def GaussianElimination_unb(A):
"""
GaussianElimination_unb(matrix)
Computes the Gauss Transform of the input matrix.
Traverses matrix A from TOP-LEFT to BOTTOM-RIGHT.
"""
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')
laff.invscal( alpha11, a21 ) # a21 := a21 / alpha11
laff.ger( -1.0, a21, a12t, A22 ) # A22 := A22 - a21 * a12t
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 Set_to_identity_unb_var1(A):
"""
Set_to_identity_unb_var1(matrix)
Sets the input matrix to the Identity matrix.
Traverses input matrix from TOP-LEFT to BOTTOM-RIGHT
and sets results column-wise.
"""
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')
laff.zerov(a01)
laff.onev(alpha11)
laff.zerov(a21)
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 GaussianElimination_unb(A):
"""
GaussianElimination_unb(matrix)
Computes the Gauss Transform of the input matrix.
Traverses matrix A from TOP-LEFT to BOTTOM-RIGHT.
"""
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')
laff.invscal(alpha11, a21) # a21 := a21 / alpha11
laff.ger(-1.0, a21, a12t, A22) # A22 := A22 - a21 * a12t
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 Set_to_lower_triangular_matrix_unb_var1(A):
"""
Set_to_lower_triangular_matrix_unb_var1(matrix)
Sets the above diagonal elements of A to zero.
Traverses matrix A from TOP-LEFT to BOTTOM-RIGHT,
and sets results column-wise.
"""
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')
laff.zerov(a01)
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 Symmetrize_from_lower_triangle_unb_var1(A):
"""
Symmetrize_from_lower_triangle_unb_var1(matrix)
Makes square matrix A symmetric by copying the
lower triangular part in its upper triangular part.
Traverses matrix A from TOP-LEFT to BOTTOM-RIGHT.
"""
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')
laff.copy(a01,a10t)
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 Symmetrize_from_lower_triangle_unb_var1(A):
"""
Symmetrize_from_lower_triangle_unb_var1(matrix)
Makes square matrix A symmetric by copying the
lower triangular part in its upper triangular part.
Traverses matrix A from TOP-LEFT to BOTTOM-RIGHT.
"""
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')
laff.copy(a01, a10t)
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 Set_to_identity_unb_var1(A):
"""
Set_to_identity_unb_var1(matrix)
Sets the input matrix to the Identity matrix.
Traverses input matrix from TOP-LEFT to BOTTOM-RIGHT
and sets results column-wise.
"""
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')
laff.zerov(a01)
laff.onev(alpha11)
laff.zerov(a21)
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 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 Set_to_lower_triangular_matrix_unb_var1(A):
"""
Set_to_lower_triangular_matrix_unb_var1(matrix)
Sets the above diagonal elements of A to zero.
Traverses matrix A from TOP-LEFT to BOTTOM-RIGHT,
and sets results column-wise.
"""
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")
laff.zerov(a01)
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)
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)