[WIP] Update LAPACK to 3.9.0 (#2353)

* Update make.inc entries for LAPACK 3.9.0

Reference-LAPACK PR 347 changed some variable names and relative paths

* Update LAPACK to 3.9.0

* Add new functions from LAPACK 3.9.0

* Add new functions from LAPACK 3.9.0

* Restore LOADER command 

as it makes it easier to specify pthread as needed

* Restore LOADER

* Restore EIG/LIN prefixes in cmdbase

* add binary path to lapack_testing.py call

* Restore OpenMP version check

* Restore OpenMP version check

* Restore fix for out-of-bounds array accesses

from #2096

lapack-netlib/SRC/slansy.f

@@ -127,6 +127,7 @@
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     December 2016
 *
+      IMPLICIT NONE
 *     .. Scalar Arguments ..
       CHARACTER          NORM, UPLO
       INTEGER            LDA, N
@@ -143,15 +144,18 @@
 *     ..
 *     .. Local Scalars ..
       INTEGER            I, J
-      REAL               ABSA, SCALE, SUM, VALUE
+      REAL               ABSA, SUM, VALUE
 *     ..
-*     .. External Subroutines ..
-      EXTERNAL           SLASSQ
+*     .. Local Arrays ..
+      REAL               SSQ( 2 ), COLSSQ( 2 )
 *     ..
 *     .. External Functions ..
       LOGICAL            LSAME, SISNAN
       EXTERNAL           LSAME, SISNAN
 *     ..
+*     .. External Subroutines ..
+      EXTERNAL           SLASSQ, SCOMBSSQ
+*     ..
 *     .. Intrinsic Functions ..
       INTRINSIC          ABS, SQRT
 *     ..
@@ -216,21 +220,39 @@
       ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
 *
 *        Find normF(A).
+*        SSQ(1) is scale
+*        SSQ(2) is sum-of-squares
+*        For better accuracy, sum each column separately.
+*
+         SSQ( 1 ) = ZERO
+         SSQ( 2 ) = ONE
+*
+*        Sum off-diagonals
 *
-         SCALE = ZERO
-         SUM = ONE
          IF( LSAME( UPLO, 'U' ) ) THEN
             DO 110 J = 2, N
-               CALL SLASSQ( J-1, A( 1, J ), 1, SCALE, SUM )
+               COLSSQ( 1 ) = ZERO
+               COLSSQ( 2 ) = ONE
+               CALL SLASSQ( J-1, A( 1, J ), 1, COLSSQ(1), COLSSQ(2) )
+               CALL SCOMBSSQ( SSQ, COLSSQ )
   110       CONTINUE
          ELSE
             DO 120 J = 1, N - 1
-               CALL SLASSQ( N-J, A( J+1, J ), 1, SCALE, SUM )
+               COLSSQ( 1 ) = ZERO
+               COLSSQ( 2 ) = ONE
+               CALL SLASSQ( N-J, A( J+1, J ), 1, COLSSQ(1), COLSSQ(2) )
+               CALL SCOMBSSQ( SSQ, COLSSQ )
   120       CONTINUE
          END IF
-         SUM = 2*SUM
-         CALL SLASSQ( N, A, LDA+1, SCALE, SUM )
-         VALUE = SCALE*SQRT( SUM )
+         SSQ( 2 ) = 2*SSQ( 2 )
+*
+*        Sum diagonal
+*
+         COLSSQ( 1 ) = ZERO
+         COLSSQ( 2 ) = ONE
+         CALL SLASSQ( N, A, LDA+1, COLSSQ( 1 ), COLSSQ( 2 ) )
+         CALL SCOMBSSQ( SSQ, COLSSQ )
+         VALUE = SSQ( 1 )*SQRT( SSQ( 2 ) )
       END IF
 *
       SLANSY = VALUE