--- rpl/lapack/lapack/dgejsv.f 2012/08/22 09:48:13 1.9
+++ rpl/lapack/lapack/dgejsv.f 2017/06/17 10:53:48 1.16
@@ -2,18 +2,18 @@
*
* =========== DOCUMENTATION ===========
*
-* Online html documentation available at
-* http://www.netlib.org/lapack/explore-html/
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
-*> Download DGEJSV + dependencies
-*>
-*> [TGZ]
-*>
-*> [ZIP]
-*>
+*> Download DGEJSV + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
*> [TXT]
-*> \endhtmlonly
+*> \endhtmlonly
*
* Definition:
* ===========
@@ -21,7 +21,7 @@
* SUBROUTINE DGEJSV( JOBA, JOBU, JOBV, JOBR, JOBT, JOBP,
* M, N, A, LDA, SVA, U, LDU, V, LDV,
* WORK, LWORK, IWORK, INFO )
-*
+*
* .. Scalar Arguments ..
* IMPLICIT NONE
* INTEGER INFO, LDA, LDU, LDV, LWORK, M, N
@@ -32,7 +32,7 @@
* INTEGER IWORK( * )
* CHARACTER*1 JOBA, JOBP, JOBR, JOBT, JOBU, JOBV
* ..
-*
+*
*
*> \par Purpose:
* =============
@@ -51,6 +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.
+*> 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:
@@ -85,7 +87,7 @@
*> rows, then using this condition number gives too pessimistic
*> error bound.
*> = 'A': Small singular values are the noise and the matrix is treated
-*> as numerically rank defficient. The error in the computed
+*> as numerically rank deficient. The error in the computed
*> singular values is bounded by f(m,n)*epsilon*||A||.
*> The computed SVD A = U * S * V^t restores A up to
*> f(m,n)*epsilon*||A||.
@@ -235,7 +237,7 @@
*> copied back to the V array. This 'W' option is just
*> a reminder to the caller that in this case U is
*> reserved as workspace of length N*N.
-*> If JOBU = 'N' U is not referenced.
+*> If JOBU = 'N' U is not referenced, unless JOBT='T'.
*> \endverbatim
*>
*> \param[in] LDU
@@ -257,7 +259,7 @@
*> copied back to the U array. This 'W' option is just
*> a reminder to the caller that in this case V is
*> reserved as workspace of length N*N.
-*> If JOBV = 'N' V is not referenced.
+*> If JOBV = 'N' V is not referenced, unless JOBT='T'.
*> \endverbatim
*>
*> \param[in] LDV
@@ -270,7 +272,7 @@
*> \param[out] WORK
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension at least LWORK.
-*> On exit, if N.GT.0 .AND. M.GT.0 (else not referenced),
+*> On exit, if N.GT.0 .AND. M.GT.0 (else not referenced),
*> WORK(1) = SCALE = WORK(2) / WORK(1) is the scaling factor such
*> that SCALE*SVA(1:N) are the computed singular values
*> of A. (See the description of SVA().)
@@ -317,24 +319,24 @@
*> ->> For optimal performance (blocked code) the optimal value
*> is LWORK >= max(2*M+N,3*N+(N+1)*NB,7). Here NB is the optimal
*> block size for DGEQP3 and DGEQRF.
-*> In general, optimal LWORK is computed as
-*> LWORK >= max(2*M+N,N+LWORK(DGEQP3),N+LWORK(DGEQRF), 7).
+*> In general, optimal LWORK is computed as
+*> LWORK >= max(2*M+N,N+LWORK(DGEQP3),N+LWORK(DGEQRF), 7).
*> -> .. an estimate of the scaled condition number of A is
*> required (JOBA='E', 'G'). In this case, LWORK is the maximum
*> of the above and N*N+4*N, i.e. LWORK >= max(2*M+N,N*N+4*N,7).
-*> ->> For optimal performance (blocked code) the optimal value
+*> ->> For optimal performance (blocked code) the optimal value
*> is LWORK >= max(2*M+N,3*N+(N+1)*NB, N*N+4*N, 7).
*> In general, the optimal length LWORK is computed as
-*> LWORK >= max(2*M+N,N+LWORK(DGEQP3),N+LWORK(DGEQRF),
+*> LWORK >= max(2*M+N,N+LWORK(DGEQP3),N+LWORK(DGEQRF),
*> N+N*N+LWORK(DPOCON),7).
*>
*> If SIGMA and the right singular vectors are needed (JOBV.EQ.'V'),
*> -> the minimal requirement is LWORK >= max(2*M+N,4*N+1,7).
*> -> For optimal performance, LWORK >= max(2*M+N,3*N+(N+1)*NB,7),
-*> where NB is the optimal block size for DGEQP3, DGEQRF, DGELQ,
+*> where NB is the optimal block size for DGEQP3, DGEQRF, DGELQF,
*> DORMLQ. In general, the optimal length LWORK is computed as
-*> LWORK >= max(2*M+N,N+LWORK(DGEQP3), N+LWORK(DPOCON),
-*> N+LWORK(DGELQ), 2*N+LWORK(DGEQRF), N+LWORK(DORMLQ)).
+*> LWORK >= max(2*M+N,N+LWORK(DGEQP3), N+LWORK(DPOCON),
+*> N+LWORK(DGELQF), 2*N+LWORK(DGEQRF), N+LWORK(DORMLQ)).
*>
*> If SIGMA and the left singular vectors are needed
*> -> the minimal requirement is LWORK >= max(2*M+N,4*N+1,7).
@@ -344,14 +346,14 @@
*> where NB is the optimal block size for DGEQP3, DGEQRF, DORMQR.
*> In general, the optimal length LWORK is computed as
*> LWORK >= max(2*M+N,N+LWORK(DGEQP3),N+LWORK(DPOCON),
-*> 2*N+LWORK(DGEQRF), N+LWORK(DORMQR)).
-*> Here LWORK(DORMQR) equals N*NB (for JOBU.EQ.'U') or
+*> 2*N+LWORK(DGEQRF), N+LWORK(DORMQR)).
+*> Here LWORK(DORMQR) equals N*NB (for JOBU.EQ.'U') or
*> M*NB (for JOBU.EQ.'F').
-*>
-*> If the full SVD is needed: (JOBU.EQ.'U' or JOBU.EQ.'F') and
-*> -> if JOBV.EQ.'V'
-*> the minimal requirement is LWORK >= max(2*M+N,6*N+2*N*N).
-*> -> if JOBV.EQ.'J' the minimal requirement is
+*>
+*> If the full SVD is needed: (JOBU.EQ.'U' or JOBU.EQ.'F') and
+*> -> if JOBV.EQ.'V'
+*> the minimal requirement is LWORK >= max(2*M+N,6*N+2*N*N).
+*> -> if JOBV.EQ.'J' the minimal requirement is
*> LWORK >= max(2*M+N, 4*N+N*N,2*N+N*N+6).
*> -> For optimal performance, LWORK should be additionally
*> larger than N+M*NB, where NB is the optimal block size
@@ -376,7 +378,7 @@
*> \verbatim
*> INFO is INTEGER
*> < 0 : if INFO = -i, then the i-th argument had an illegal value.
-*> = 0 : successfull exit;
+*> = 0 : successful exit;
*> > 0 : DGEJSV did not converge in the maximal allowed number
*> of sweeps. The computed values may be inaccurate.
*> \endverbatim
@@ -384,14 +386,14 @@
* Authors:
* ========
*
-*> \author Univ. of Tennessee
-*> \author Univ. of California Berkeley
-*> \author Univ. of Colorado Denver
-*> \author NAG Ltd.
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
*
-*> \date November 2011
+*> \date June 2016
*
-*> \ingroup doubleGEcomputational
+*> \ingroup doubleGEsing
*
*> \par Further Details:
* =====================
@@ -426,8 +428,8 @@
*> The rank revealing QR factorization (in this code: DGEQP3) should be
*> implemented as in [3]. We have a new version of DGEQP3 under development
*> that is more robust than the current one in LAPACK, with a cleaner cut in
-*> rank defficient cases. It will be available in the SIGMA library [4].
-*> If M is much larger than N, it is obvious that the inital QRF with
+*> rank deficient cases. It will be available in the SIGMA library [4].
+*> If M is much larger than N, it is obvious that the initial QRF with
*> column pivoting can be preprocessed by the QRF without pivoting. That
*> well known trick is not used in DGEJSV because in some cases heavy row
*> weighting can be treated with complete pivoting. The overhead in cases
@@ -474,10 +476,10 @@
$ M, N, A, LDA, SVA, U, LDU, V, LDV,
$ WORK, LWORK, IWORK, INFO )
*
-* -- LAPACK computational routine (version 3.4.0) --
+* -- LAPACK computational routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* November 2011
+* June 2016
*
* .. Scalar Arguments ..
IMPLICIT NONE
@@ -506,8 +508,7 @@
$ 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
@@ -561,19 +562,19 @@
ELSE IF ( LSVEC .AND. ( LDU .LT. M ) ) THEN
INFO = - 13
ELSE IF ( RSVEC .AND. ( LDV .LT. N ) ) THEN
- INFO = - 14
+ INFO = - 15
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)))
+ & (LSVEC .AND. RSVEC .AND. (.NOT.JRACC) .AND.
+ & (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
@@ -589,7 +590,11 @@
*
* Quick return for void matrix (Y3K safe)
* #:)
- IF ( ( M .EQ. 0 ) .OR. ( N .EQ. 0 ) ) RETURN
+ IF ( ( M .EQ. 0 ) .OR. ( N .EQ. 0 ) ) THEN
+ IWORK(1:3) = 0
+ WORK(1:7) = 0
+ RETURN
+ ENDIF
*
* Determine whether the matrix U should be M x N or M x M
*
@@ -644,8 +649,8 @@
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
@@ -715,6 +720,7 @@
IWORK(1) = 0
IWORK(2) = 0
END IF
+ IWORK(3) = 0
IF ( ERREST ) WORK(3) = ONE
IF ( LSVEC .AND. RSVEC ) THEN
WORK(4) = ONE
@@ -749,14 +755,14 @@
* 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
*
@@ -961,7 +967,7 @@
ELSE IF ( L2RANK ) THEN
* .. similarly as above, only slightly more gentle (less agressive).
* Sudden drop on the diagonal of R1 is used as the criterion for
-* close-to-rank-defficient.
+* close-to-rank-deficient.
TEMP1 = DSQRT(SFMIN)
DO 3401 p = 2, N
IF ( ( DABS(A(p,p)) .LT. (EPSLN*DABS(A(p-1,p-1))) ) .OR.
@@ -994,7 +1000,7 @@
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 +1058,7 @@
* 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 +1314,7 @@
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 +1353,7 @@
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 +1366,7 @@
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 +1677,7 @@
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