class_docstr: Class for product of Riemannian metrics.
class_docstr_tok: ["Class","for","product","of","Riemannian","metrics","."]
code: def __init__(self, space):
      factors = [factor.metric for factor in space.factors]
      factor_signatures = [metric.signature for metric in factors]
  
      sig_pos = sum(sig[0] for sig in factor_signatures)
      sig_neg = sum(sig[1] for sig in factor_signatures)
  
      super().__init__(
          space=space,
          factors=factors,
          cum_index=space._cum_index,
          pool_outputs=False,
          has_mixed_fields=space._has_mixed_fields,
          signature=(sig_pos, sig_neg),
      )
  
imports: import math
  import geomstats.backend
  import geomstats.errors
  from geomstats.geometry.complex_manifold import ComplexManifold
  from geomstats.geometry.complex_riemannian_metric import ComplexRiemannianMetric
  from geomstats.geometry.manifold import Manifold
  from geomstats.geometry.riemannian_metric import RiemannianMetric
  from geomstats.vectorization import get_batch_shape
label_desc: Use image node_id 1 to create a new ProductRiemannianMetric object from inherited base classes: _IterateOverFactorsMixins, RiemannianMetric with example: obj = ProductRiemannianMetric(space)