Merge pull request #4055 from martin-frbg/lapack830

Fix scaling in LAPACK STGSNA/DTGSNA (Reference-LAPACK PR 830)

Author: martin-frbg

lapack-netlib/SRC/dtgsna.f

@@ -632,8 +632,8 @@ SUBROUTINE DTGSNA( JOB, HOWMNY, SELECT, N, A, LDA, B, LDB, VL,
                C1 = TWO*( ALPHAR*ALPHAR+ALPHAI*ALPHAI+BETA*BETA )
                C2 = FOUR*BETA*BETA*ALPHAI*ALPHAI
                ROOT1 = C1 + SQRT( C1*C1-4.0D0*C2 )
-               ROOT2 = C2 / ROOT1
                ROOT1 = ROOT1 / TWO
+               ROOT2 = C2 / ROOT1
                COND = MIN( SQRT( ROOT1 ), SQRT( ROOT2 ) )
             END IF
 *

lapack-netlib/SRC/stgsna.f

@@ -632,8 +632,8 @@ SUBROUTINE STGSNA( JOB, HOWMNY, SELECT, N, A, LDA, B, LDB, VL,
                C1 = TWO*( ALPHAR*ALPHAR+ALPHAI*ALPHAI+BETA*BETA )
                C2 = FOUR*BETA*BETA*ALPHAI*ALPHAI
                ROOT1 = C1 + SQRT( C1*C1-4.0*C2 )
-               ROOT2 = C2 / ROOT1
                ROOT1 = ROOT1 / TWO
+               ROOT2 = C2 / ROOT1
                COND = MIN( SQRT( ROOT1 ), SQRT( ROOT2 ) )
             END IF
 *