# LAPACK95 users' guide by V. A. Barker, L. S. Blackford, J. Dongarra, J. Du Croz, S.

By V. A. Barker, L. S. Blackford, J. Dongarra, J. Du Croz, S. Hammarling, M. Marinova, J. Waœniewski, P. Yalamov

LAPACK95 is a Fortran ninety five interface to the Fortran seventy seven LAPACK library. it truly is proper for a person who writes within the Fortran ninety five language and wishes trustworthy software program for simple numerical linear algebra. It improves upon the unique user-interface to the LAPACK package deal, profiting from the significant simplifications that Fortran ninety five permits. LAPACK95 clients' consultant offers an creation to the layout of the LAPACK95 package deal, a close description of its contents, reference manuals for the top reviews of the exercises, and instance courses

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**Example text**

If SP is replaced by DP then the precision is set to double precision. mod module of LAPACK95. All driver routine interfaces are contained in this module. Statement 7 defines arguments A and B to be allocatable real single-precision arrays. The program works in complex arithmetic if REAL(WP) is replaced by COMPLEX(WP). Statements 9-11 allocate A and B and assign data to these arrays. Statement 12 calls LA_GESV to solve the system. On exit, the solution matrix X is stored in array B. 1: Example program calling an LAPACK95 driver routine.

Mod module of LAPACK95. All driver routine interfaces are contained in this module. Statement 7 defines arguments A and B to be allocatable real single-precision arrays. The program works in complex arithmetic if REAL(WP) is replaced by COMPLEX(WP). Statements 9-11 allocate A and B and assign data to these arrays. Statement 12 calls LA_GESV to solve the system. On exit, the solution matrix X is stored in array B. 1: Example program calling an LAPACK95 driver routine. Example 2 The program in Fig.

22 Chapter 2. Contents of LAPACK95 EI and £2 have the following detailed structures, depending on whether m — r > 0 or m — r < 0. In the first case, m — r > 0, then Here / is the rank of 5, k — r — /, C and 5 are diagonal matrices satisfying C2 + S2 = /, and S is nonsingular. , /. , otk//3k are infinite, and the remaining / generalized singular values are finite. In the second case, when m — r < 0, and Again, / is the rank of B, k — r — /, C and S are diagonal matrices satisfying C2 + S2 = /, 5 is nonsingular, and we may identify a\ = • • • = otk = 1, &k+i — ca for i = l , .