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from mpmath import mp |
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from mpmath import libmp |
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xrange = libmp.backend.xrange |
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def run_hessenberg(A, verbose = 0): |
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if verbose > 1: |
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print("original matrix (hessenberg):\n", A) |
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n = A.rows |
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Q, H = mp.hessenberg(A) |
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if verbose > 1: |
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print("Q:\n",Q) |
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print("H:\n",H) |
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B = Q * H * Q.transpose_conj() |
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eps = mp.exp(0.8 * mp.log(mp.eps)) |
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err0 = 0 |
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for x in xrange(n): |
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for y in xrange(n): |
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err0 += abs(A[y,x] - B[y,x]) |
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err0 /= n * n |
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err1 = 0 |
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for x in xrange(n): |
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for y in xrange(x + 2, n): |
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err1 += abs(H[y,x]) |
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if verbose > 0: |
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print("difference (H):", err0, err1) |
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if verbose > 1: |
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print("B:\n", B) |
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assert err0 < eps |
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assert err1 == 0 |
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def run_schur(A, verbose = 0): |
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if verbose > 1: |
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print("original matrix (schur):\n", A) |
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n = A.rows |
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Q, R = mp.schur(A) |
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if verbose > 1: |
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print("Q:\n", Q) |
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print("R:\n", R) |
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B = Q * R * Q.transpose_conj() |
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C = Q * Q.transpose_conj() |
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eps = mp.exp(0.8 * mp.log(mp.eps)) |
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err0 = 0 |
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for x in xrange(n): |
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for y in xrange(n): |
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err0 += abs(A[y,x] - B[y,x]) |
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err0 /= n * n |
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err1 = 0 |
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for x in xrange(n): |
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for y in xrange(n): |
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if x == y: |
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C[y,x] -= 1 |
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err1 += abs(C[y,x]) |
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err1 /= n * n |
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err2 = 0 |
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for x in xrange(n): |
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for y in xrange(x + 1, n): |
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err2 += abs(R[y,x]) |
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if verbose > 0: |
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print("difference (S):", err0, err1, err2) |
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if verbose > 1: |
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print("B:\n", B) |
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assert err0 < eps |
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assert err1 < eps |
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assert err2 == 0 |
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def run_eig(A, verbose = 0): |
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if verbose > 1: |
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print("original matrix (eig):\n", A) |
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n = A.rows |
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E, EL, ER = mp.eig(A, left = True, right = True) |
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if verbose > 1: |
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print("E:\n", E) |
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print("EL:\n", EL) |
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print("ER:\n", ER) |
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eps = mp.exp(0.8 * mp.log(mp.eps)) |
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err0 = 0 |
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for i in xrange(n): |
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B = A * ER[:,i] - E[i] * ER[:,i] |
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err0 = max(err0, mp.mnorm(B)) |
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B = EL[i,:] * A - EL[i,:] * E[i] |
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err0 = max(err0, mp.mnorm(B)) |
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err0 /= n * n |
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if verbose > 0: |
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print("difference (E):", err0) |
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assert err0 < eps |
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def test_eig_dyn(): |
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v = 0 |
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for i in xrange(5): |
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n = 1 + int(mp.rand() * 5) |
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if mp.rand() > 0.5: |
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A = 2 * mp.randmatrix(n, n) - 1 |
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if mp.rand() > 0.5: |
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A *= 10 |
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for x in xrange(n): |
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for y in xrange(n): |
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A[x,y] = int(A[x,y]) |
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else: |
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A = (2 * mp.randmatrix(n, n) - 1) + 1j * (2 * mp.randmatrix(n, n) - 1) |
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if mp.rand() > 0.5: |
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A *= 10 |
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for x in xrange(n): |
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for y in xrange(n): |
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A[x,y] = int(mp.re(A[x,y])) + 1j * int(mp.im(A[x,y])) |
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run_hessenberg(A, verbose = v) |
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run_schur(A, verbose = v) |
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run_eig(A, verbose = v) |
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def test_eig(): |
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v = 0 |
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AS = [] |
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A = mp.matrix([[2, 1, 0], |
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[0, 2, 1], |
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[0, 0, 2]]) |
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AS.append(A) |
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AS.append(A.transpose()) |
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A = mp.matrix([[2, 0, 0], |
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[0, 2, 1], |
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[0, 0, 2]]) |
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AS.append(A) |
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AS.append(A.transpose()) |
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A = mp.matrix([[2, 0, 1], |
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[0, 2, 0], |
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[0, 0, 2]]) |
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AS.append(A) |
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AS.append(A.transpose()) |
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A= mp.matrix([[0, 0, 1], |
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[1, 0, 0], |
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[0, 1, 0]]) |
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AS.append(A) |
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AS.append(A.transpose()) |
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for A in AS: |
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run_hessenberg(A, verbose = v) |
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run_schur(A, verbose = v) |
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run_eig(A, verbose = v) |
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