--- rpl/lapack/lapack/dgejsv.f 2014/01/27 09:28:16 1.12 +++ rpl/lapack/lapack/dgejsv.f 2015/11/26 11:44:15 1.13 @@ -51,7 +51,8 @@ *> the right singular vectors of [A], respectively. The matrices [U] and [V] *> are computed and stored in the arrays U and V, respectively. The diagonal *> of [SIGMA] is computed and stored in the array SVA. -*> \endverbatim +*> DGEJSV can sometimes compute tiny singular values and their singular vectors much +*> more accurately than other SVD routines, see below under Further Details.*> \endverbatim * * Arguments: * ========== @@ -389,7 +390,7 @@ *> \author Univ. of Colorado Denver *> \author NAG Ltd. * -*> \date September 2012 +*> \date November 2015 * *> \ingroup doubleGEsing * @@ -474,10 +475,10 @@ $ M, N, A, LDA, SVA, U, LDU, V, LDV, $ WORK, LWORK, IWORK, INFO ) * -* -- LAPACK computational routine (version 3.4.2) -- +* -- LAPACK computational routine (version 3.6.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* September 2012 +* November 2015 * * .. Scalar Arguments .. IMPLICIT NONE @@ -506,8 +507,7 @@ $ NOSCAL, ROWPIV, RSVEC, TRANSP * .. * .. Intrinsic Functions .. - INTRINSIC DABS, DLOG, DMAX1, DMIN1, DBLE, - $ MAX0, MIN0, IDNINT, DSIGN, DSQRT + INTRINSIC DABS, DLOG, MAX, MIN, DBLE, IDNINT, DSIGN, DSQRT * .. * .. External Functions .. DOUBLE PRECISION DLAMCH, DNRM2 @@ -563,17 +563,17 @@ ELSE IF ( RSVEC .AND. ( LDV .LT. N ) ) THEN INFO = - 14 ELSE IF ( (.NOT.(LSVEC .OR. RSVEC .OR. ERREST).AND. - & (LWORK .LT. MAX0(7,4*N+1,2*M+N))) .OR. + & (LWORK .LT. MAX(7,4*N+1,2*M+N))) .OR. & (.NOT.(LSVEC .OR. RSVEC) .AND. ERREST .AND. - & (LWORK .LT. MAX0(7,4*N+N*N,2*M+N))) .OR. - & (LSVEC .AND. (.NOT.RSVEC) .AND. (LWORK .LT. MAX0(7,2*M+N,4*N+1))) + & (LWORK .LT. MAX(7,4*N+N*N,2*M+N))) .OR. + & (LSVEC .AND. (.NOT.RSVEC) .AND. (LWORK .LT. MAX(7,2*M+N,4*N+1))) & .OR. - & (RSVEC .AND. (.NOT.LSVEC) .AND. (LWORK .LT. MAX0(7,2*M+N,4*N+1))) + & (RSVEC .AND. (.NOT.LSVEC) .AND. (LWORK .LT. MAX(7,2*M+N,4*N+1))) & .OR. & (LSVEC .AND. RSVEC .AND. (.NOT.JRACC) .AND. - & (LWORK.LT.MAX0(2*M+N,6*N+2*N*N))) + & (LWORK.LT.MAX(2*M+N,6*N+2*N*N))) & .OR. (LSVEC .AND. RSVEC .AND. JRACC .AND. - & LWORK.LT.MAX0(2*M+N,4*N+N*N,2*N+N*N+6))) + & LWORK.LT.MAX(2*M+N,4*N+N*N,2*N+N*N+6))) & THEN INFO = - 17 ELSE @@ -644,8 +644,8 @@ AAPP = ZERO AAQQ = BIG DO 4781 p = 1, N - AAPP = DMAX1( AAPP, SVA(p) ) - IF ( SVA(p) .NE. ZERO ) AAQQ = DMIN1( AAQQ, SVA(p) ) + AAPP = MAX( AAPP, SVA(p) ) + IF ( SVA(p) .NE. ZERO ) AAQQ = MIN( AAQQ, SVA(p) ) 4781 CONTINUE * * Quick return for zero M x N matrix @@ -749,14 +749,14 @@ * in one pass through the vector WORK(M+N+p) = XSC * SCALEM WORK(N+p) = XSC * (SCALEM*DSQRT(TEMP1)) - AATMAX = DMAX1( AATMAX, WORK(N+p) ) - IF (WORK(N+p) .NE. ZERO) AATMIN = DMIN1(AATMIN,WORK(N+p)) + AATMAX = MAX( AATMAX, WORK(N+p) ) + IF (WORK(N+p) .NE. ZERO) AATMIN = MIN(AATMIN,WORK(N+p)) 1950 CONTINUE ELSE DO 1904 p = 1, M WORK(M+N+p) = SCALEM*DABS( A(p,IDAMAX(N,A(p,1),LDA)) ) - AATMAX = DMAX1( AATMAX, WORK(M+N+p) ) - AATMIN = DMIN1( AATMIN, WORK(M+N+p) ) + AATMAX = MAX( AATMAX, WORK(M+N+p) ) + AATMIN = MIN( AATMIN, WORK(M+N+p) ) 1904 CONTINUE END IF * @@ -994,7 +994,7 @@ MAXPRJ = ONE DO 3051 p = 2, N TEMP1 = DABS(A(p,p)) / SVA(IWORK(p)) - MAXPRJ = DMIN1( MAXPRJ, TEMP1 ) + MAXPRJ = MIN( MAXPRJ, TEMP1 ) 3051 CONTINUE IF ( MAXPRJ**2 .GE. ONE - DBLE(N)*EPSLN ) ALMORT = .TRUE. END IF @@ -1052,7 +1052,7 @@ * Singular Values only * * .. transpose A(1:NR,1:N) - DO 1946 p = 1, MIN0( N-1, NR ) + DO 1946 p = 1, MIN( N-1, NR ) CALL DCOPY( N-p, A(p,p+1), LDA, A(p+1,p), 1 ) 1946 CONTINUE * @@ -1308,7 +1308,7 @@ XSC = DSQRT(SMALL)/EPSLN DO 3959 p = 2, NR DO 3958 q = 1, p - 1 - TEMP1 = XSC * DMIN1(DABS(V(p,p)),DABS(V(q,q))) + TEMP1 = XSC * MIN(DABS(V(p,p)),DABS(V(q,q))) IF ( DABS(V(q,p)) .LE. TEMP1 ) $ V(q,p) = DSIGN( TEMP1, V(q,p) ) 3958 CONTINUE @@ -1347,7 +1347,7 @@ XSC = DSQRT(SMALL) DO 3969 p = 2, NR DO 3968 q = 1, p - 1 - TEMP1 = XSC * DMIN1(DABS(V(p,p)),DABS(V(q,q))) + TEMP1 = XSC * MIN(DABS(V(p,p)),DABS(V(q,q))) IF ( DABS(V(q,p)) .LE. TEMP1 ) $ V(q,p) = DSIGN( TEMP1, V(q,p) ) 3968 CONTINUE @@ -1360,7 +1360,7 @@ XSC = DSQRT(SMALL) DO 8970 p = 2, NR DO 8971 q = 1, p - 1 - TEMP1 = XSC * DMIN1(DABS(V(p,p)),DABS(V(q,q))) + TEMP1 = XSC * MIN(DABS(V(p,p)),DABS(V(q,q))) V(p,q) = - DSIGN( TEMP1, V(q,p) ) 8971 CONTINUE 8970 CONTINUE @@ -1671,7 +1671,7 @@ XSC = DSQRT(SMALL/EPSLN) DO 9970 q = 2, NR DO 9971 p = 1, q - 1 - TEMP1 = XSC * DMIN1(DABS(U(p,p)),DABS(U(q,q))) + TEMP1 = XSC * MIN(DABS(U(p,p)),DABS(U(q,q))) U(p,q) = - DSIGN( TEMP1, U(q,p) ) 9971 CONTINUE 9970 CONTINUE