This is a convenience function for scaling elements of a tensor with different numbers based on their position in the tensor.

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`X` |
The tensor to be scaled |

`D` |
A tensor containing scaling constants |

`i` |
numeric of character vector giving the dimensions of X to be used for the product. |

`j` |
numeric of character vector giving the dimensions of D to be used for the product. |

`by` |
Every operation is parallel for all levels of by in X and/or D. |

Let

*X_{i_1… i_d k_1 … k_d}*

and

*D_{j_1… j_d}*

than the result is:

*E_{i_1… i_d k_1 … k_d}=X_{i_1… i_d k_1 … k_d}D_{j_1… j_d}*

A tensor with the shape and dimensions as X with entries
*X_ik* scaled by *D_im*, where *i* and
*k* can represent multi-indices.

K. Gerald van den Boogaart

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