame.repart_2x1_to_3x1(xT, \
xB, \
1, 'TOP')
laff.axpy(chi1, u12t, x2)
laff.scal(upsilon11, chi1)
UTL, UTR, \
UBL, UBR = flame.cont_with_3x3_to_2x2(U00, u01, U02, \
u10t, upsilon11, u12t, \
U20, u21, U22, \
'BR')
xT, \
xB = flame.cont_with_3x1_to_2x1(x0, \
chi1, \
x2, \
'BOTTOM')
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 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 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_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 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_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 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 Transpose_unb_var1(A, B):
"""
Transpose_unb_var1(matrix, matrix)
Transposes matrix A and stores result in matrix B.
Traverses matrix A from LEFT to RIGHT,
matrix B from TOP to BOTTOM,
and copies columns of A to rows of B.
"""
AL, AR = flame.part_1x2(A, \
0, 'LEFT')
BT, \
BB = flame.part_2x1(B, \
0, 'TOP')
while AL.shape[1] < A.shape[1]:
A0, a1, A2 = flame.repart_1x2_to_1x3(AL, AR, \
1, 'RIGHT')
B0, \
b1t, \
B2 = flame.repart_2x1_to_3x1(BT, \
BB, \
1, 'BOTTOM')
laff.copy( a1, b1t )
AL, AR = flame.cont_with_1x3_to_1x2(A0, a1, A2, \
'LEFT')
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 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 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_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 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 Tmvmult_un_unb_var2(U, x, y):
"""
Tmvmult_un_unb_var2(matrix, vector, vector)
Computes y = U * x + y using AXPY operations.
U is the upper triangular matrix.
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.axpy(chi1, u01, y0)
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 Tmvmult_un_unb_var1(U, x, y):
"""
Tmvmult_un_unb_var1(matrix, vector, vector)
Computes y = U * x + y using DOT products.
U is the upper triangular matrix.
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( u12t, x2, 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)
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)