Merge pull request #3830 from martin-frbg/lapack691+698

Add quick return in ?LASCL; use normwise criterion for INF in QZ; fix workspace calcn for ?SYEVD (Reference-LAPACK PRs 674+691+698)

lapack-netlib/SRC/cheevd.f

@@ -284,7 +284,7 @@
                LIWMIN = 1
             END IF
             LOPT = MAX( LWMIN, N +
-     $                  ILAENV( 1, 'CHETRD', UPLO, N, -1, -1, -1 ) )
+     $                  N*ILAENV( 1, 'CHETRD', UPLO, N, -1, -1, -1 ) )
             LROPT = LRWMIN
             LIOPT = LIWMIN
          END IF

lapack-netlib/SRC/chgeqz.f

@@ -523,9 +523,7 @@
             END IF
          END IF
 *
-         IF( ABS( T( ILAST, ILAST ) ).LE.MAX( SAFMIN, ULP*( 
-     $         ABS( T( ILAST - 1, ILAST ) ) + ABS( T( ILAST-1, ILAST-1 )
-     $          ) ) ) ) THEN
+         IF( ABS( T( ILAST, ILAST ) ).LE.BTOL ) THEN
             T( ILAST, ILAST ) = CZERO
             GO TO 50
          END IF
@@ -551,10 +549,7 @@
 *
 *           Test 2: for T(j,j)=0
 *
-            TEMP = ABS ( T( J, J + 1 ) )
-            IF ( J .GT. ILO )
-     $           TEMP = TEMP + ABS ( T( J - 1, J ) )
-            IF( ABS( T( J, J ) ).LT.MAX( SAFMIN,ULP*TEMP ) ) THEN
+            IF( ABS( T( J, J ) ).LT.BTOL ) THEN
                T( J, J ) = CZERO
 *
 *              Test 1a: Check for 2 consecutive small subdiagonals in A

lapack-netlib/SRC/clascl.f

@@ -272,6 +272,8 @@
          ELSE
             MUL = CTOC / CFROMC
             DONE = .TRUE.
+            IF (MUL .EQ. ONE)
+     $         RETURN
          END IF
       END IF
 *

lapack-netlib/SRC/dhgeqz.f

@@ -536,9 +536,7 @@
             END IF
          END IF
 *
-         IF( ABS( T( ILAST, ILAST ) ).LE.MAX( SAFMIN, ULP*( 
-     $         ABS( T( ILAST - 1, ILAST ) ) + ABS( T( ILAST-1, ILAST-1 )
-     $          ) ) ) ) THEN
+         IF( ABS( T( ILAST, ILAST ) ).LE.BTOL ) THEN
             T( ILAST, ILAST ) = ZERO
             GO TO 70
          END IF
@@ -564,10 +562,7 @@
 *
 *           Test 2: for T(j,j)=0
 *
-            TEMP = ABS ( T( J, J + 1 ) )
-            IF ( J .GT. ILO )
-     $           TEMP = TEMP + ABS ( T( J - 1, J ) )
-            IF( ABS( T( J, J ) ).LT.MAX( SAFMIN,ULP*TEMP ) ) THEN
+            IF( ABS( T( J, J ) ).LT.BTOL ) THEN
                T( J, J ) = ZERO
 *
 *              Test 1a: Check for 2 consecutive small subdiagonals in A

lapack-netlib/SRC/dlascl.f

@@ -272,6 +272,8 @@
          ELSE
             MUL = CTOC / CFROMC
             DONE = .TRUE.
+            IF (MUL .EQ. ONE)
+     $         RETURN
          END IF
       END IF
 *

lapack-netlib/SRC/dsyevd.f

@@ -257,7 +257,7 @@
                LWMIN = 2*N + 1
             END IF
             LOPT = MAX( LWMIN, 2*N +
-     $                  ILAENV( 1, 'DSYTRD', UPLO, N, -1, -1, -1 ) )
+     $                  N*ILAENV( 1, 'DSYTRD', UPLO, N, -1, -1, -1 ) )
             LIOPT = LIWMIN
          END IF
          WORK( 1 ) = LOPT

lapack-netlib/SRC/shgeqz.f

@@ -536,9 +536,7 @@
             END IF
          END IF
 *
-         IF( ABS( T( ILAST, ILAST ) ).LE.MAX( SAFMIN, ULP*( 
-     $         ABS( T( ILAST - 1, ILAST ) ) + ABS( T( ILAST-1, ILAST-1 )
-     $          ) ) ) ) THEN
+         IF( ABS( T( ILAST, ILAST ) ).LE.BTOL ) THEN
             T( ILAST, ILAST ) = ZERO
             GO TO 70
          END IF
@@ -564,10 +562,7 @@
 *
 *           Test 2: for T(j,j)=0
 *
-            TEMP = ABS ( T( J, J + 1 ) )
-            IF ( J .GT. ILO )
-     $           TEMP = TEMP + ABS ( T( J - 1, J ) )
-            IF( ABS( T( J, J ) ).LT.MAX( SAFMIN,ULP*TEMP ) ) THEN
+            IF( ABS( T( J, J ) ).LT.BTOL ) THEN
                T( J, J ) = ZERO
 *
 *              Test 1a: Check for 2 consecutive small subdiagonals in A

lapack-netlib/SRC/slascl.f

@@ -272,6 +272,8 @@
          ELSE
             MUL = CTOC / CFROMC
             DONE = .TRUE.
+            IF (MUL .EQ. ONE)
+     $         RETURN
          END IF
       END IF
 *

lapack-netlib/SRC/ssyevd.f

@@ -255,7 +255,7 @@
                LWMIN = 2*N + 1
             END IF
             LOPT = MAX( LWMIN, 2*N +
-     $                  ILAENV( 1, 'SSYTRD', UPLO, N, -1, -1, -1 ) )
+     $                  N*ILAENV( 1, 'SSYTRD', UPLO, N, -1, -1, -1 ) )
             LIOPT = LIWMIN
          END IF
          WORK( 1 ) = LOPT

lapack-netlib/SRC/zheevd.f

@@ -284,7 +284,7 @@
                LIWMIN = 1
             END IF
             LOPT = MAX( LWMIN, N +
-     $                  ILAENV( 1, 'ZHETRD', UPLO, N, -1, -1, -1 ) )
+     $                  N*ILAENV( 1, 'ZHETRD', UPLO, N, -1, -1, -1 ) )
             LROPT = LRWMIN
             LIOPT = LIWMIN
          END IF

lapack-netlib/SRC/zhgeqz.f

@@ -524,9 +524,7 @@
             END IF
          END IF
 *
-         IF( ABS( T( ILAST, ILAST ) ).LE.MAX( SAFMIN, ULP*( 
-     $         ABS( T( ILAST - 1, ILAST ) ) + ABS( T( ILAST-1, ILAST-1 )
-     $          ) ) ) ) THEN
+         IF( ABS( T( ILAST, ILAST ) ).LE.BTOL ) THEN
             T( ILAST, ILAST ) = CZERO
             GO TO 50
          END IF
@@ -552,10 +550,7 @@
 *
 *           Test 2: for T(j,j)=0
 *
-            TEMP = ABS ( T( J, J + 1 ) )
-            IF ( J .GT. ILO )
-     $           TEMP = TEMP + ABS ( T( J - 1, J ) )
-            IF( ABS( T( J, J ) ).LT.MAX( SAFMIN,ULP*TEMP ) ) THEN
+            IF( ABS( T( J, J ) ).LT.BTOL ) THEN
                T( J, J ) = CZERO
 *
 *              Test 1a: Check for 2 consecutive small subdiagonals in A

lapack-netlib/SRC/zlascl.f

@@ -272,6 +272,8 @@
          ELSE
             MUL = CTOC / CFROMC
             DONE = .TRUE.
+            IF (MUL .EQ. ONE)
+     $         RETURN
          END IF
       END IF
 *