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Scale convergence thresholds in ?BBCSD to fix accuracy (Reference-LAPACK PR 1293) #5862

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Scale convergence thresholds in ?BBCSD to fix accuracy (Reference-LAPACK PR 1293) #5862

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93 changes: 63 additions & 30 deletions lapack-netlib/SRC/cbbcsd.f
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Original file line number Diff line number Diff line change
Expand Up @@ -5,15 +5,13 @@
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download CBBCSD + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cbbcsd.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cbbcsd.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cbbcsd.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
Expand Down Expand Up @@ -322,13 +320,15 @@
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup complexOTHERcomputational
*> \ingroup bbcsd
*
* =====================================================================
SUBROUTINE CBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q,
SUBROUTINE CBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P,
$ Q,
$ THETA, PHI, U1, LDU1, U2, LDU2, V1T, LDV1T,
$ V2T, LDV2T, B11D, B11E, B12D, B12E, B21D, B21E,
$ B22D, B22E, RWORK, LRWORK, INFO )
IMPLICIT NONE
*
* -- LAPACK computational routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
Expand Down Expand Up @@ -372,7 +372,8 @@ SUBROUTINE CBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q,
$ UNFL, X1, X2, Y1, Y2
*
* .. External Subroutines ..
EXTERNAL CLASR, CSCAL, CSWAP, SLARTGP, SLARTGS, SLAS2,
EXTERNAL CLASR, CSCAL, CSWAP, SLARTGP, SLARTGS,
$ SLAS2,
$ XERBLA
* ..
* .. External Functions ..
Expand Down Expand Up @@ -417,7 +418,7 @@ SUBROUTINE CBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q,
*
IF( INFO .EQ. 0 .AND. Q .EQ. 0 ) THEN
LRWORKMIN = 1
RWORK(1) = LRWORKMIN
RWORK(1) = REAL( LRWORKMIN )
RETURN
END IF
*
Expand All @@ -434,7 +435,7 @@ SUBROUTINE CBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q,
IV2TSN = IV2TCS + Q
LRWORKOPT = IV2TSN + Q - 1
LRWORKMIN = LRWORKOPT
RWORK(1) = LRWORKOPT
RWORK(1) = REAL( LRWORKOPT )
IF( LRWORK .LT. LRWORKMIN .AND. .NOT. LQUERY ) THEN
INFO = -28
END IF
Expand All @@ -453,7 +454,7 @@ SUBROUTINE CBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q,
UNFL = SLAMCH( 'Safe minimum' )
TOLMUL = MAX( TEN, MIN( HUNDRED, EPS**MEIGHTH ) )
TOL = TOLMUL*EPS
THRESH = MAX( TOL, MAXITR*Q*Q*UNFL )
THRESH = MAX( TOL, REAL( MAXITR*Q*Q )*UNFL )
*
* Test for negligible sines or cosines
*
Expand Down Expand Up @@ -559,9 +560,11 @@ SUBROUTINE CBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q,
*
* Compute shifts for B11 and B21 and use the lesser
*
CALL SLAS2( B11D(IMAX-1), B11E(IMAX-1), B11D(IMAX), SIGMA11,
CALL SLAS2( B11D(IMAX-1), B11E(IMAX-1), B11D(IMAX),
$ SIGMA11,
$ DUMMY )
CALL SLAS2( B21D(IMAX-1), B21E(IMAX-1), B21D(IMAX), SIGMA21,
CALL SLAS2( B21D(IMAX-1), B21E(IMAX-1), B21D(IMAX),
$ SIGMA21,
$ DUMMY )
*
IF( SIGMA11 .LE. SIGMA21 ) THEN
Expand Down Expand Up @@ -613,7 +616,9 @@ SUBROUTINE CBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q,
*
* Chase the bulges in B11(IMIN+1,IMIN) and B21(IMIN+1,IMIN)
*
IF( B11D(IMIN)**2+B11BULGE**2 .GT. THRESH**2 ) THEN
IF( B11D(IMIN)**2+B11BULGE**2 .GT.
$ (THRESH*MAX( ABS(B11D(IMIN)),
$ ABS(B11D(IMIN+1)), UNFL ))**2 ) THEN
CALL SLARTGP( B11BULGE, B11D(IMIN), RWORK(IU1SN+IMIN-1),
$ RWORK(IU1CS+IMIN-1), R )
ELSE IF( MU .LE. NU ) THEN
Expand All @@ -623,7 +628,9 @@ SUBROUTINE CBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q,
CALL SLARTGS( B12D( IMIN ), B12E( IMIN ), NU,
$ RWORK(IU1CS+IMIN-1), RWORK(IU1SN+IMIN-1) )
END IF
IF( B21D(IMIN)**2+B21BULGE**2 .GT. THRESH**2 ) THEN
IF( B21D(IMIN)**2+B21BULGE**2 .GT.
$ (THRESH*MAX( ABS(B21D(IMIN)),
$ ABS(B21D(IMIN+1)), UNFL ))**2 ) THEN
CALL SLARTGP( B21BULGE, B21D(IMIN), RWORK(IU2SN+IMIN-1),
$ RWORK(IU2CS+IMIN-1), R )
ELSE IF( NU .LT. MU ) THEN
Expand Down Expand Up @@ -687,10 +694,18 @@ SUBROUTINE CBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q,
* Determine if there are bulges to chase or if a new direct
* summand has been reached
*
RESTART11 = B11E(I-1)**2 + B11BULGE**2 .LE. THRESH**2
RESTART21 = B21E(I-1)**2 + B21BULGE**2 .LE. THRESH**2
RESTART12 = B12D(I-1)**2 + B12BULGE**2 .LE. THRESH**2
RESTART22 = B22D(I-1)**2 + B22BULGE**2 .LE. THRESH**2
RESTART11 = B11E(I-1)**2 + B11BULGE**2 .LE.
$ (THRESH*MAX( ABS(B11D(I-1)), ABS(B11D(I)),
$ UNFL ))**2
RESTART21 = B21E(I-1)**2 + B21BULGE**2 .LE.
$ (THRESH*MAX( ABS(B21D(I-1)), ABS(B21D(I)),
$ UNFL ))**2
RESTART12 = B12D(I-1)**2 + B12BULGE**2 .LE.
$ (THRESH*MAX( ABS(B12E(I-1)), ABS(B12D(I)),
$ UNFL ))**2
RESTART22 = B22D(I-1)**2 + B22BULGE**2 .LE.
$ (THRESH*MAX( ABS(B22E(I-1)), ABS(B22D(I)),
$ UNFL ))**2
*
* If possible, chase bulges from B11(I-1,I+1), B12(I-1,I),
* B21(I-1,I+1), and B22(I-1,I). If necessary, restart bulge-
Expand Down Expand Up @@ -718,10 +733,12 @@ SUBROUTINE CBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q,
CALL SLARTGP( Y2, Y1, RWORK(IV2TSN+I-1-1),
$ RWORK(IV2TCS+I-1-1), R )
ELSE IF( .NOT. RESTART12 .AND. RESTART22 ) THEN
CALL SLARTGP( B12BULGE, B12D(I-1), RWORK(IV2TSN+I-1-1),
CALL SLARTGP( B12BULGE, B12D(I-1),
$ RWORK(IV2TSN+I-1-1),
$ RWORK(IV2TCS+I-1-1), R )
ELSE IF( RESTART12 .AND. .NOT. RESTART22 ) THEN
CALL SLARTGP( B22BULGE, B22D(I-1), RWORK(IV2TSN+I-1-1),
CALL SLARTGP( B22BULGE, B22D(I-1),
$ RWORK(IV2TSN+I-1-1),
$ RWORK(IV2TCS+I-1-1), R )
ELSE IF( NU .LT. MU ) THEN
CALL SLARTGS( B12E(I-1), B12D(I), NU,
Expand Down Expand Up @@ -770,17 +787,26 @@ SUBROUTINE CBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q,
* Determine if there are bulges to chase or if a new direct
* summand has been reached
*
RESTART11 = B11D(I)**2 + B11BULGE**2 .LE. THRESH**2
RESTART12 = B12E(I-1)**2 + B12BULGE**2 .LE. THRESH**2
RESTART21 = B21D(I)**2 + B21BULGE**2 .LE. THRESH**2
RESTART22 = B22E(I-1)**2 + B22BULGE**2 .LE. THRESH**2
RESTART11 = B11D(I)**2 + B11BULGE**2 .LE.
$ (THRESH*MAX( ABS(B11E(I)), ABS(B11D(I+1)),
$ UNFL ))**2
RESTART12 = B12E(I-1)**2 + B12BULGE**2 .LE.
$ (THRESH*MAX( ABS(B12D(I)), ABS(B12E(I)),
$ UNFL ))**2
RESTART21 = B21D(I)**2 + B21BULGE**2 .LE.
$ (THRESH*MAX( ABS(B21E(I)), ABS(B21D(I+1)),
$ UNFL ))**2
RESTART22 = B22E(I-1)**2 + B22BULGE**2 .LE.
$ (THRESH*MAX( ABS(B22D(I)), ABS(B22E(I)),
$ UNFL ))**2
*
* If possible, chase bulges from B11(I+1,I), B12(I+1,I-1),
* B21(I+1,I), and B22(I+1,I-1). If necessary, restart bulge-
* chasing by applying the original shift again.
*
IF( .NOT. RESTART11 .AND. .NOT. RESTART12 ) THEN
CALL SLARTGP( X2, X1, RWORK(IU1SN+I-1), RWORK(IU1CS+I-1),
CALL SLARTGP( X2, X1, RWORK(IU1SN+I-1),
$ RWORK(IU1CS+I-1),
$ R )
ELSE IF( .NOT. RESTART11 .AND. RESTART12 ) THEN
CALL SLARTGP( B11BULGE, B11D(I), RWORK(IU1SN+I-1),
Expand All @@ -789,14 +815,16 @@ SUBROUTINE CBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q,
CALL SLARTGP( B12BULGE, B12E(I-1), RWORK(IU1SN+I-1),
$ RWORK(IU1CS+I-1), R )
ELSE IF( MU .LE. NU ) THEN
CALL SLARTGS( B11E(I), B11D(I+1), MU, RWORK(IU1CS+I-1),
CALL SLARTGS( B11E(I), B11D(I+1), MU,
$ RWORK(IU1CS+I-1),
$ RWORK(IU1SN+I-1) )
ELSE
CALL SLARTGS( B12D(I), B12E(I), NU, RWORK(IU1CS+I-1),
$ RWORK(IU1SN+I-1) )
END IF
IF( .NOT. RESTART21 .AND. .NOT. RESTART22 ) THEN
CALL SLARTGP( Y2, Y1, RWORK(IU2SN+I-1), RWORK(IU2CS+I-1),
CALL SLARTGP( Y2, Y1, RWORK(IU2SN+I-1),
$ RWORK(IU2CS+I-1),
$ R )
ELSE IF( .NOT. RESTART21 .AND. RESTART22 ) THEN
CALL SLARTGP( B21BULGE, B21D(I), RWORK(IU2SN+I-1),
Expand All @@ -805,7 +833,8 @@ SUBROUTINE CBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q,
CALL SLARTGP( B22BULGE, B22E(I-1), RWORK(IU2SN+I-1),
$ RWORK(IU2CS+I-1), R )
ELSE IF( NU .LT. MU ) THEN
CALL SLARTGS( B21E(I), B21D(I+1), NU, RWORK(IU2CS+I-1),
CALL SLARTGS( B21E(I), B21D(I+1), NU,
$ RWORK(IU2CS+I-1),
$ RWORK(IU2SN+I-1) )
ELSE
CALL SLARTGS( B22D(I), B22E(I), MU, RWORK(IU2CS+I-1),
Expand Down Expand Up @@ -857,8 +886,10 @@ SUBROUTINE CBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q,
*
* Chase bulges from B12(IMAX-1,IMAX) and B22(IMAX-1,IMAX)
*
RESTART12 = B12D(IMAX-1)**2 + B12BULGE**2 .LE. THRESH**2
RESTART22 = B22D(IMAX-1)**2 + B22BULGE**2 .LE. THRESH**2
RESTART12 = B12D(IMAX-1)**2 + B12BULGE**2 .LE.
$ (THRESH*MAX( ABS(B12E(IMAX-1)), UNFL ))**2
RESTART22 = B22D(IMAX-1)**2 + B22BULGE**2 .LE.
$ (THRESH*MAX( ABS(B22E(IMAX-1)), UNFL ))**2
*
IF( .NOT. RESTART12 .AND. .NOT. RESTART22 ) THEN
CALL SLARTGP( Y2, Y1, RWORK(IV2TSN+IMAX-1-1),
Expand Down Expand Up @@ -991,7 +1022,8 @@ SUBROUTINE CBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q,
IF( B12D(IMAX)+B22D(IMAX) .LT. 0 ) THEN
IF( WANTV2T ) THEN
IF( COLMAJOR ) THEN
CALL CSCAL( M-Q, NEGONECOMPLEX, V2T(IMAX,1), LDV2T )
CALL CSCAL( M-Q, NEGONECOMPLEX, V2T(IMAX,1),
$ LDV2T )
ELSE
CALL CSCAL( M-Q, NEGONECOMPLEX, V2T(1,IMAX), 1 )
END IF
Expand Down Expand Up @@ -1058,7 +1090,8 @@ SUBROUTINE CBBCSD( JOBU1, JOBU2, JOBV1T, JOBV2T, TRANS, M, P, Q,
IF( WANTU2 )
$ CALL CSWAP( M-P, U2(1,I), 1, U2(1,MINI), 1 )
IF( WANTV1T )
$ CALL CSWAP( Q, V1T(I,1), LDV1T, V1T(MINI,1), LDV1T )
$ CALL CSWAP( Q, V1T(I,1), LDV1T, V1T(MINI,1),
$ LDV1T )
IF( WANTV2T )
$ CALL CSWAP( M-Q, V2T(I,1), LDV2T, V2T(MINI,1),
$ LDV2T )
Expand Down
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