Tricks of the Trade In and Out Trott's Corner New Products New Publications Calendar News Bulletins New Resources Classifieds Download This Issue Editorial Policy Staff Submissions Subscriptions Advertising Back Issues Contact Information |
What's New in
Mathematica 5Performance Enhancements Fast Dense Numerical Linear Algebra Dense numerical linear algebra is an important building block for most of Here are some examples of speedups between
High-Speed Sparse Linear Algebra A large number of real-world problems deal with sparse matrices, that is, matrices in which most of the elements are zero. Examples of operations that involve sparse matrices include solving ordinary and partial differential equations, optimization problems, and large-scale simulations. Creating Sparse Arrays and Converting between Sparse and Dense Arrays Adding the head SparseArray forces the creation of a sparse array object.
Applying Normal to a sparse array object gives the corresponding dense array.
Operations on Sparse Matrices The sparse array data structure and the specialized sparse algorithms allow
Notice the big difference in size between sparse and dense representation. The dense representation requires eight terabytes of memory for storage, while the sparse array object needs only a bit over 40 megabytes.
Operations on sparse arrays are extremely fast. Notice that LinearSolve correctly detects that it has been given a sparse array object.
We just solved an equation system with 1,000,000 equations and 1,000,000 variables. Inverting a large sparse matrix is also very fast.
Large-Scale Linear Programming
Example: Solving a Standard Test Problem The following Import command loads a standard linear programming test problem that comes with
The 80bau3b problem has about 2,000 constraints and about 10,000 variables.
This solves the linear programming problem and returns the optimizing argument.
This is the optimal value.
This problem could not have been solved in Example: Solving Another Standard Test Problem This is an example of solving a linear programming problem with 232,000 variables and 10,000 inequalities.
As in the previous example, here is the optimal value.
Big-Number Arithmetic
The big-number performance in
64-Bit Platform Support Users running increasingly larger computations and applications can now access nearly a million terabytes (1 terabyte = 1,024 gigabytes), overcoming the 4-gigabyte address ceiling in 32-bit systems like the current Intel IA-32-bit architecture. The combination of a 64-bit address space and fast
numerics, part of Wolfram Research’s gigaNumerics
initiative, lets
This 64-bit optimization will also let Faster
A new TCP/IP protocol allows Because all |
||||||

About Mathematica Download Mathematica
PlayerCopyright © Wolfram Media, Inc. All rights reserved. |