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serial_bbd_matrix.py
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serial_bbd_matrix.py
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#!/usr/bin/env python
# coding: utf-8
import numpy as np
import scipy.sparse.linalg as la
import scipy.sparse as sp
import time
from bbd_matrix import *
def schur_lu(A_bbd, dense_corner=False):
L = bbd_matrix(A_bbd.block_dim)
U = bbd_matrix(A_bbd.block_dim)
for idx in A_bbd.diag_blocks.keys():
Aii = A_bbd.diag_blocks[idx]
Ain = A_bbd.right_blocks[idx]
Ani = A_bbd.lower_blocks[idx]
N = Aii.shape[0]
lu = la.splu(Aii.tocsc(), permc_spec="NATURAL")
L.diag_blocks[idx] = lu.L[lu.perm_r,:]
U.diag_blocks[idx] = lu.U
L.lower_blocks[idx] = la.spsolve(lu.U.transpose().tocsc(),
Ani.transpose().tocsc()
).transpose()
U.right_blocks[idx] = la.spsolve(L.diag_blocks[idx], Ain.tocsc())
N = A_bbd.corner.shape[0]
B = sp.csc_matrix((N,N))
for idx in A_bbd.diag_blocks.keys():
B += L.lower_blocks[idx] @ U.right_blocks[idx]
lu = la.splu(A_bbd.corner.tocsc() - B)
L.corner = lu.L[lu.perm_r,:]
U.corner = lu.U[:,lu.perm_c]
if dense_corner:
L.corner = L.corner.todense()
U.corner = U.corner.todense()
L.complete = True
U.complete = True
return (L, U)
class schur_bbd_lu:
def __init__(self, A_bbd, dense_corner=False):
(self.L, self.U) = schur_lu(A_bbd, dense_corner=dense_corner)
self.block_sizes = A_bbd.block_sizes
self.dense_corner = dense_corner
self.t_formbv = 0.0
self.t_forward = 0.0
self.t_backward = 0.0
self.tf_yloop = 0.0
self.tf_csolve = 0.0
self.tb_csolve = 0.0
self.tb_loop = 0.0
self.solves = 0
return
def _schur_forward(self, b_bv):
t0 = time.time()
L = self.L
y = {}
c = np.zeros(L.corner.shape[0])
for idx in L.diag_blocks.keys():
y[idx] = la.spsolve(L.diag_blocks[idx], b_bv[idx])
c += L.lower_blocks[idx] @ y[idx]
t1 = time.time()
if self.dense_corner:
yn = dla.solve(L.corner, b_bv[L.block_dim - 1] - c)
else:
yn = la.spsolve(L.corner, b_bv[L.block_dim - 1] - c)
t2 = time.time()
self.tf_yloop += t1 - t0
self.tf_csolve += t2 - t1
return (y, yn)
def _schur_backward(self, y, yn, block_sizes):
t0 = time.time()
U = self.U
if self.dense_corner:
xn = dla.solve(U.corner, yn)
else:
xn = la.spsolve(U.corner, yn)
t1 = time.time()
x_bv = block_vector(block_sizes)
for idx in U.diag_blocks.keys():
rhs_i = y[idx] - U.right_blocks[idx] @ xn
x_bv[idx] = la.spsolve(U.diag_blocks[idx], rhs_i, permc_spec="NATURAL")
x_bv[U.block_dim - 1] = xn
t2 = time.time()
self.tb_csolve += t1 - t0
self.tb_loop += t2 - t1
return x_bv.to_dense()
def schur_solve(self, b_dense):
t0 = time.time()
b_bv = block_vector(self.block_sizes, x_dense=b_dense)
t1 = time.time()
(y, yn) = self._schur_forward(b_bv)
t2 = time.time()
x_bv = self._schur_backward(y, yn, b_bv.sizes)
t3 = time.time()
self.t_formbv += t1 - t0
self.t_forward += t2 - t1
self.t_backward += t3 - t2
self.solves += 1
return x_bv
def print_timing(self):
total = self.t_forward + self.t_backward
time_str = """
Calls: {:d}
BlkVectr: {:10.2e} {:8.2%} {:8.2e}
Forward: {:10.2e} {:8.2%} {:8.2e}
FLoop: {:10.2e} {:8.2%} {:8.2e}
FCSolve: {:10.2e} {:8.2%} {:8.2e}
Backward: {:10.2e} {:8.2%} {:8.2e}
BCSolve: {:10.2e} {:8.2%} {:8.2e}
BLoop: {:10.2e} {:8.2%} {:8.2e}
SchurSolve: {:10.2e}
""".format(
self.solves,
self.t_formbv, self.t_formbv/total, self.t_formbv/self.solves,
self.t_forward, self.t_forward/total, self.t_forward/self.solves,
self.tf_yloop, self.tf_yloop/total, self.tf_yloop/self.solves,
self.tf_csolve, self.tf_csolve/total, self.tf_csolve/self.solves,
self.t_backward, self.t_backward/total, self.t_backward/self.solves,
self.tb_csolve, self.tb_csolve/total, self.tb_csolve/self.solves,
self.tb_loop, self.tb_loop/total, self.tb_loop/self.solves,
total,
)
print(time_str)
return
def print_summary(self):
lsum = self.L.summarize()
usum = self.U.summarize()
bbd_str = """
**** {0} Summary ****
{0} Total NNZ: {1:7d}
{0} Min Block Size: {2:7d}
{0} Min Block NNZ: {3:7d}
{0} Max Block Size: {4:7d}
{0} Max Block NNZ: {5:7d}
{0} Corner Size: {6:7d}
{0} Corner NNZ: {7:7d}
"""
print(bbd_str.format(
'L',
lsum[0],
lsum[1],
lsum[2],
lsum[3],
lsum[4],
lsum[5],
lsum[6],
))
print(bbd_str.format(
'U',
usum[0],
usum[1],
usum[2],
usum[3],
usum[4],
usum[5],
usum[6],
))
return