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_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 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 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 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 Transpose_unb_var2(A, B):
"""
Transpose_unb_var1(matrix, matrix)
Transposes matrix A and stores result in matrix B.
Traverses matrix A from TOP to BOTTOM,
matrix B from LEFT to RIGHT,
and copies rows of A to columns of B.
"""
AT, \
AB = flame.part_2x1(A, \
0, 'TOP')
BL, BR = flame.part_1x2(B, \
0, 'LEFT')
while AT.shape[0] < A.shape[0]:
A0, \
a1t, \
A2 = flame.repart_2x1_to_3x1(AT, \
AB, \
1, 'BOTTOM')
B0, b1, B2 = flame.repart_1x2_to_1x3(BL, BR, \
1, 'RIGHT')
laff.copy( a1t, b1 )
AT, \
AB = flame.cont_with_3x1_to_2x1(A0, \
a1t, \
A2, \
'TOP')
BL, BR = flame.cont_with_1x3_to_1x2(B0, b1, B2, \
'LEFT')
flame.merge_1x2(BL, BR, B)
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