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Help With Search Form

The following is a list of the search fields present on the Matrix Market Search Form, along with a brief explanation of their purpose.

Linear Algebra Problem Type

This indicates the general linear algebraic problem for which the matrix was originally generated. The choices are as follows. (In this discussion, A and B denote matrices, x a vector, and z a scalar.)

Included in each of these problems are the study of matrix factorizations peculiar to those problems.

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Number Field

This indicates the scalar field from which the matrix elements are drawn. The choices are as follows.

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Numerical Symmetry Property

This indicates one of several numerical symmetry properties of the matrix. The choices are as follows.

A matrix A is positive definite if and only if xTAx > 0 for all nonzero vectors x. A symmetric positive definite matrix has all positive real eigenvalues. A is negative definite if and only if -A is positive definite. For semidefiniteness, the inequality above is relaxed to admit equality; a semidefinite matrix has at least one zero eigenvalue. An indefinite matrix has none of these special properties.

Only half the elements of symmetric, Hermitian and skew symmetric matrices are present in the matrices downloaded from Matrix Market.

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Nonzero Structure

This is used to informally characterize the nonzero structure of the matrix. Note that a given matrix may have more than one of these properties. Additional properties will be added to this list as the Matrix Market collection grows. The choices are as follows.

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Storage Mode

Applies only to matrices, i.e. not to generators.

Indicates the general text file storage format used to represent the matrix. The choices are as follows.

Details on the text file formats are also available.

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Indicates the general shape of the matrix. The choices are as follows.

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Applies only to matrices, i.e. not to generators.

This allows you to indicate constraints on the size of the matrix, including

The desired bounds are indicated by typing the appropriate numbers into the text fields displayed on the form.

Note that entries corresponds to matrix elements stored in Matrix Market or Harwell-Boeing files. Typically this is the same as the number of nonzeros in the matrix. However, in some cases explicit zero entries are stored in the files; in these cases there may be more entries than nonzeros.

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Associated Materials Required

Applies only to matrices, i.e. not to generators.

This allows you to demand that certain associated material be available to supplement the matrix data, including

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Applies only to generators, i.e. not to individual matrices.

Indicates the language in which the matrix generator is coded. The choices are as follows.

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Output Type

Applies only to generators, i.e. not to individual matrices.

Indicates the form in which the genertor supplies the matrix. The choices are as follows.

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Text Field

The text field in the Matrix Market Search Tool specifies a pattern to search for in the Matrix Market meta-database. This database contains, in ASCII form, all of the words visible on the various matrix and set home pages. We suggest that you browse through set and matrix pages to familiarize yourself with the type of information found there.

If the pattern is matched in a matrix entry, then that matrix will be retireved; if the pattern is matched in a set entry, then all matrices in the set will be retrieved.

Most patterns acceptable to egrep are acceptable, with the following restrictions:

For those who are not Unix afficionados, the following synopsis covers the main points.

Special Characters

The following characters have special meanings in patterns: .+*$()\{}^|\. In general, they should be avoided, except for the few cases we give below.

Simple Patterns

A simple pattern is a string of characters that does not contain one of the special characters given above. This pattern must be matched exactly. Note that it can contain blanks, and that it can be only part of a word. For example, oil pan will match both oil pan and foil panda, but not oily pan.

Wild Cards

The period character (.) matches any single character. Thus, p.t matches pat, pot, put, and even computation.

A one-character pattern followed by an asterisk (*) matches zero or more occurrences of the single character preceeding it. Thus, be*t matches bet, beet as well as subtle.

Combining the two wildcards above yields the following pattern: .* This matches zero or more arbitrary characters, i.e. anything. It is useful in cases where you want to specify the beginning and end of the pattern, but not the middle. For example, b.*t will match any string beginning with b and ending with t, e.g., bat, boat, or even big grey cat. As you can see, such wildcards can give unexpected results.


Here are some examples of search patterns and the matrices they retrieve.

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The Matrix Market is a service of the Mathematical and Computational Sciences Division / Information Technology Laboratory / National Institute of Standards and Technology

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Last change in this page : December 3, 1999. [ ].