class_docstr: Test the utility function _generate_tapes_and_coeffs.
class_docstr_tok: ["Test","the","utility","function","_generate_tapes_and_coeffs","."]
docstr: Test the tape generation for multiple parameters of multiple Hamiltonians in a tape.
docstr_tok: ["Test","the","tape","generation","for","multiple","parameters","of","multiple","Hamiltonians","in","a","tape","."]
code: def test_multi_op_multi_term(self):
      """Test the tape generation for multiple parameters of multiple Hamiltonians in a tape."""
      import jax
      import jax.numpy as jnp
  
      def _sin(p, t):
          """Compute the function a * sin(b * t + c)."""
          return p[0] * jnp.sin(p[1] * t + p[2])
  
      def _int_sin(p, t):
          """Compute the (time) integral of the function a * sin(b * t + c)."""
          if qml.math.ndim(t) == 0:
              t = [0, t]
          args = (p[1] * t[1] + p[2], p[1] * t[0] + p[2])
          return -p[0] / p[1] * jnp.cos(args[0]) + p[0] / p[
              1
          ] * jnp.cos(args[1])
  
      H0 = qml.pulse.constant * X(0) + jnp.polyval * Z(1)
      H1 = jnp.polyval * (Y(1) @ Y(0)) + _sin * (Z(0) @ Z(1))
      params0 = [jnp.array(0.4), jnp.array([0.3, 0.2, 0.1])]
      params1 = [
          jnp.array([0.3, 0.2, 0.1, 1.2]),
          jnp.array([0.4, 1.2, -0.9]),
      ]
  
      exp_coeffs0 = [
          [jnp.array(0), jnp.array(2 * self.T)],
          [
              2 * jax.grad(integral_of_polyval)(params0[1], self.T),
              jnp.zeros(3),
          ],
      ]
      exp_coeffs1 = [
          [
              2 * jax.grad(integral_of_polyval)(params1[0], self.T),
              jnp.zeros(4),
          ],
          [jnp.zeros(3), 2 * jax.grad(_int_sin)(params1[1], self.T)],
      ]
  
      tape = self.make_tape([H0, H1], [params0, params1])
      cache = {"total_num_tapes": 0}
      # First trainable parameter - everything for H0 is computed
      (
          grad_tapes,
          (start, end, coeffs),
          cache,
      ) = _generate_tapes_and_coeffs(tape, 0, self.atol, cache)
  
      words = ["IZ", "XI"]
      wires = [0, 1]
      expected = (0, 4, 4, words, wires, tape, 0, exp_coeffs0[0])
      exp_cache = {"total_num_tapes": 4, 0: (0, 4, exp_coeffs0)}
  
      self.check_tapes_and_coeffs_equality(
          grad_tapes, (start, end, coeffs), expected
      )
      self.check_cache_equality(cache, exp_cache)
  
      # Second trainable parameter - everything for H0 is cached
      (
          grad_tapes,
          (start, end, coeffs),
          cache,
      ) = _generate_tapes_and_coeffs(tape, 1, self.atol, cache)
  
      expected = (0, 4, 0, [], None, tape, None, exp_coeffs0[1])
  
      self.check_tapes_and_coeffs_equality(
          grad_tapes, (start, end, coeffs), expected
      )
      self.check_cache_equality(cache, exp_cache)
  
      # Third trainable parameter - everything for H1 is computed
      (
          grad_tapes,
          (start, end, coeffs),
          cache,
      ) = _generate_tapes_and_coeffs(tape, 2, self.atol, cache)
  
      words = ["YY", "ZZ"]
      wires = [1, 0]
      expected = (4, 8, 4, words, wires, tape, 1, exp_coeffs1[0])
      exp_cache["total_num_tapes"] = 8
      exp_cache[1] = (4, 8, exp_coeffs1)
  
      self.check_tapes_and_coeffs_equality(
          grad_tapes, (start, end, coeffs), expected
      )
      self.check_cache_equality(cache, exp_cache)
  
      # Fourth trainable parameter - everything for H1 is cached
      (
          grad_tapes,
          (start, end, coeffs),
          cache,
      ) = _generate_tapes_and_coeffs(tape, 3, self.atol, cache)
  
      expected = (4, 8, 0, [], None, tape, 1, exp_coeffs1[1])
  
      self.check_tapes_and_coeffs_equality(
          grad_tapes, (start, end, coeffs), expected
      )
      self.check_cache_equality(cache, exp_cache)
  
imports: import copy
  import pytest
  import numpy
  import pennylane
  from pennylane import numpy
  from pennylane.ops.qubit.special_unitary import pauli_basis_matrices, pauli_basis_strings
  from pennylane.math import expand_matrix
  from pennylane.gradients.pulse_gradient_odegen import _generate_tapes_and_coeffs, pulse_odegen, _insert_op, _nonzero_coeffs_and_words, _one_parameter_generators, _one_parameter_paulirot_coeffs, _parshift_and_contract
label_desc: Use image node_id 7 for calling the TestGenerateTapesAndCoeffs obj's underlying member method code with example usage: obj.test_multi_op_multi_term() and returns: unknown, unknown