Persistent diagram of one-dimensional data

Mahdi Kooshkbaghi
 

Dear all,
It could be more conceptual issue about the topic rather than software issue.
I wonder how can I generate persistent diagrams for the scalar field via Dionysus?
I have attached the figure from "Persistent homology survey by H. E. and J. H".
I am trying to understand and plot something similar.
Thanks,
Mahdi
PS: for two and more-dimensional data I can understand and play with package to get the persistence diagrams.

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