diff options
author | julie <julielangou@users.noreply.github.com> | 2008-12-16 17:06:58 +0000 |
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committer | julie <julielangou@users.noreply.github.com> | 2008-12-16 17:06:58 +0000 |
commit | ff981f106bde4ce6a74aa4f4a572c943f5a395b2 (patch) | |
tree | a386cad907bcaefd6893535c31d67ec9468e693e /SRC/dgsvj1.f | |
parent | e58b61578b55644f6391f3333262b72c1dc88437 (diff) |
Diffstat (limited to 'SRC/dgsvj1.f')
-rw-r--r-- | SRC/dgsvj1.f | 611 |
1 files changed, 611 insertions, 0 deletions
diff --git a/SRC/dgsvj1.f b/SRC/dgsvj1.f new file mode 100644 index 00000000..ddc7a6c0 --- /dev/null +++ b/SRC/dgsvj1.f @@ -0,0 +1,611 @@ + SUBROUTINE DGSVJ1( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV, + & EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO ) +* +* -- LAPACK routine (version 3.2) -- +* +* -- Contributed by Zlatko Drmac of the University of Zagreb and -- +* -- Kresimir Veselic of the Fernuniversitaet Hagen -- +* -- November 2008 -- +* +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* +* This routine is also part of SIGMA (version 1.23, October 23. 2008.) +* SIGMA is a library of algorithms for highly accurate algorithms for +* computation of SVD, PSVD, QSVD, (H,K)-SVD, and for solution of the +* eigenvalue problems Hx = lambda M x, H M x = lambda x with H, M > 0. +* +* -#- Scalar Arguments -#- +* + IMPLICIT NONE + DOUBLE PRECISION EPS, SFMIN, TOL + INTEGER INFO, LDA, LDV, LWORK, M, MV, N, N1, NSWEEP + CHARACTER*1 JOBV +* +* -#- Array Arguments -#- +* + DOUBLE PRECISION A( LDA, * ), D( N ), SVA( N ), V( LDV, * ), + & WORK( LWORK ) +* .. +* +* Purpose +* ~~~~~~~ +* DGSVJ1 is called from SGESVJ as a pre-processor and that is its main +* purpose. It applies Jacobi rotations in the same way as SGESVJ does, but +* it targets only particular pivots and it does not check convergence +* (stopping criterion). Few tunning parameters (marked by [TP]) are +* available for the implementer. +* +* Further details +* ~~~~~~~~~~~~~~~ +* DGSVJ1 applies few sweeps of Jacobi rotations in the column space of +* the input M-by-N matrix A. The pivot pairs are taken from the (1,2) +* off-diagonal block in the corresponding N-by-N Gram matrix A^T * A. The +* block-entries (tiles) of the (1,2) off-diagonal block are marked by the +* [x]'s in the following scheme: +* +* | * * * [x] [x] [x]| +* | * * * [x] [x] [x]| Row-cycling in the nblr-by-nblc [x] blocks. +* | * * * [x] [x] [x]| Row-cyclic pivoting inside each [x] block. +* |[x] [x] [x] * * * | +* |[x] [x] [x] * * * | +* |[x] [x] [x] * * * | +* +* In terms of the columns of A, the first N1 columns are rotated 'against' +* the remaining N-N1 columns, trying to increase the angle between the +* corresponding subspaces. The off-diagonal block is N1-by(N-N1) and it is +* tiled using quadratic tiles of side KBL. Here, KBL is a tunning parmeter. +* The number of sweeps is given in NSWEEP and the orthogonality threshold +* is given in TOL. +* +* Contributors +* ~~~~~~~~~~~~ +* Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany) +* +* Arguments +* ~~~~~~~~~ +* +* JOBV (input) CHARACTER*1 +* Specifies whether the output from this procedure is used +* to compute the matrix V: +* = 'V': the product of the Jacobi rotations is accumulated +* by postmulyiplying the N-by-N array V. +* (See the description of V.) +* = 'A': the product of the Jacobi rotations is accumulated +* by postmulyiplying the MV-by-N array V. +* (See the descriptions of MV and V.) +* = 'N': the Jacobi rotations are not accumulated. +* +* M (input) INTEGER +* The number of rows of the input matrix A. M >= 0. +* +* N (input) INTEGER +* The number of columns of the input matrix A. +* M >= N >= 0. +* +* N1 (input) INTEGER +* N1 specifies the 2 x 2 block partition, the first N1 columns are +* rotated 'against' the remaining N-N1 columns of A. +* +* A (input/output) REAL array, dimension (LDA,N) +* On entry, M-by-N matrix A, such that A*diag(D) represents +* the input matrix. +* On exit, +* A_onexit * D_onexit represents the input matrix A*diag(D) +* post-multiplied by a sequence of Jacobi rotations, where the +* rotation threshold and the total number of sweeps are given in +* TOL and NSWEEP, respectively. +* (See the descriptions of N1, D, TOL and NSWEEP.) +* +* LDA (input) INTEGER +* The leading dimension of the array A. LDA >= max(1,M). +* +* D (input/workspace/output) REAL array, dimension (N) +* The array D accumulates the scaling factors from the fast scaled +* Jacobi rotations. +* On entry, A*diag(D) represents the input matrix. +* On exit, A_onexit*diag(D_onexit) represents the input matrix +* post-multiplied by a sequence of Jacobi rotations, where the +* rotation threshold and the total number of sweeps are given in +* TOL and NSWEEP, respectively. +* (See the descriptions of N1, A, TOL and NSWEEP.) +* +* SVA (input/workspace/output) REAL array, dimension (N) +* On entry, SVA contains the Euclidean norms of the columns of +* the matrix A*diag(D). +* On exit, SVA contains the Euclidean norms of the columns of +* the matrix onexit*diag(D_onexit). +* +* MV (input) INTEGER +* If JOBV .EQ. 'A', then MV rows of V are post-multipled by a +* sequence of Jacobi rotations. +* If JOBV = 'N', then MV is not referenced. +* +* V (input/output) REAL array, dimension (LDV,N) +* If JOBV .EQ. 'V' then N rows of V are post-multipled by a +* sequence of Jacobi rotations. +* If JOBV .EQ. 'A' then MV rows of V are post-multipled by a +* sequence of Jacobi rotations. +* If JOBV = 'N', then V is not referenced. +* +* LDV (input) INTEGER +* The leading dimension of the array V, LDV >= 1. +* If JOBV = 'V', LDV .GE. N. +* If JOBV = 'A', LDV .GE. MV. +* +* EPS (input) INTEGER +* EPS = SLAMCH('Epsilon') +* +* SFMIN (input) INTEGER +* SFMIN = SLAMCH('Safe Minimum') +* +* TOL (input) REAL +* TOL is the threshold for Jacobi rotations. For a pair +* A(:,p), A(:,q) of pivot columns, the Jacobi rotation is +* applied only if DABS(COS(angle(A(:,p),A(:,q)))) .GT. TOL. +* +* NSWEEP (input) INTEGER +* NSWEEP is the number of sweeps of Jacobi rotations to be +* performed. +* +* WORK (workspace) REAL array, dimension LWORK. +* +* LWORK (input) INTEGER +* LWORK is the dimension of WORK. LWORK .GE. M. +* +* INFO (output) INTEGER +* = 0 : successful exit. +* < 0 : if INFO = -i, then the i-th argument had an illegal value +* +* -#- Local Parameters -#- +* + DOUBLE PRECISION ZERO, HALF, ONE, TWO + PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0, TWO = 2.0D0 ) + +* -#- Local Scalars -#- +* + DOUBLE PRECISION AAPP, AAPP0, AAPQ, AAQQ, APOAQ, AQOAP, BIG, + & BIGTHETA, CS, LARGE, MXAAPQ, MXSINJ, ROOTBIG, ROOTEPS, + & ROOTSFMIN, ROOTTOL, SMALL, SN, T, TEMP1, THETA, THSIGN + INTEGER BLSKIP, EMPTSW, i, ibr, igl, IERR, IJBLSK, ISWROT, jbc, + & jgl, KBL, MVL, NOTROT, nblc, nblr, p, PSKIPPED, q, + & ROWSKIP, SWBAND + LOGICAL APPLV, ROTOK, RSVEC +* +* Local Arrays +* + DOUBLE PRECISION FASTR(5) +* +* Intrinsic Functions +* + INTRINSIC DABS, DMAX1, DBLE, MIN0, DSIGN, DSQRT +* +* External Functions +* + DOUBLE PRECISION DDOT, DNRM2 + INTEGER IDAMAX + LOGICAL LSAME + EXTERNAL IDAMAX, LSAME, DDOT, DNRM2 +* +* External Subroutines +* + EXTERNAL DAXPY, DCOPY, DLASCL, DLASSQ, DROTM, DSWAP +* +* + APPLV = LSAME(JOBV,'A') + RSVEC = LSAME(JOBV,'V') + IF ( .NOT.( RSVEC .OR. APPLV .OR. LSAME(JOBV,'N'))) THEN + INFO = -1 + ELSE IF ( M .LT. 0 ) THEN + INFO = -2 + ELSE IF ( ( N .LT. 0 ) .OR. ( N .GT. M )) THEN + INFO = -3 + ELSE IF ( N1 .LT. 0 ) THEN + INFO = -4 + ELSE IF ( LDA .LT. M ) THEN + INFO = -6 + ELSE IF ( MV .LT. 0 ) THEN + INFO = -9 + ELSE IF ( LDV .LT. M ) THEN + INFO = -11 + ELSE IF ( TOL .LE. EPS ) THEN + INFO = -14 + ELSE IF ( NSWEEP .LT. 0 ) THEN + INFO = -15 + ELSE IF ( LWORK .LT. M ) THEN + INFO = -17 + ELSE + INFO = 0 + END IF +* +* #:( + IF ( INFO .NE. 0 ) THEN + CALL XERBLA( 'DGSVJ1', -INFO ) + RETURN + END IF +* + IF ( RSVEC ) THEN + MVL = N + ELSE IF ( APPLV ) THEN + MVL = MV + END IF + RSVEC = RSVEC .OR. APPLV + + ROOTEPS = DSQRT(EPS) + ROOTSFMIN = DSQRT(SFMIN) + SMALL = SFMIN / EPS + BIG = ONE / SFMIN + ROOTBIG = ONE / ROOTSFMIN + LARGE = BIG / DSQRT(DBLE(M*N)) + BIGTHETA = ONE / ROOTEPS + ROOTTOL = DSQRT(TOL) +* +* -#- Initialize the right singular vector matrix -#- +* +* RSVEC = LSAME( JOBV, 'Y' ) +* + EMPTSW = N1 * ( N - N1 ) + NOTROT = 0 + FASTR(1) = ZERO +* +* -#- Row-cyclic pivot strategy with de Rijk's pivoting -#- +* + KBL = MIN0(8,N) + NBLR = N1 / KBL + IF ( ( NBLR * KBL ) .NE. N1 ) NBLR = NBLR + 1 + +* .. the tiling is nblr-by-nblc [tiles] + + NBLC = ( N - N1 ) / KBL + IF ( ( NBLC * KBL ) .NE. ( N - N1 ) ) NBLC = NBLC + 1 + BLSKIP = ( KBL**2 ) + 1 +*[TP] BLKSKIP is a tuning parameter that depends on SWBAND and KBL. + + ROWSKIP = MIN0( 5, KBL ) +*[TP] ROWSKIP is a tuning parameter. + SWBAND = 0 +*[TP] SWBAND is a tuning parameter. It is meaningful and effective +* if SGESVJ is used as a computational routine in the preconditioned +* Jacobi SVD algorithm SGESVJ. +* +* +* | * * * [x] [x] [x]| +* | * * * [x] [x] [x]| Row-cycling in the nblr-by-nblc [x] blocks. +* | * * * [x] [x] [x]| Row-cyclic pivoting inside each [x] block. +* |[x] [x] [x] * * * | +* |[x] [x] [x] * * * | +* |[x] [x] [x] * * * | +* +* + DO 1993 i = 1, NSWEEP +* .. go go go ... +* + MXAAPQ = ZERO + MXSINJ = ZERO + ISWROT = 0 +* + NOTROT = 0 + PSKIPPED = 0 +* + DO 2000 ibr = 1, NBLR + + igl = ( ibr - 1 ) * KBL + 1 +* +* +*........................................................ +* ... go to the off diagonal blocks + + igl = ( ibr - 1 ) * KBL + 1 + + DO 2010 jbc = 1, NBLC + + jgl = N1 + ( jbc - 1 ) * KBL + 1 + +* doing the block at ( ibr, jbc ) + + IJBLSK = 0 + DO 2100 p = igl, MIN0( igl + KBL - 1, N1 ) + + AAPP = SVA(p) + + IF ( AAPP .GT. ZERO ) THEN + + PSKIPPED = 0 + + DO 2200 q = jgl, MIN0( jgl + KBL - 1, N ) +* + AAQQ = SVA(q) + + IF ( AAQQ .GT. ZERO ) THEN + AAPP0 = AAPP +* +* -#- M x 2 Jacobi SVD -#- +* +* -#- Safe Gram matrix computation -#- +* + IF ( AAQQ .GE. ONE ) THEN + IF ( AAPP .GE. AAQQ ) THEN + ROTOK = ( SMALL*AAPP ) .LE. AAQQ + ELSE + ROTOK = ( SMALL*AAQQ ) .LE. AAPP + END IF + IF ( AAPP .LT. ( BIG / AAQQ ) ) THEN + AAPQ = ( DDOT(M, A(1,p), 1, A(1,q), 1 ) * + & D(p) * D(q) / AAQQ ) / AAPP + ELSE + CALL DCOPY( M, A(1,p), 1, WORK, 1 ) + CALL DLASCL( 'G', 0, 0, AAPP, D(p), M, + & 1, WORK, LDA, IERR ) + AAPQ = DDOT( M, WORK, 1, A(1,q), 1 ) * + & D(q) / AAQQ + END IF + ELSE + IF ( AAPP .GE. AAQQ ) THEN + ROTOK = AAPP .LE. ( AAQQ / SMALL ) + ELSE + ROTOK = AAQQ .LE. ( AAPP / SMALL ) + END IF + IF ( AAPP .GT. ( SMALL / AAQQ ) ) THEN + AAPQ = ( DDOT( M, A(1,p), 1, A(1,q), 1 ) * + & D(p) * D(q) / AAQQ ) / AAPP + ELSE + CALL DCOPY( M, A(1,q), 1, WORK, 1 ) + CALL DLASCL( 'G', 0, 0, AAQQ, D(q), M, 1, + & WORK, LDA, IERR ) + AAPQ = DDOT(M,WORK,1,A(1,p),1) * D(p) / AAPP + END IF + END IF + + MXAAPQ = DMAX1( MXAAPQ, DABS(AAPQ) ) + +* TO rotate or NOT to rotate, THAT is the question ... +* + IF ( DABS( AAPQ ) .GT. TOL ) THEN + NOTROT = 0 +* ROTATED = ROTATED + 1 + PSKIPPED = 0 + ISWROT = ISWROT + 1 +* + IF ( ROTOK ) THEN +* + AQOAP = AAQQ / AAPP + APOAQ = AAPP / AAQQ + THETA = - HALF * DABS( AQOAP - APOAQ ) / AAPQ + IF ( AAQQ .GT. AAPP0 ) THETA = - THETA + + IF ( DABS( THETA ) .GT. BIGTHETA ) THEN + T = HALF / THETA + FASTR(3) = T * D(p) / D(q) + FASTR(4) = -T * D(q) / D(p) + CALL DROTM( M, A(1,p), 1, A(1,q), 1, FASTR ) + IF ( RSVEC ) + & CALL DROTM( MVL, V(1,p), 1, V(1,q), 1, FASTR ) + SVA(q) = AAQQ*DSQRT( DMAX1(ZERO,ONE + T*APOAQ*AAPQ) ) + AAPP = AAPP*DSQRT( DMAX1(ZERO,ONE - T*AQOAP*AAPQ) ) + MXSINJ = DMAX1( MXSINJ, DABS(T) ) + ELSE +* +* .. choose correct signum for THETA and rotate +* + THSIGN = - DSIGN(ONE,AAPQ) + IF ( AAQQ .GT. AAPP0 ) THSIGN = - THSIGN + T = ONE / ( THETA + THSIGN*DSQRT(ONE+THETA*THETA) ) + CS = DSQRT( ONE / ( ONE + T*T ) ) + SN = T * CS + MXSINJ = DMAX1( MXSINJ, DABS(SN) ) + SVA(q) = AAQQ*DSQRT( DMAX1(ZERO, ONE+T*APOAQ*AAPQ) ) + AAPP = AAPP*DSQRT( ONE - T*AQOAP*AAPQ) + + APOAQ = D(p) / D(q) + AQOAP = D(q) / D(p) + IF ( D(p) .GE. ONE ) THEN +* + IF ( D(q) .GE. ONE ) THEN + FASTR(3) = T * APOAQ + FASTR(4) = - T * AQOAP + D(p) = D(p) * CS + D(q) = D(q) * CS + CALL DROTM( M, A(1,p),1, A(1,q),1, FASTR ) + IF ( RSVEC ) + & CALL DROTM( MVL, V(1,p),1, V(1,q),1, FASTR ) + ELSE + CALL DAXPY( M, -T*AQOAP, A(1,q),1, A(1,p),1 ) + CALL DAXPY( M, CS*SN*APOAQ, A(1,p),1, A(1,q),1 ) + IF ( RSVEC ) THEN + CALL DAXPY( MVL, -T*AQOAP, V(1,q),1, V(1,p),1 ) + CALL DAXPY( MVL,CS*SN*APOAQ,V(1,p),1, V(1,q),1 ) + END IF + D(p) = D(p) * CS + D(q) = D(q) / CS + END IF + ELSE + IF ( D(q) .GE. ONE ) THEN + CALL DAXPY( M, T*APOAQ, A(1,p),1, A(1,q),1 ) + CALL DAXPY( M,-CS*SN*AQOAP, A(1,q),1, A(1,p),1 ) + IF ( RSVEC ) THEN + CALL DAXPY(MVL,T*APOAQ, V(1,p),1, V(1,q),1 ) + CALL DAXPY(MVL,-CS*SN*AQOAP,V(1,q),1, V(1,p),1 ) + END IF + D(p) = D(p) / CS + D(q) = D(q) * CS + ELSE + IF ( D(p) .GE. D(q) ) THEN + CALL DAXPY( M,-T*AQOAP, A(1,q),1,A(1,p),1 ) + CALL DAXPY( M,CS*SN*APOAQ,A(1,p),1,A(1,q),1 ) + D(p) = D(p) * CS + D(q) = D(q) / CS + IF ( RSVEC ) THEN + CALL DAXPY( MVL, -T*AQOAP, V(1,q),1,V(1,p),1) + CALL DAXPY(MVL,CS*SN*APOAQ,V(1,p),1,V(1,q),1) + END IF + ELSE + CALL DAXPY(M, T*APOAQ, A(1,p),1,A(1,q),1) + CALL DAXPY(M,-CS*SN*AQOAP,A(1,q),1,A(1,p),1) + D(p) = D(p) / CS + D(q) = D(q) * CS + IF ( RSVEC ) THEN + CALL DAXPY(MVL, T*APOAQ, V(1,p),1,V(1,q),1) + CALL DAXPY(MVL,-CS*SN*AQOAP,V(1,q),1,V(1,p),1) + END IF + END IF + END IF + ENDIF + END IF + + ELSE + IF ( AAPP .GT. AAQQ ) THEN + CALL DCOPY( M, A(1,p), 1, WORK, 1 ) + CALL DLASCL('G',0,0,AAPP,ONE,M,1,WORK,LDA,IERR) + CALL DLASCL('G',0,0,AAQQ,ONE,M,1, A(1,q),LDA,IERR) + TEMP1 = -AAPQ * D(p) / D(q) + CALL DAXPY(M,TEMP1,WORK,1,A(1,q),1) + CALL DLASCL('G',0,0,ONE,AAQQ,M,1,A(1,q),LDA,IERR) + SVA(q) = AAQQ*DSQRT(DMAX1(ZERO, ONE - AAPQ*AAPQ)) + MXSINJ = DMAX1( MXSINJ, SFMIN ) + ELSE + CALL DCOPY( M, A(1,q), 1, WORK, 1 ) + CALL DLASCL('G',0,0,AAQQ,ONE,M,1,WORK,LDA,IERR) + CALL DLASCL('G',0,0,AAPP,ONE,M,1, A(1,p),LDA,IERR) + TEMP1 = -AAPQ * D(q) / D(p) + CALL DAXPY(M,TEMP1,WORK,1,A(1,p),1) + CALL DLASCL('G',0,0,ONE,AAPP,M,1,A(1,p),LDA,IERR) + SVA(p) = AAPP*DSQRT(DMAX1(ZERO, ONE - AAPQ*AAPQ)) + MXSINJ = DMAX1( MXSINJ, SFMIN ) + END IF + END IF +* END IF ROTOK THEN ... ELSE +* +* In the case of cancellation in updating SVA(q) +* .. recompute SVA(q) + IF ( (SVA(q) / AAQQ )**2 .LE. ROOTEPS ) THEN + IF ((AAQQ .LT. ROOTBIG).AND.(AAQQ .GT. ROOTSFMIN)) THEN + SVA(q) = DNRM2( M, A(1,q), 1 ) * D(q) + ELSE + T = ZERO + AAQQ = ZERO + CALL DLASSQ( M, A(1,q), 1, T, AAQQ ) + SVA(q) = T * DSQRT(AAQQ) * D(q) + END IF + END IF + IF ( (AAPP / AAPP0 )**2 .LE. ROOTEPS ) THEN + IF ((AAPP .LT. ROOTBIG).AND.(AAPP .GT. ROOTSFMIN)) THEN + AAPP = DNRM2( M, A(1,p), 1 ) * D(p) + ELSE + T = ZERO + AAPP = ZERO + CALL DLASSQ( M, A(1,p), 1, T, AAPP ) + AAPP = T * DSQRT(AAPP) * D(p) + END IF + SVA(p) = AAPP + END IF +* end of OK rotation + ELSE + NOTROT = NOTROT + 1 +* SKIPPED = SKIPPED + 1 + PSKIPPED = PSKIPPED + 1 + IJBLSK = IJBLSK + 1 + END IF + ELSE + NOTROT = NOTROT + 1 + PSKIPPED = PSKIPPED + 1 + IJBLSK = IJBLSK + 1 + END IF + +* IF ( NOTROT .GE. EMPTSW ) GO TO 2011 + IF ( ( i .LE. SWBAND ) .AND. ( IJBLSK .GE. BLSKIP ) ) THEN + SVA(p) = AAPP + NOTROT = 0 + GO TO 2011 + END IF + IF ( ( i .LE. SWBAND ) .AND. ( PSKIPPED .GT. ROWSKIP ) ) THEN + AAPP = -AAPP + NOTROT = 0 + GO TO 2203 + END IF + +* + 2200 CONTINUE +* end of the q-loop + 2203 CONTINUE + + SVA(p) = AAPP +* + ELSE + IF ( AAPP .EQ. ZERO ) NOTROT=NOTROT+MIN0(jgl+KBL-1,N)-jgl+1 + IF ( AAPP .LT. ZERO ) NOTROT = 0 +*** IF ( NOTROT .GE. EMPTSW ) GO TO 2011 + END IF + + 2100 CONTINUE +* end of the p-loop + 2010 CONTINUE +* end of the jbc-loop + 2011 CONTINUE +*2011 bailed out of the jbc-loop + DO 2012 p = igl, MIN0( igl + KBL - 1, N ) + SVA(p) = DABS(SVA(p)) + 2012 CONTINUE +*** IF ( NOTROT .GE. EMPTSW ) GO TO 1994 + 2000 CONTINUE +*2000 :: end of the ibr-loop +* +* .. update SVA(N) + IF ((SVA(N) .LT. ROOTBIG).AND.(SVA(N) .GT. ROOTSFMIN)) THEN + SVA(N) = DNRM2( M, A(1,N), 1 ) * D(N) + ELSE + T = ZERO + AAPP = ZERO + CALL DLASSQ( M, A(1,N), 1, T, AAPP ) + SVA(N) = T * DSQRT(AAPP) * D(N) + END IF +* +* Additional steering devices +* + IF ( ( i.LT.SWBAND ) .AND. ( ( MXAAPQ.LE.ROOTTOL ) .OR. + & ( ISWROT .LE. N ) ) ) + & SWBAND = i + + IF ((i.GT.SWBAND+1).AND. (MXAAPQ.LT.DBLE(N)*TOL).AND. + & (DBLE(N)*MXAAPQ*MXSINJ.LT.TOL))THEN + GO TO 1994 + END IF + +* + IF ( NOTROT .GE. EMPTSW ) GO TO 1994 + + 1993 CONTINUE +* end i=1:NSWEEP loop +* #:) Reaching this point means that the procedure has completed the given +* number of sweeps. + INFO = NSWEEP - 1 + GO TO 1995 + 1994 CONTINUE +* #:) Reaching this point means that during the i-th sweep all pivots were +* below the given threshold, causing early exit. + + INFO = 0 +* #:) INFO = 0 confirms successful iterations. + 1995 CONTINUE +* +* Sort the vector D +* + DO 5991 p = 1, N - 1 + q = IDAMAX( N-p+1, SVA(p), 1 ) + p - 1 + IF ( p .NE. q ) THEN + TEMP1 = SVA(p) + SVA(p) = SVA(q) + SVA(q) = TEMP1 + TEMP1 = D(p) + D(p) = D(q) + D(q) = TEMP1 + CALL DSWAP( M, A(1,p), 1, A(1,q), 1 ) + IF ( RSVEC ) CALL DSWAP( MVL, V(1,p), 1, V(1,q), 1 ) + END IF + 5991 CONTINUE +* + RETURN +* .. +* .. END OF DGSVJ1 +* .. + END +* |