Fix -ZERO singular value in bdsqr

[D,Z]BDSQR returns for

D = [ -4.0, -3.0, -2.0, -1.0, 0.0, 1.0, 2.0, 3.0, 4.0, 5.0]
E = [ 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0]

as singular value  D(10) = -ZERO. By definition, singular values
are non-negative. LASQ1 already fixes the sign and returns +ZERO.

Author: angsch

SRC/cbdsqr.f

@@ -809,6 +809,12 @@ SUBROUTINE CBDSQR( UPLO, N, NCVT, NRU, NCC, D, E, VT, LDVT, U,
 *
   160 CONTINUE
       DO 170 I = 1, N
+         IF( D( I ).EQ.ZERO ) THEN
+*
+*           Avoid -ZERO
+*
+            D( I ) = ZERO
+         END IF
          IF( D( I ).LT.ZERO ) THEN
             D( I ) = -D( I )
 *

SRC/dbdsqr.f

@@ -817,6 +817,12 @@ SUBROUTINE DBDSQR( UPLO, N, NCVT, NRU, NCC, D, E, VT, LDVT, U,
 *
   160 CONTINUE
       DO 170 I = 1, N
+         IF( D( I ).EQ.ZERO ) THEN
+*
+*           Avoid -ZERO
+*
+            D( I ) = ZERO
+         END IF
          IF( D( I ).LT.ZERO ) THEN
             D( I ) = -D( I )
 *

SRC/sbdsqr.f

@@ -817,7 +817,14 @@ SUBROUTINE SBDSQR( UPLO, N, NCVT, NRU, NCC, D, E, VT, LDVT, U,
 *
   160 CONTINUE
       DO 170 I = 1, N
+         IF( D( I ).EQ.ZERO ) THEN
+*
+*           Avoid -ZERO
+*
+            D( I ) = ZERO
+         END IF
          IF( D( I ).LT.ZERO ) THEN
+
             D( I ) = -D( I )
 *
 *           Change sign of singular vectors, if desired

SRC/zbdsqr.f

@@ -807,6 +807,12 @@ SUBROUTINE ZBDSQR( UPLO, N, NCVT, NRU, NCC, D, E, VT, LDVT, U,
 *
   160 CONTINUE
       DO 170 I = 1, N
+         IF( D( I ).EQ.ZERO ) THEN
+*
+*           Avoid -ZERO
+*
+            D( I ) = ZERO
+         END IF
          IF( D( I ).LT.ZERO ) THEN
             D( I ) = -D( I )
 *