TESTING/LIN/sorhr_col02.f(3)

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

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