TESTING/LIN/sorhr_col02.f(3)                          Library Functions Manual

NAME
       TESTING/LIN/sorhr_col02.f

SYNOPSIS
   Functions/Subroutines
       subroutine sorhr_col02 (m, n, mb1, nb1, nb2, result)
           SORHR_COL02

Function/Subroutine Documentation
   subroutine sorhr_col02 (integer m, integer n, integer mb1, integer nb1,
       integer nb2, real, dimension(6) result)
       SORHR_COL02

       Purpose:


            SORHR_COL02 tests SORGTSQR_ROW and SORHR_COL inside SGETSQRHRT
            (which calls SLATSQR, SORGTSQR_ROW and SORHR_COL) using SGEMQRT.
            Therefore, SLATSQR (part of SGEQR), SGEMQRT (part of SGEMQR)
            have to be tested before this test.

       Parameters
           M

                     M is INTEGER
                     Number of rows in test matrix.

           N

                     N is INTEGER
                     Number of columns in test matrix.

           MB1

                     MB1 is INTEGER
                     Number of row in row block in an input test matrix.

           NB1

                     NB1 is INTEGER
                     Number of columns in column block an input test matrix.

           NB2

                     NB2 is INTEGER
                     Number of columns in column block in an output test matrix.

           RESULT

                     RESULT is REAL array, dimension (6)
                     Results of each of the six tests below.

                       A is a m-by-n test input matrix to be factored.
                       so that A = Q_gr * ( R )
                                          ( 0 ),

                       Q_qr is an implicit m-by-m orthogonal Q matrix, the result
                       of factorization in blocked WY-representation,
                       stored in SGEQRT output format.

                       R is a n-by-n upper-triangular matrix,

                       0 is a (m-n)-by-n zero matrix,

                       Q is an explicit m-by-m orthogonal matrix Q = Q_gr * I

                       C is an m-by-n random matrix,

                       D is an n-by-m random matrix.

                     The six tests are:

                     RESULT(1) = |R - (Q**H) * A| / ( eps * m * |A| )
                       is equivalent to test for | A - Q * R | / (eps * m * |A|),

                     RESULT(2) = |I - (Q**H) * Q| / ( eps * m ),

                     RESULT(3) = | Q_qr * C - Q * C | / (eps * m * |C|),

                     RESULT(4) = | (Q_gr**H) * C - (Q**H) * C | / (eps * m * |C|)

                     RESULT(5) = | D * Q_qr - D * Q | / (eps * m * |D|)

                     RESULT(6) = | D * (Q_qr**H) - D * (Q**H) | / (eps * m * |D|),

                     where:
                       Q_qr * C, (Q_gr**H) * C, D * Q_qr, D * (Q_qr**H) are
                       computed using SGEMQRT,

                       Q * C, (Q**H) * C, D * Q, D * (Q**H)  are
                       computed using SGEMM.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Definition at line 119 of file sorhr_col02.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0    TESTING/LIN/sorhr_col02.f(3)