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 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 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_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_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 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 norm2( x ):
"""
Compute the 2-norm of a vector, returning alpha
x can be a row or column vector.
"""
assert type(x) is np.matrix and len(x.shape) is 2, \
"laff.norm2: vector x must be a 2D numpy.matrix"
m, n = np.shape(x)
assert m is 1 or n is 1, \
"laff.norm2: x is not a vector"
#Ensure that we don't modify x in
#any way by copying it to a new vector, y
y = np.matrix( np.zeros( (m,n) ) )
laff.copy( x, y )
#Initialize variables that we will use to appropriate values
alpha = 0
maxval = y[ 0, 0 ]
if m is 1: #y is a row
#Find a value to scale by to avoid under/overflow
for i in range(n):
if abs(y[ 0, i ]) > maxval:
maxval = abs(y[ 0, i ])
elif n is 1: #y is a column
#Find a value to scale by to avoid under/overflow
for i in range(m):
if abs(y[ i, 0 ]) > maxval:
maxval = abs(y[ i, 0 ])
#If y is the zero vector, return 0
if abs(maxval) < 1e-7:
return 0
#Scale all of the values by 1/maxval to prevent under/overflow
laff.scal( 1.0/maxval, y )
alpha = maxval * sqrt( laff.dot( y, y ) )
return alpha
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 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_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 norm2( x ):
"""
Compute the 2-norm of a vector, returning alpha
x can be a row or column vector.
"""
assert type(x) is np.matrix and len(x.shape) is 2, \
"laff.norm2: vector x must be a 2D numpy.matrix"
m, n = np.shape(x)
assert m is 1 or n is 1, \
"laff.norm2: x is not a vector"
#Ensure that we don't modify x in
#any way by copying it to a new vector, y
y = np.matrix( np.zeros( (m,n) ) )
laff.copy( x, y )
#Initialize variables that we will use to appropriate values
alpha = 0
maxval = y[ 0, 0 ]
if m is 1: #y is a row
#Find a value to scale by to avoid under/overflow
for i in range(n):
if abs(y[ 0, i ]) > maxval:
maxval = y[ 0, i ]
elif n is 1: #y is a column
#Find a value to scale by to avoid under/overflow
for i in range(m):
if abs(y[ i, 0 ]) > maxval:
maxval = y[ i, 0 ]
#If y is the zero vector, return 0
if maxval is 0:
return 0
#Scale all of the values by 1/maxval to prevent under/overflow
laff.scal( 1.0/maxval, y )
alpha = maxval * sqrt( laff.dot( y, y ) )
return alpha
def Scale_a_matrix_unb_var1(beta, A):
"""
Scale_a_matrix_unb_var1(scalar, matrix)
Scales matrix A by a factor of beta.
Traverses matrix A from LEFT to RIGHT.
"""
AL, AR = flame.part_1x2(A, \
0, 'LEFT')
while AL.shape[1] < A.shape[1]:
A0, a1, A2 = flame.repart_1x2_to_1x3(AL, AR, \
1, 'RIGHT')
laff.scal(beta,a1)
AL, AR = flame.cont_with_1x3_to_1x2(A0, a1, A2, \
'LEFT')
flame.merge_1x2(AL, AR, A)
def norm2(x):
"""
"""
assert type(x) is np.matrix and len(
x.shape) is 2, "laff.norm2: vector x must be a 2D numpy.matrix"
m, n = np.shape(x)
assert m is 1 or n is 1, "laff.norm2: x is not a vector"
y = np.matrix(np.zeros((m, n)))
laff.copy(x, y)
alpha = 0
maxval = y[0, 0]
if m is 1: #y is a row
for i in range(n):
if abs(y[0, i]) > maxval:
maxval = abs(y[0, i])
elif n is 1: #y is a column
for i in range(m):
if abs(y[i, 0]) > maxval:
maxval = abs(y[i, 0])
if abs(maxval) < 1e-7:
return 0
laff.scal(1.0 / maxval, y)
alpha = maxval * sqrt(laff.dot(y, y))
return alpha
def norm2( x ):
"""
"""
assert type(x) is np.matrix and len(x.shape) is 2, "laff.norm2: vector x must be a 2D numpy.matrix"
m, n = np.shape(x)
assert m is 1 or n is 1, "laff.norm2: x is not a vector"
y = np.matrix( np.zeros( (m,n) ) )
laff.copy( x, y )
alpha = 0
maxval = y[ 0, 0 ]
if m is 1: #y is a row
for i in range(n):
if abs(y[ 0, i ]) > maxval:
maxval = abs(y[ 0, i ])
elif n is 1: #y is a column
for i in range(m):
if abs(y[ i, 0 ]) > maxval:
maxval = abs(y[ i, 0 ])
if abs(maxval) < 1e-7:
return 0
laff.scal( 1.0/maxval, y )
alpha = maxval * sqrt( laff.dot( y, y ) )
return alpha
