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feat: example 5 updated to new version
This commit is contained in:
Fabian Joswig
parent
7b3d7a76a5
commit
615411337c
1 changed files with 45 additions and 102 deletions
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@ -97,6 +97,31 @@
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"print(matrix @ np.identity(2))"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"For large matrices overloading the standard operator `@` can become inefficient as pyerrors has to perform a large number of elementary opeations. For these situations pyerrors provides the function `linalg.matmul` which optimizes the required automatic differentiation. The function can take an arbitray number of operands."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 16,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"[[Obs[78.12099999999998] Obs[-22.909999999999997]]\n",
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" [Obs[-22.909999999999997] Obs[7.1]]]\n"
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]
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}
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],
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"source": [
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"print(pe.linalg.matmul(matrix, matrix, matrix)) # Equivalent to matrix @ matrix @ matrix but faster for large matrices"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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@ -167,7 +192,7 @@
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"[Obs[7.2(1.7)] Obs[-1.00(45)]]\n"
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"[Obs[7.2(1.7)] Obs[-1.00(46)]]\n"
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]
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}
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],
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@ -182,8 +207,7 @@
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Matrix to scalar operations\n",
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"If we want to apply a numpy matrix function with a scalar return value we can use `scalar_mat_op`. __Here we need to use the autograd wrapped version of numpy__ (imported as anp) to use automatic differentiation."
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"`pyerrors` provides the user with wrappers to the `numpy.linalg` functions which work on `Obs` valued matrices. We can for example calculate the determinant of the matrix via"
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]
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},
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{
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@ -195,50 +219,14 @@
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"det \t Obs[3.10(28)]\n",
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"trace \t Obs[5.10(20)]\n",
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"norm \t Obs[4.45(19)]\n"
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"3.10(28)\n"
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]
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}
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],
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"source": [
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"import autograd.numpy as anp # Thinly-wrapped numpy\n",
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"funcs = [anp.linalg.det, anp.trace, anp.linalg.norm]\n",
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"\n",
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"for i, func in enumerate(funcs):\n",
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" res = pe.linalg.scalar_mat_op(func, matrix)\n",
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" res.gamma_method()\n",
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" print(func.__name__, '\\t', res)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"For matrix operations which are not supported by autograd we can use numerical differentiation"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"cond \t Obs[6.23(58)]\n",
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"expm_cond \t Obs[4.45(19)]\n"
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]
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}
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],
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"source": [
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"funcs = [np.linalg.cond, scipy.linalg.expm_cond]\n",
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"\n",
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"for i, func in enumerate(funcs):\n",
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" res = pe.linalg.scalar_mat_op(func, matrix, num_grad=True)\n",
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" res.gamma_method()\n",
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" print(func.__name__, ' \\t', res)"
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"det = pe.linalg.det(matrix)\n",
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"det.gamma_method()\n",
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"print(det)"
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]
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},
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{
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@ -251,7 +239,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"execution_count": 9,
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"metadata": {},
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"outputs": [
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{
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@ -259,12 +247,12 @@
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"output_type": "stream",
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"text": [
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"[[Obs[2.025(49)] Obs[0.0]]\n",
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" [Obs[-0.494(51)] Obs[0.870(29)]]]\n"
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" [Obs[-0.494(50)] Obs[0.870(29)]]]\n"
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]
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}
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],
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"source": [
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"cholesky = pe.linalg.mat_mat_op(anp.linalg.cholesky, matrix)\n",
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"cholesky = pe.linalg.cholesky(matrix)\n",
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"for (i, j), entry in np.ndenumerate(cholesky):\n",
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" entry.gamma_method()\n",
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"print(cholesky)"
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@ -279,7 +267,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 11,
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"execution_count": 10,
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"metadata": {},
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"outputs": [
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{
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@ -305,7 +293,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 12,
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"execution_count": 11,
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"metadata": {},
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"outputs": [
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{
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@ -313,7 +301,7 @@
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"output_type": "stream",
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"text": [
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"[[Obs[0.494(12)] Obs[0.0]]\n",
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" [Obs[0.280(40)] Obs[1.150(39)]]]\n",
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" [Obs[0.280(39)] Obs[1.150(38)]]]\n",
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"Check:\n",
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"[[Obs[1.0] Obs[0.0]]\n",
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" [Obs[0.0] Obs[1.0]]]\n"
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@ -321,7 +309,7 @@
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}
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],
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"source": [
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"inv = pe.linalg.mat_mat_op(anp.linalg.inv, cholesky)\n",
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"inv = pe.linalg.inv(cholesky)\n",
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"for (i, j), entry in np.ndenumerate(inv):\n",
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" entry.gamma_method()\n",
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"print(inv)\n",
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@ -330,51 +318,6 @@
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"print(check_inv)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Matrix to matrix operations which are not supported by autograd can also be computed with numeric differentiation"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 13,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"orth\n",
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"[[Obs[-0.9592(76)] Obs[0.283(26)]]\n",
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" [Obs[0.283(26)] Obs[0.9592(76)]]]\n",
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"expm\n",
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"[[Obs[75(15)] Obs[-21.4(4.1)]]\n",
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" [Obs[-21.4(4.1)] Obs[8.3(1.4)]]]\n",
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"logm\n",
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"[[Obs[1.334(57)] Obs[-0.496(61)]]\n",
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" [Obs[-0.496(61)] Obs[-0.203(50)]]]\n",
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"sinhm\n",
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"[[Obs[37.3(7.4)] Obs[-10.8(2.1)]]\n",
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" [Obs[-10.8(2.1)] Obs[3.94(68)]]]\n",
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"sqrtm\n",
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"[[Obs[1.996(51)] Obs[-0.341(37)]]\n",
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" [Obs[-0.341(37)] Obs[0.940(14)]]]\n"
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]
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}
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],
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"source": [
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"funcs = [scipy.linalg.orth, scipy.linalg.expm, scipy.linalg.logm, scipy.linalg.sinhm, scipy.linalg.sqrtm]\n",
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"\n",
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"for i,func in enumerate(funcs):\n",
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" res = pe.linalg.mat_mat_op(func, matrix, num_grad=True)\n",
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" for (i, j), entry in np.ndenumerate(res):\n",
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" entry.gamma_method()\n",
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" print(func.__name__)\n",
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" print(res)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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@ -385,7 +328,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 14,
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"execution_count": 12,
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"metadata": {},
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"outputs": [
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{
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@ -393,10 +336,10 @@
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"output_type": "stream",
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"text": [
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"Eigenvalues:\n",
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"[Obs[0.705(57)] Obs[4.39(19)]]\n",
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"[Obs[0.705(56)] Obs[4.39(20)]]\n",
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"Eigenvectors:\n",
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"[[Obs[-0.283(26)] Obs[-0.9592(76)]]\n",
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" [Obs[-0.9592(76)] Obs[0.283(26)]]]\n"
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"[[Obs[-0.283(25)] Obs[-0.9592(74)]]\n",
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" [Obs[-0.9592(74)] Obs[0.283(25)]]]\n"
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]
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}
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],
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@ -421,7 +364,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 15,
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"execution_count": 13,
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"metadata": {},
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"outputs": [
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{
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@ -451,7 +394,7 @@
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"display_name": "Python 3 (ipykernel)",
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"language": "python",
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"name": "python3"
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},
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@ -465,7 +408,7 @@
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.6.9"
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"version": "3.8.10"
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}
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},
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"nbformat": 4,
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