"""

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, \