def get_response_content(fs):
np.set_printoptions(linewidth=200)
n = len(fs.D)
# create the distance matrix with the extra node added
D_dup = get_duplicate_edm(fs.D)
# get the principal axis projection from the distance dup matrix
HSH = -(0.5) * MatrixUtil.double_centered(D_dup)
X_w, X_v = EigUtil.principal_eigh(HSH)
D_dup_x = X_v * math.sqrt(X_w)
# get masses summing to one
m = np.array([1]*(n-1) + [2], dtype=float) / (n+1)
# get the principal axis projection using the weight formula
M = np.diag(np.sqrt(m))
I = np.eye(n, dtype=float)
E = I - np.outer(np.ones(n, dtype=float), m)
ME = np.dot(M, E)
Q = -(0.5) * np.dot(ME, np.dot(fs.D, ME.T))
Q_w, Q_v = EigUtil.principal_eigh(Q)
Q_x = Q_v * math.sqrt(Q_w) / np.sqrt(m)
# make the response
out = StringIO()
print >> out, 'distance matrix with exact duplicate node:'
print >> out, D_dup
print >> out
print >> out, 'principal axis projection:'
print >> out, D_dup_x
print >> out
print >> out, 'principal axis projection using the weight formula:'
print >> out, Q_x
return out.getvalue()
def get_response_content(fs):
np.set_printoptions(linewidth=200)
n = len(fs.D)
# create the Laplacian matrix
L = Euclid.edm_to_laplacian(fs.D)
# create the Laplacian matrix with the extra node added
L_dup = get_pseudoduplicate_laplacian(L, fs.strength)
# get the principal axis projection from the Laplacian dup matrix
X_w, X_v = EigUtil.principal_eigh(np.linalg.pinv(L_dup))
L_dup_x = X_v * math.sqrt(X_w)
# get masses summing to one
m = np.array([1] * (n - 1) + [2], dtype=float) / (n + 1)
# get the principal axis projection using the weight formula
M = np.diag(np.sqrt(m))
L_pinv = np.linalg.pinv(L)
I = np.eye(n, dtype=float)
E = I - np.outer(np.ones(n, dtype=float), m)
ME = np.dot(M, E)
Q = np.dot(ME, np.dot(L_pinv, ME.T))
Q_w, Q_v = EigUtil.principal_eigh(Q)
Q_x = Q_v * math.sqrt(Q_w) / np.sqrt(m)
# make the response
out = StringIO()
print >> out, 'Laplacian matrix with pseudo-duplicate node:'
print >> out, L_dup
print >> out
print >> out, 'principal axis projection:'
print >> out, L_dup_x
print >> out
print >> out, 'principal axis projection using the weight formula:'
print >> out, Q_x
return out.getvalue()
def get_response_content(fs):
np.set_printoptions(linewidth=200)
n = len(fs.D)
# create the distance matrix with the extra node added
D_dup = get_duplicate_edm(fs.D)
# get the principal axis projection from the distance dup matrix
HSH = -(0.5) * MatrixUtil.double_centered(D_dup)
X_w, X_v = EigUtil.principal_eigh(HSH)
D_dup_x = X_v * math.sqrt(X_w)
# get masses summing to one
m = np.array([1] * (n - 1) + [2], dtype=float) / (n + 1)
# get the principal axis projection using the weight formula
M = np.diag(np.sqrt(m))
I = np.eye(n, dtype=float)
E = I - np.outer(np.ones(n, dtype=float), m)
ME = np.dot(M, E)
Q = -(0.5) * np.dot(ME, np.dot(fs.D, ME.T))
Q_w, Q_v = EigUtil.principal_eigh(Q)
Q_x = Q_v * math.sqrt(Q_w) / np.sqrt(m)
# make the response
out = StringIO()
print >> out, 'distance matrix with exact duplicate node:'
print >> out, D_dup
print >> out
print >> out, 'principal axis projection:'
print >> out, D_dup_x
print >> out
print >> out, 'principal axis projection using the weight formula:'
print >> out, Q_x
return out.getvalue()
def get_response_content(fs):
np.set_printoptions(linewidth=200)
n = len(fs.D)
# create the Laplacian matrix
L = Euclid.edm_to_laplacian(fs.D)
# create the Laplacian matrix with the extra node added
L_dup = get_pseudoduplicate_laplacian(L, fs.strength)
# get the principal axis projection from the Laplacian dup matrix
X_w, X_v = EigUtil.principal_eigh(np.linalg.pinv(L_dup))
L_dup_x = X_v * math.sqrt(X_w)
# get masses summing to one
m = np.array([1]*(n-1) + [2], dtype=float) / (n+1)
# get the principal axis projection using the weight formula
M = np.diag(np.sqrt(m))
L_pinv = np.linalg.pinv(L)
I = np.eye(n, dtype=float)
E = I - np.outer(np.ones(n, dtype=float), m)
ME = np.dot(M, E)
Q = np.dot(ME, np.dot(L_pinv, ME.T))
Q_w, Q_v = EigUtil.principal_eigh(Q)
Q_x = Q_v * math.sqrt(Q_w) / np.sqrt(m)
# make the response
out = StringIO()
print >> out, 'Laplacian matrix with pseudo-duplicate node:'
print >> out, L_dup
print >> out
print >> out, 'principal axis projection:'
print >> out, L_dup_x
print >> out
print >> out, 'principal axis projection using the weight formula:'
print >> out, Q_x
return out.getvalue()
def get_response_content(fs):
# build the newick tree from the string
tree = NewickIO.parse(fs.tree_string, FelTree.NewickTree)
nvertices = len(list(tree.preorder()))
nleaves = len(list(tree.gen_tips()))
# get ordered ids with the leaves first
ordered_ids = get_ordered_ids(tree)
# get the adjacency matrix and the augmented adjacency matrix
A = np.array(tree.get_affinity_matrix(ordered_ids))
A_aug = get_augmented_adjacency(A, nleaves, fs.ndups, fs.strength)
# get the laplacian matrices
L = Euclid.adjacency_to_laplacian(A)
L_aug = Euclid.adjacency_to_laplacian(A_aug)
# get the schur complement
R = SchurAlgebra.mschur(L, set(range(nleaves, nvertices)))
R_pinv = np.linalg.pinv(R)
vals, vecs = EigUtil.eigh(R_pinv)
# get the scaled Fiedler vector for the Schur complement
w, v = EigUtil.principal_eigh(R_pinv)
fiedler = v * math.sqrt(w)
# get the eigendecomposition of the augmented Laplacian
L_aug_pinv = np.linalg.pinv(L_aug)
vals_aug, vecs_aug = EigUtil.eigh(L_aug_pinv)
# get the scaled Fiedler vector for the augmented Laplacian
w_aug, v_aug = EigUtil.principal_eigh(L_aug_pinv)
fiedler_aug = v_aug * math.sqrt(w_aug)
# report the results
np.set_printoptions(linewidth=300)
out = StringIO()
print >> out, 'Laplacian matrix:'
print >> out, L
print >> out
print >> out, 'Schur complement of Laplacian matrix:'
print >> out, R
print >> out
print >> out, 'scaled Fiedler vector of Schur complement:'
print >> out, fiedler
print >> out
print >> out, 'eigenvalues of pinv of Schur complement:'
print >> out, vals
print >> out
print >> out, 'corresponding eigenvectors of pinv of Schur complement:'
print >> out, np.array(vecs).T
print >> out
print >> out
print >> out, 'augmented Laplacian matrix:'
print >> out, L_aug
print >> out
print >> out, 'scaled Fiedler vector of augmented Laplacian:'
print >> out, fiedler_aug
print >> out
print >> out, 'eigenvalues of pinv of augmented Laplacian:'
print >> out, vals_aug
print >> out
print >> out, 'rows are eigenvectors of pinv of augmented Laplacian:'
print >> out, np.array(vecs_aug)
return out.getvalue()
def get_response_content(fs):
# build the newick tree from the string
tree = NewickIO.parse(fs.tree_string, FelTree.NewickTree)
nvertices = len(list(tree.preorder()))
nleaves = len(list(tree.gen_tips()))
# get ordered ids with the leaves first
ordered_ids = get_ordered_ids(tree)
# get the adjacency matrix and the augmented adjacency matrix
A = np.array(tree.get_affinity_matrix(ordered_ids))
A_aug = get_augmented_adjacency(A, nleaves, fs.ndups, fs.strength)
# get the laplacian matrices
L = Euclid.adjacency_to_laplacian(A)
L_aug = Euclid.adjacency_to_laplacian(A_aug)
# get the schur complement
R = SchurAlgebra.mschur(L, set(range(nleaves, nvertices)))
R_pinv = np.linalg.pinv(R)
vals, vecs = EigUtil.eigh(R_pinv)
# get the scaled Fiedler vector for the Schur complement
w, v = EigUtil.principal_eigh(R_pinv)
fiedler = v * math.sqrt(w)
# get the eigendecomposition of the augmented Laplacian
L_aug_pinv = np.linalg.pinv(L_aug)
vals_aug, vecs_aug = EigUtil.eigh(L_aug_pinv)
# get the scaled Fiedler vector for the augmented Laplacian
w_aug, v_aug = EigUtil.principal_eigh(L_aug_pinv)
fiedler_aug = v_aug * math.sqrt(w_aug)
# report the results
np.set_printoptions(linewidth=300)
out = StringIO()
print >> out, 'Laplacian matrix:'
print >> out, L
print >> out
print >> out, 'Schur complement of Laplacian matrix:'
print >> out, R
print >> out
print >> out, 'scaled Fiedler vector of Schur complement:'
print >> out, fiedler
print >> out
print >> out, 'eigenvalues of pinv of Schur complement:'
print >> out, vals
print >> out
print >> out, 'corresponding eigenvectors of pinv of Schur complement:'
print >> out, np.array(vecs).T
print >> out
print >> out
print >> out, 'augmented Laplacian matrix:'
print >> out, L_aug
print >> out
print >> out, 'scaled Fiedler vector of augmented Laplacian:'
print >> out, fiedler_aug
print >> out
print >> out, 'eigenvalues of pinv of augmented Laplacian:'
print >> out, vals_aug
print >> out
print >> out, 'rows are eigenvectors of pinv of augmented Laplacian:'
print >> out, np.array(vecs_aug)
return out.getvalue()
def get_response_content(fs):
# build the newick tree from the string
tree = NewickIO.parse(fs.tree_string, FelTree.NewickTree)
nvertices = len(list(tree.preorder()))
nleaves = len(list(tree.gen_tips()))
# get ordered ids with the leaves first
ordered_ids = get_ordered_ids(tree)
# get the distance matrix and the augmented distance matrix
D = np.array(tree.get_partial_distance_matrix(ordered_ids))
D_aug = get_augmented_distance(D, nleaves, fs.ndups)
# get the laplacian matrix
L = Euclid.edm_to_laplacian(D)
# get the schur complement
R = SchurAlgebra.mschur(L, set(range(nleaves, nvertices)))
R_pinv = np.linalg.pinv(R)
vals, vecs = EigUtil.eigh(R_pinv)
# get the scaled Fiedler vector for the Schur complement
w, v = EigUtil.principal_eigh(R_pinv)
fiedler = v * math.sqrt(w)
# get the eigendecomposition of the centered augmented distance matrix
L_aug_pinv = Euclid.edm_to_dccov(D_aug)
vals_aug, vecs_aug = EigUtil.eigh(L_aug_pinv)
# get the scaled Fiedler vector for the augmented Laplacian
w_aug, v_aug = EigUtil.principal_eigh(L_aug_pinv)
fiedler_aug = v_aug * math.sqrt(w_aug)
# report the results
np.set_printoptions(linewidth=300, threshold=10000)
out = StringIO()
print >> out, "Laplacian matrix:"
print >> out, L
print >> out
print >> out, "Schur complement of Laplacian matrix:"
print >> out, R
print >> out
print >> out, "scaled Fiedler vector of Schur complement:"
print >> out, fiedler
print >> out
print >> out, "eigenvalues of pinv of Schur complement:"
print >> out, vals
print >> out
print >> out, "corresponding eigenvectors of pinv of Schur complement:"
print >> out, np.array(vecs).T
print >> out
print >> out
print >> out, "augmented distance matrix:"
print >> out, D_aug
print >> out
print >> out, "scaled Fiedler vector of augmented Laplacian limit:"
print >> out, fiedler_aug
print >> out
print >> out, "eigenvalues of pinv of augmented Laplacian limit:"
print >> out, vals_aug
print >> out
print >> out, "rows are eigenvectors of pinv of augmented Laplacian limit:"
print >> out, np.array(vecs_aug)
return out.getvalue()
def get_response_content(fs):
# build the newick tree from the string
tree = NewickIO.parse(fs.tree_string, FelTree.NewickTree)
nvertices = len(list(tree.preorder()))
nleaves = len(list(tree.gen_tips()))
# get ordered ids with the leaves first
ordered_ids = get_ordered_ids(tree)
# get the adjacency matrix and the augmented adjacency matrix
A = np.array(tree.get_affinity_matrix(ordered_ids))
A_aug = get_augmented_adjacency(A, nleaves, fs.strength)
# get the laplacian matrices
L = Euclid.adjacency_to_laplacian(A)
L_aug = Euclid.adjacency_to_laplacian(A_aug)
# get the schur complements
R = SchurAlgebra.mschur(L, set(range(nleaves, nvertices)))
R_aug = SchurAlgebra.mschur(L_aug, set(range(nleaves, nvertices)))
# get the scaled Fiedler vectors
w, v = EigUtil.principal_eigh(np.linalg.pinv(R))
fiedler = v * math.sqrt(w)
w_aug, v_aug = EigUtil.principal_eigh(np.linalg.pinv(R_aug))
fiedler_aug = v_aug * math.sqrt(w_aug)
# report the results
np.set_printoptions(linewidth=200)
out = StringIO()
print >> out, 'Laplacian matrix:'
print >> out, L
print >> out
print >> out, 'Schur complement of Laplacian matrix:'
print >> out, R
print >> out
print >> out, 'scaled Fiedler vector:'
print >> out, fiedler
print >> out
print >> out, 'augmented Laplacian matrix:'
print >> out, L_aug
print >> out
print >> out, 'Schur complement of augmented Laplacian matrix:'
print >> out, R_aug
print >> out
print >> out, 'scaled Fiedler vector of augmented matrix:'
print >> out, fiedler_aug
print >> out
return out.getvalue()
def get_response_content(fs):
# build the newick tree from the string
tree = NewickIO.parse(fs.tree_string, FelTree.NewickTree)
nvertices = len(list(tree.preorder()))
nleaves = len(list(tree.gen_tips()))
# get ordered ids with the leaves first
ordered_ids = get_ordered_ids(tree)
# get the adjacency matrix and the augmented adjacency matrix
A = np.array(tree.get_affinity_matrix(ordered_ids))
A_aug = get_augmented_adjacency(A, nleaves, fs.strength)
# get the laplacian matrices
L = Euclid.adjacency_to_laplacian(A)
L_aug = Euclid.adjacency_to_laplacian(A_aug)
# get the schur complements
R = SchurAlgebra.mschur(L, set(range(nleaves, nvertices)))
R_aug = SchurAlgebra.mschur(L_aug, set(range(nleaves, nvertices)))
# get the scaled Fiedler vectors
w, v = EigUtil.principal_eigh(np.linalg.pinv(R))
fiedler = v * math.sqrt(w)
w_aug, v_aug = EigUtil.principal_eigh(np.linalg.pinv(R_aug))
fiedler_aug = v_aug * math.sqrt(w_aug)
# report the results
np.set_printoptions(linewidth=200)
out = StringIO()
print >> out, "Laplacian matrix:"
print >> out, L
print >> out
print >> out, "Schur complement of Laplacian matrix:"
print >> out, R
print >> out
print >> out, "scaled Fiedler vector:"
print >> out, fiedler
print >> out
print >> out, "augmented Laplacian matrix:"
print >> out, L_aug
print >> out
print >> out, "Schur complement of augmented Laplacian matrix:"
print >> out, R_aug
print >> out
print >> out, "scaled Fiedler vector of augmented matrix:"
print >> out, fiedler_aug
print >> out
return out.getvalue()
