SORHR_COL01 tests SORGTSQR and SORHR_COL using SLATSQR, SGEMQRT.


 Therefore, SLATSQR (part of SGEQR), SGEMQRT (part of SGEMQR)


 have to be tested before this test.

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.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.