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## Purpose

LA_GGSVD computes the generalized singular values and, optionally, the transformation matrices from the generalized singular value decomposition of a real or complex matrix pair , where is and is . The of is written where , and are orthogonal (unitary) matrices of dimensions , and , respectively. Let be the rank of and the rank of the matrix , and let . Then and are and diagonal'' matrices, respectively, and is a nonsingular upper triangular matrix. The detailed structure of , and R depends on the sign of as follows:
The case :   where . We define  The case :   where . We define  In both cases the generalized singular values of the pair are the ratios The first singular values are infinite. The finite singular values are real and nonnegative.
LA_GGSVD computes the real (nonnegative) scalars , the matrix , and, optionally, the transformation matrices , and .

Note: Some important special cases of the are given in Section 2.2.5.3.     Next: Arguments Up: Generalized Singular Value Problems Previous: LA_GGSVD   Contents   Index
Susan Blackford 2001-08-19