{ "cells": [ { "cell_type": "markdown", "id": "da8a241f", "metadata": {}, "source": [ "# 3. Hessian and Variation\n", "\n", "The Herman–Kluk pre-factor requires the monodromy matrix $M_t = \\frac{\\partial (Q_t, P_t)}{\\partial (Q_0, P_0)}$ in the physical space.\n", "\n", "PySCIVR computes it by propagating the variation along the trajectory in the redundant Cartesian coordinates with the linearized SHAKE/RATTLE equations, which require the Hessian of the potential at each step.\n", "\n", "In this tutorial, the ro-vibrational trajectory of H2 (`h2_rovib_pi2_traj.npz`) from the previous tutorial is used:\n", "| Redundant space | Integrator | Physical space |\n", "|---|---|---|\n", "| Cartesian (6 DOFs) with 3 constraints (3 translations) | `ShakeRattle` | bond length $r$, polar $\\theta$ and azimuthal angle $\\phi$ |\n", "\n", "We first compute the monodromy matrix with the full Hessian at every step, and then show how to reduce the cost of the Hessian evaluation." ] }, { "cell_type": "code", "execution_count": 1, "id": "9558b4a4", "metadata": {}, "outputs": [], "source": [ "# import necessary libraries\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", " \n", "from pyscivr.coordinates import InternalCoordinates\n", "from pyscivr.hessian import eval_hess_active, interpolate_hessian, projected_hessian\n", "from pyscivr.potentials import H2SplinePotential\n", "from pyscivr.save import load_hessian, load_trajectory, save_hessian\n", "from pyscivr.units import FemtoSec\n", "from pyscivr.variations import make_jacobi_func, make_vari_propagator, propagate_variation, to_internal" ] }, { "cell_type": "markdown", "id": "4441d647", "metadata": {}, "source": [ "## Set system\n", "\n", "The system, the constraints `coord_const` and the curvilinear coordinates `coord_all` are the same as in the previous tutorial.\n", "\n", "The active (physical) coordinates are the bond length, polar angle, and azimuthal angle." ] }, { "cell_type": "code", "execution_count": 2, "id": "bad106ac", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Build complete: 3 coordinates\n", "Build complete: 6 coordinates\n", "active_idx = [3 4 5]\n" ] } ], "source": [ "mass = np.array([1.008, 1.008]) # [amu]\n", "r_e = 0.74160392 # equilibrium bond length [Angs]\n", "posi_ref = np.array([[-r_e / 2, 0.0, 0.0], [r_e / 2, 0.0, 0.0]])\n", "\n", "calc = H2SplinePotential()\n", "\n", "coord_const = InternalCoordinates(posi_ref, mass)\n", "coord_const.add_translation()\n", "coord_const.build()\n", "\n", "coord_all = InternalCoordinates(posi_ref, mass)\n", "coord_all.add_translation()\n", "coord_all.add_polar(0, 1)\n", "coord_all.add_azimuthal(0, 1)\n", "coord_all.add_bond(0, 1)\n", "coord_all.build()\n", "\n", "active_idx = np.array([coord_all.find_coordinate(kind, (0, 1))[0] for kind in (\"bond\", \"polar\", \"azimuthal\")])\n", "\n", "print('active_idx =', active_idx)" ] }, { "cell_type": "markdown", "id": "543767b0", "metadata": {}, "source": [ "## Load the trajectory" ] }, { "cell_type": "code", "execution_count": 3, "id": "e4500150", "metadata": {}, "outputs": [], "source": [ "traj = load_trajectory(\"h2_rovib_pi2_traj.npz\", coord_const=coord_const)\n", "posi, mome, lam, mu, dt = traj[\"posi\"], traj[\"mome\"], traj[\"lam\"], traj[\"mu\"], traj[\"dt\"]\n", "values = coord_all.get_value_batch(posi)\n", "B = coord_all.get_const_grad_batch(posi)\n", "\n", "n_step = len(posi)\n", "t_fs = dt / FemtoSec * np.arange(n_step)" ] }, { "cell_type": "markdown", "id": "a6303f1f", "metadata": {}, "source": [ "## Monodromy matrix with the full Hessian\n", "\n", "`H2SplinePotential` supports the analytical Hessian, so we first use the full $3N \\times 3N$ Hessian at every step. The monodromy matrix is computed in the following steps:\n", "\n", "1. `make_jacobi_func` makes the Jacobians between the redundant and physical spaces.\n", "2. The initial variation is set to $J_{\\text{rev}}(0)$, which maps the physical space to the redundant space.\n", "3. `propagate_variation` propagates the variation in the redundant space using the Hessians and the Lagrange multipliers.\n", "4. `to_internal` transforms the variation to the physical space by $J(t)$, giving the monodromy matrix $M_t = J(t) M_t^{\\text{red}} J_{\\text{rev}}(0)$.\n", "\n", "The monodromy matrix of a Hamiltonian system is symplectic. If it is computed correctly, $M_t$ should satisfy\n", "\n", "$$\n", "M_t^T \\Omega M_t = \\Omega, \\quad\n", "\\Omega = \\begin{pmatrix} 0 & I \\\\ -I & 0 \\end{pmatrix},\n", "$$\n", "\n", "where $I$ is the $m \\times m$ identity matrix. `to_internal` returns the symplectic error\n", "\n", "$$\n", "\\epsilon_t = \\max \\left| M_t^T \\Omega M_t - \\Omega \\right|,\n", "$$\n", "\n", "which is used to check the consistency of the calculation.\n", "\n", "As shown in the previous tutorial, the singular points can be detected by the condition number of $B$.\n", "Since the transformation to the physical space does not exist at the singular points, the elements of $M_t$\n", "become large in their vicinity, and the symplectic error $\\epsilon_t$ may increase due to the loss of numerical precision.\n", "\n", "See [`pyscivr.variations`](https://tsumura-m.github.io/PySCIVR/pyscivr.variations.html) for details." ] }, { "cell_type": "code", "execution_count": 4, "id": "55b950f6", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "_, jacobi_rev_func, _, monodromy_func = make_jacobi_func(coord_all, active_idx)\n", "J_rev_init = np.asarray(jacobi_rev_func(posi[0], mome[0])) # (6N, 2m)\n", "vari_propagator = make_vari_propagator(coord_const, dt)\n", "\n", "hess_full = calc.hessian(posi) # (T, 3N, 3N)\n", "vari_full = propagate_variation(vari_propagator, posi, mome, lam, mu, hess_full, J_rev_init)\n", "_, _, mono_full, symp_err_full = to_internal(monodromy_func, posi, mome, vari_full) # mono_full : (T, 2m, 2m)\n", "\n", "fig, ax = plt.subplots(4, 1, sharex=True, figsize=(6, 8))\n", "\n", "ax[0].set_ylabel(\"polar angle (rad)\")\n", "ax[0].plot(t_fs, values[:, active_idx[1]], color='blue')\n", "ax[1].semilogy(t_fs, np.linalg.cond(B), color='blue')\n", "ax[1].set_ylabel(\"Condition number of B\")\n", "ax[2].semilogy(t_fs, np.max(np.abs(mono_full), axis=(1, 2)), color='blue')\n", "ax[2].set_ylabel(\"max |$M_t$|\")\n", "ax[3].semilogy(t_fs, symp_err_full, color='blue')\n", "ax[3].set_ylabel(\"Symplectic error\")\n", "ax[3].set_xlabel(\"Time (fs)\")\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "23c6b9d2", "metadata": {}, "source": [ "At the singular points, where the condition number of $B$ diverges, the transformation to the physical space does not exist. As the trajectory approaches these points, the elements of $M_t$ therefore diverge, which can lead to numerical errors in the symplectic condition.\n", "\n", "In this trajectory, the time steps happen to approach the singular points only to the extent that this effect is negligible, and the symplectic error remains small.\n", "\n", "Since the SC-IVR calculation relies on the symplectic condition, the symplectic error should always be checked, and only the steps where it is small can be used (see the next tutorial)." ] }, { "cell_type": "markdown", "id": "3cc81014", "metadata": {}, "source": [ "## Reducing the cost of the Hessian\n", "\n", "The full Hessian at every step is expensive for ab initio potentials: analytical Hessians are often unavailable, and the numerical Hessian requires $2 \\times 3N$ force evaluations per step.\n", "\n", "The Hessian evaluation therefore becomes the bottleneck of a straightforward SC-IVR calculation, costing $O(N)$ times more than the trajectory itself.\n", "\n", "PySCIVR reduces this cost in two ways:\n", "\n", "- **Only the active directions**: the propagation only needs the Hessian projected onto the active coordinates,\n", " which is obtained from $\\nabla^2 V A_A$ with $A_A \\equiv \\partial q / \\partial Q_A$.\n", " `eval_hess_active` computes it by central differences of the forces along the $m$ columns of $A_A$,\n", " requiring $2m$ force evaluations per step instead of $2 \\times 3N$.\n", "- **Only at selected steps**: the projected Hessian is evaluated every $I$ steps and interpolated\n", " to all steps by cubic spline.\n", "\n", "As a result, the number of force evaluations for the Hessian along a trajectory of $T$ steps is reduced\n", "from $6NT$ to $\\frac{2mT}{I}$, **independent of the number of atoms $N$**:\n", "\n", "| | Number of Force evaluations | Butane torsion ($N = 14$, $m = 1$, $I = 20$, $T=10000$) |\n", "|---|---|---|\n", "| Trajectory | $T$ | $10000$ |\n", "| Full numerical Hessian at every step | $6NT$ | $840000$ |\n", "| Projected Hessian at selected steps | $\\frac{2mT}{I}$ | $1000$ |\n", "\n", "For the torsion of butane, the cost of the Hessian is reduced by a factor of 840,\n", "and becomes only 10 % of that of the trajectory.\n", "\n", "Since $A_A$ is the active component of the inverse of $B$, it is not defined at the singular points. The projected Hessian therefore should not be evaluated in their vicinity, which is detected by the condition number of $B$; these steps are filled by the interpolation together with the skipped steps.\n", "\n", "The interval $I$ should be chosen sufficiently small compared with the period of the fastest motion in the active coordinates, and its convergence should be checked as shown below.\n", "\n", "See [`pyscivr.hessian`](https://tsumura-m.github.io/PySCIVR/pyscivr.hessian.html) for details." ] }, { "cell_type": "markdown", "id": "f5f1dc68", "metadata": {}, "source": [ "First, we exclude the points near singularities to avoid numerical instability. \n", "Here, points where the condition number of B exceeds 100 are excluded." ] }, { "cell_type": "code", "execution_count": 5, "id": "ed17dd1c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "43 of 5001 steps are near the singular points.\n" ] } ], "source": [ "x = posi.reshape(n_step, -1) # (T, 3N)\n", "cond_B = np.linalg.cond(np.asarray(coord_all.get_const_grad_batch(x)))\n", "steps_valid = np.where(cond_B <= 1e2)[0]\n", "print(f\"{n_step - len(steps_valid)} of {n_step} steps are near the singular points.\")" ] }, { "cell_type": "markdown", "id": "4b2d4d46", "metadata": {}, "source": [ "Compare numerical projected Hessians and analytical one." ] }, { "cell_type": "code", "execution_count": 6, "id": "330795d5", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "max |numerical - analytical| = 4.655e-09\n" ] } ], "source": [ "steps = steps_valid[::5] # take every 5th step of the valid steps\n", " \n", "KA, AA, BA = eval_hess_active(calc, coord_all, active_idx, posi, steps, eps=1e-6)\n", "\n", "K_analytical = calc.hessian(posi[steps]) # (S, 3N, 3N)\n", "KA_analytical = K_analytical @ AA # (S, 3N, m)\n", "\n", "print(f\"max |numerical - analytical| = {np.max(np.abs(KA - KA_analytical)):.3e}\")" ] }, { "cell_type": "markdown", "id": "2be49077", "metadata": {}, "source": [ "`KA` ($\\nabla^2 V A_A$) is converted into the projected Hessian ($\\mathfrak{P}^T(\\nabla^2 V A_A) B_A, \\quad \\mathfrak{P} \\equiv A_A B_A$) via `projected_hessian` function and used in subsequent calculations." ] }, { "cell_type": "code", "execution_count": 7, "id": "f255f9a0", "metadata": {}, "outputs": [], "source": [ "hess_proj = projected_hessian(KA, AA, BA)" ] }, { "cell_type": "markdown", "id": "b8eb65b3", "metadata": {}, "source": [ "## Save and load the Hessians\n", "\n", "`save_hessian` stores the Hessians as $\\nabla^2 V A_A$ of shape `(S, 3N, m)` to reduce the file size.\n", "`load_hessian` restores the projected Hessians, and interpolates them to all steps if `n_step` is given.\n", "\n", "See [`pyscivr.save`](https://tsumura-m.github.io/PySCIVR/pyscivr.save.html) for details." ] }, { "cell_type": "code", "execution_count": 8, "id": "af63cb95", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "max |loaded - saved| = 2.842e-14\n", "(5001, 6, 6)\n" ] } ], "source": [ "save_hessian(\"h2_rovib_pi2_hess.npz\", steps, hess_proj, posi, coord_all, active_idx)\n", "\n", "_, hess_loaded = load_hessian(\"h2_rovib_pi2_hess.npz\", coord_all, posi)\n", "print(f\"max |loaded - saved| = {np.max(np.abs(hess_loaded - hess_proj)):.3e}\")\n", "\n", "_, hess_interp = load_hessian(\"h2_rovib_pi2_hess.npz\", coord_all, posi, n_step=n_step)\n", "print(hess_interp.shape) # (T, 3N, 3N)" ] }, { "cell_type": "markdown", "id": "69b3f1f3", "metadata": {}, "source": [ "## Effect of the interpolation on the monodromy matrix\n", "\n", "The numerical Hessians are evaluated every `interval` steps (excluding the vicinity of the singular points) and interpolated, and the resulting monodromy matrices are compared with that from the full Hessian." ] }, { "cell_type": "code", "execution_count": 9, "id": "7c29307a", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(2, 1, sharex=True, figsize=(6, 8))\n", "\n", "for interval in [1, 5, 10, 20]:\n", " steps = steps_valid[::interval]\n", " HA, AA, BA = eval_hess_active(calc, coord_all, active_idx, posi, steps)\n", " hess = interpolate_hessian(steps, projected_hessian(HA, AA, BA), n_step) \n", " vari = propagate_variation(vari_propagator, posi, mome, lam, mu, hess, J_rev_init)\n", " _, _, mono, symp_err = to_internal(monodromy_func, posi, mome, vari)\n", "\n", " deviation = np.max(np.abs(mono - mono_full), axis=(1, 2)) / np.max(np.abs(mono_full), axis=(1, 2))\n", " ax[0].semilogy(t_fs, deviation, label=f\"interval = {interval} ({len(steps)} steps)\")\n", " ax[1].semilogy(t_fs, symp_err, label=f\"interval = {interval} ({len(steps)} steps)\", linestyle='dashed')\n", "\n", "ax[1].plot(t_fs, symp_err_full, color='blue', label=\"full Hessian (all steps)\")\n", "ax[0].set_xlabel(\"Time (fs)\")\n", "ax[0].set_ylabel(\"max |M - M_full|/ max |M_full|\")\n", "ax[1].set_xlabel(\"Time (fs)\")\n", "ax[1].set_ylabel(\"Symplectic error\")\n", "ax[0].legend()\n", "ax[1].legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "0addb56f", "metadata": {}, "source": [ "The relative deviation from the monodromy matrix with the full Hessian decreases systematically\n", "as the interval of the Hessian evaluation is reduced:\n", "\n", "- `interval = 1` (about 80 evaluations per vibrational period of about 8 fs): below 0.1 %.\n", "- `interval = 5` (about 16 evaluations per period): a few %.\n", "- `interval = 10` (about 8 evaluations per period): comparable to the monodromy matrix itself at long times.\n", "- `interval = 20` (about 4 evaluations per period): the cubic spline cannot follow the vibration,\n", " and the deviation grows exponentially.\n", "\n", "The symplectic error remains as small as that with the full Hessian except for `interval = 20`,\n", "where the precision is lost as the elements of $M_t$ grow exponentially.\n", "The symplectic error thus detects only severe failures, and is not sufficient to judge the accuracy of the Hessian.\n", "\n", "Therefore, the interval should be chosen so that the fastest motion in the active coordinates is sampled\n", "sufficiently (here, at least about 16 evaluations per period for an accuracy of a few %),\n", "and its convergence should be checked by comparing the results with different intervals." ] } ], "metadata": { "kernelspec": { "display_name": "pyscivr (3.13.11)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.13.11" } }, "nbformat": 4, "nbformat_minor": 5 }