def find_matrix_class():
aFile = 'Archive/A.txt'
bFile = 'Archive/b.txt'
nCols = 100000
maxL = 1e-3
maxLerror = 1e-2
(aLists, b) = l.read_data(aFile, bFile)
vals = aLists[2]
rows = aLists[0]
cols = aLists[1]
nRows = len(b)
A = (vals, (rows, cols))
myShape = (nRows, nCols)
aSparses = []
aSparses.append(sp.csr_matrix(A, shape = myShape))
aSparses.append(sp.coo_matrix(A, shape = myShape))
aSparses.append(sp.csc_matrix(A, shape = myShape))
#aSparses.append(sp.dok_matrix(aSparses[0]))
times = []
for aSparse in aSparses:
print("Class " + str(type(aSparse)))
t0 = tm.time()
res = sp.linalg.lsqr(aSparse, b, atol = 1e-6, btol = 1e-7, iter_lim = 150)
t1 = tm.time()
L = l.cost(l.difference_vector(aLists, res[0], b))
Lemp = 0.5 * res[3] * res[3]
if np.abs(L - Lemp) / Lemp > maxLerror or L > 1e-3:
print("ERROR: wrong cost for class " + str(type(aSparse)))
times.append(t1 - t0)
mp.plot(range(len(times)), times)
mp.show()
def lsqr_test(aTol, bTol, nTests):
lenX = 100000
maxL = 1e-3
maxFracDiff = 1e-2
maxXValue = 10
multFac = 1. / bTol
print("Reading the real data...")
aAndRealB = l.read_data('Archive/a.txt', 'Archive/b.txt')
A = aAndRealB[0]
realB = np.array(aAndRealB[1])
print('Getting random b vectors...')
(xs, bs) = gen_rand_b(A, realB, lenX, nTests, maxXValue, multFac)
# For each b vector, find x using lsqr
print("Converting to sparse matrix...")
aSparse = l.convert_to_sparse_matrix(A, len(realB), lenX)
predictedXs = []
iters = []
costs = []
fracDiffs = []
for i in range(len(bs)):
print("Test " + str(i))
b = bs[i]
(x, reason, nIters, r) = l.lsqr_single_sparse(aSparse, b, aTol, bTol, False, None)
predictedXs.append(x)
iters.append(nIters)
# Compare the x obtained with the one used in the input using program.py
xFracDiff = compare_x_arrays(x, xs[i])[2]
if xFracDiff > maxFracDiff:
print('ERROR: wrong x result for iteration ' + str(i))
# Make sure the cost was less than maxL in all cases
L = l.cost(l.difference_vector(A, x, b))
if L > maxL:
print("The cost is too high: " + str(L))
costs.append(L)
# Compute one of the rows manually
firstRow = A[0][0]
firstColumn = A[1][0]
firstValue = A[2][0]
absDiff = (firstValue * x[firstColumn] - b[firstRow])
if (b[firstRow] == 0 and absDiff != 0) or (b[firstRow] != 0 and absDiff / b[firstRow] > maxFracDiff):
print("Difference is too large! " + str(x[firstColumn]) + ", " + str(b[firstRow]))
fracDiffs.append(absDiff)
if b[firstRow] != 0:
fracDiffs[-1] /= b[firstRow]
# Look at the number of iterations for each test and see if they are roughly constant
mp.plot(range(len(bs)), iters)
mp.show()
# Look at the costs for each test
mp.plot(range(len(bs)), costs)
mp.show()
def test_difference_vector():
rows = [0, 1, 2]
cols = [0, 1, 2]
vals = [1, 3, 5]
x = [7, 11, 13]
b = [17, 19, 21]
dv = l.difference_vector((rows, cols, vals), x, b)
success = dv[0] == -10 and dv[1] == 14 and dv[2] == 44
if not success:
print('ERROR!!! in difference vector')
def test_random_bs():
nTests = 100
aFile = 'Archive/A.txt'
maxL = 1e-3
nCols = 100000
for i in range(nTests):
print('Test ' + str(i))
bFile = 'fakes/b' + str(i) + '.txt'
xFile = 'fakes/x' + str(i) + '.txt'
(A,b) = l.read_data(aFile, bFile)
(x, L, reason, nIters, aLists, b, aSparse) = l.lsqr(aFile, bFile, nCols, verbose = False)
myCost = l.cost(l.difference_vector(A, x, b))
if myCost > maxL:
print('Error in file ' + str(i))
def find_iters():
aFile = 'Archive/A.txt'
bFile = 'Archive/b.txt'
nCols = 100000
maxL = 1e-3
maxLerror = 1e-2
iterLims = [50, 100, 150, 200, 250, 300, 350, None]
(aLists, b) = l.read_data(aFile, bFile)
aSparse = l.convert_to_sparse_matrix(aLists, len(b), nCols)
Ls = []
for iterLim in iterLims:
print("Up to " + str(iterLim) + " iterations...")
res = sp.linalg.lsqr(aSparse, b, atol = 1e-6, btol = 1e-7, iter_lim = iterLim)
L = l.cost(l.difference_vector(aLists, res[0], b))
Lemp = 0.5 * res[3] * res[3]
if np.abs(L - Lemp) / Lemp > maxLerror:
print("ERROR: wrong cost for " + str(iterLim) + " iterations")
Ls.append(L)
mp.semilogy(range(len(Ls)), Ls)
mp.show()
def compare_algos():
aFile = 'Archive/A.txt'
bFile = 'Archive/b.txt'
nCols = 100000
maxL = 1e-3
aTol = 1e-6
bTol = 1e-7
maxErrorL = 1e-2
nFakeTests = 10
maxXValue = 10
multFac = 1. / aTol
# Read the data
(aLists,b) = l.read_data(aFile, bFile)
# Convert to a sparse matrix
aSparse = l.convert_to_sparse_matrix(aLists, len(b), nCols)
# Try LSQR
t0 = tm.time()
r = sp.linalg.lsqr(aSparse, b, atol = aTol, btol = bTol, show = False)
t1 = tm.time()
print('LSQR: ' + str(t1 - t0) + ' s')
x = r[0]
dv = l.difference_vector(aLists, x, b)
L = l.cost(dv)
res = 0.5 * r[3] * r[3]
if np.abs(L - res) / res > maxErrorL or L > maxL:
print('ERROR: wrong cost for LSQR')
# Try LSMR
t0 = tm.time()
r = sp.linalg.lsmr(aSparse, b, atol = aTol, btol = bTol, show = False)
t1 = tm.time()
print('LSMR: ' + str(t1 - t0) + ' s')
x = r[0]
dv = l.difference_vector(aLists, x, b)
L = l.cost(dv)
res = 0.5 * r[3] * r[3]
if np.abs(L - res) / res > maxErrorL or L > maxL:
print('ERROR: wrong cost for LSMR')
# Now try with fake data
(xs, bs) = gen_rand_b(aLists, np.array(b), nCols, nFakeTests, maxXValue, multFac)
lsqrTimes = []
lsmrTimes = []
for i in range(len(bs)):
t0 = tm.time()
r = sp.linalg.lsmr(aSparse, bs[i], atol = aTol, btol = bTol)
t1 = tm.time()
lsmrTimes.append(t1 - t0)
x = r[0]
dv = l.difference_vector(aLists, x, bs[i])
L = l.cost(dv)
res = 0.5 * r[3] * r[3]
if np.abs(L - res) / res > maxErrorL or L > maxL:
print('ERROR: wrong cost for LSMR')
dx = np.array([(x[j] - xs[i][j]) for j in range(len(x))])
if np.sqrt(np.sum(dx * dx)) / np.sqrt(np.sum(xs[i] * xs[i])) > maxErrorL:
print('ERROR: wrong x result for LSMR')
t0 = tm.time()
r = sp.linalg.lsqr(aSparse, bs[i], atol = aTol, btol = bTol)
t1 = tm.time()
lsqrTimes.append(t1 - t0)
x = r[0]
dv = l.difference_vector(aLists, x, bs[i])
L = l.cost(dv)
res = 0.5 * r[3] * r[3]
if np.abs(L - res) / res > maxErrorL or L > maxL:
print('ERROR: wrong cost for LSQR')
dx = np.array([(x[j] - xs[i][j]) for j in range(len(x))])
if np.sqrt(np.sum(dx * dx)) / np.sqrt(np.sum(xs[i] * xs[i])) > maxErrorL:
print('ERROR: wrong x result for LSQR')
# Plot the times
mp.plot(range(len(lsqrTimes)), lsqrTimes, color='red')
mp.plot(range(len(lsmrTimes)), lsmrTimes, color='blue')
mp.show()