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Tests for the Least Squares Driver Routines

In the SLS path, driver routines are tested for computing solutions to over- and underdetermined, possibly rank-deficient systems of linear equations 93#93 (16#16 is 3#3-by-4#4). For each test matrix type, we generate three matrices: One which is scaled near underflow, a matrix with moderate norm, and one which is scaled near overflow. The SGELS driver computes the least-squares solutions (when 94#94) and the minimum-norm solution (when 62#62) for an 3#3-by-4#4 matrix 16#16 of full rank. To test SGELS, we generate a diagonally dominant matrix 16#16, and for 95#95 and 96#96, we

The SGELSX, SGELSY, SGELSS and SGELSD drivers solve a possibly rank-deficient system 93#93 using a complete orthogonal factorization (SGELSX or SGELSY) or singular value decomposition (SGELSS or SGELSD), respectively. We generate matrices 16#16 that have rank 107#107 or rank 108#108 and are scaled to be near underflow, of moderate norm, or near overflow. We also generate the null matrix (which has rank 109#109). Given such a matrix, we then generate a right-hand side 97#97 which is in the range space of 16#16.

In the process of determining 98#98, SGELSX (or SGELSY) computes a complete orthogonal factorization 110#110, whereas SGELSS (or SGELSD) computes the singular value decomposition 111#111.


next up previous contents
Next: Tests for the Equilibration Up: The Linear Equation Test Previous: Tests for the Orthogonal   Contents
Susan Blackford 2001-08-13