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The HDF Group Introduction to HDF5 Session ? HDF5 Mathematical Concepts Copyright © 2010 The HDF Group. All Rights Reserved 1 www.hdfgroup.org Fundamental HDF5 Objects • Groups • Containers of links • Allow creating arbitrary directed graphs, including nontreelike and cyclic structures • Datasets • Multi-dimensional arrays (currently) • Based on mathematical concept of “fiber bundle” – representing the values of a field over a space Copyright © 2010 The HDF Group. All Rights Reserved 2 www.hdfgroup.org Groups - Overview • Groups are container objects in a file that follow a “set” data structure semantic: • Groups contain links • No two links in a group can have the same name • Links have two components: • Name • Destination • Three types of links currently: • Hard – Destination is object in same file • Soft – Destination is path to object in same file • External – Destination is path to object in another file Copyright © 2010 The HDF Group. All Rights Reserved 3 www.hdfgroup.org Groups • Tree, with hard links Copyright © 2010 The HDF Group. All Rights Reserved 4 www.hdfgroup.org Groups • Non-Tree, with hard links Copyright © 2010 The HDF Group. All Rights Reserved 5 www.hdfgroup.org Groups • Cyclic, with hard links Copyright © 2010 The HDF Group. All Rights Reserved 6 www.hdfgroup.org Groups • Tree, with soft links Copyright © 2010 The HDF Group. All Rights Reserved 7 www.hdfgroup.org Groups • Tree, with external links Copyright © 2010 The HDF Group. All Rights Reserved 8 www.hdfgroup.org Groups - Discussion • What would happen if links didn’t have names, but objects had names? • What other types of links are useful? Copyright © 2010 The HDF Group. All Rights Reserved 9 www.hdfgroup.org Datasets - Overview • Datasets are objects in an HDF5 that represent “real” application data • Array-like currently • Datasets have three components: • Dataspace describes current and maximum dimensions of array • Datatype describes type of elements in array • Elements are the values stored in the array Copyright © 2010 The HDF Group. All Rights Reserved 10 www.hdfgroup.org Datasets – Measurement Example • Think of algebraic concept of independent and dependent variables • X-Y Plot: Copyright © 2010 The HDF Group. All Rights Reserved 11 www.hdfgroup.org Dataset – Measurement Example, 2 • X-Y Plot data in Database: Copyright © 2010 The HDF Group. All Rights Reserved 12 www.hdfgroup.org Dataset – Measurement Example, 3 • X-Y Plot data in HDF5 Dataset: Copyright © 2010 The HDF Group. All Rights Reserved 13 www.hdfgroup.org Dataset – Measurement Example, 4 • In HDF5, independent variables are implicit and not stored (they are the coordinates of elements in array) • In Database, independent variables are explicitly stored in each record • A “packed” HDF5 dataset of N dimensions is up to N times smaller than database table storing the same data. Copyright © 2010 The HDF Group. All Rights Reserved 14 www.hdfgroup.org Datasets - Discussion • When would storing data in a database table be better than storing the same data in an HDF5 dataset? • If you were measuring two dependent values at each coordinate, what are the trade-offs between storing them as a pair for each element in a single dataset and storing each one in a separate dataset? Copyright © 2010 The HDF Group. All Rights Reserved 15 www.hdfgroup.org Review • Fundamental HDF5 Objects are: • Groups • Containers of links to objects • Create arbitrary directed graph structures • Datasets • Multi-dimensional arrays of elements • Based on mathematical concept of fiber bundles, but can be thought of in terms of independent and dependent variables Copyright © 2010 The HDF Group. All Rights Reserved 16 www.hdfgroup.org Stretch Break Copyright © 2010 The HDF Group. All Rights Reserved 17 www.hdfgroup.org Dataset – Fiber Bundles • HDF5 Datasets actually based on mathematical concept of “fiber bundles” A fiber bundle consists of the data (E, B, π, F), where E, B, and F are topological spaces and π : E → B is a continuous surjection satisfying a local triviality condition outlined below. The space B is called the base space of the bundle, E the total space, and F the fiber. Copyright © 2010 The HDF Group. All Rights Reserved 18 www.hdfgroup.org Dataset – Fiber Bundles, 2 Mathematic HDF5 Fiber Bundle Dataset Base Space Dataspace Fiber Space Datatype Section Elements Copyright © 2010 The HDF Group. All Rights Reserved 19 www.hdfgroup.org