numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
| Name | Size | Mode | |
| .. | |||
| lapack/SRC/sgsvj1.f | 31961B | -rw-r--r-- |
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*> \brief \b SGSVJ1 pre-processor for the routine sgesvj, applies Jacobi rotations targeting only particular pivots. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download SGSVJ1 + dependencies *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sgsvj1.f"> *> [TGZ]</a> *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sgsvj1.f"> *> [ZIP]</a> *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sgsvj1.f"> *> [TXT]</a> *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE SGSVJ1( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV, * EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO ) * * .. Scalar Arguments .. * REAL EPS, SFMIN, TOL * INTEGER INFO, LDA, LDV, LWORK, M, MV, N, N1, NSWEEP * CHARACTER*1 JOBV * .. * .. Array Arguments .. * REAL A( LDA, * ), D( N ), SVA( N ), V( LDV, * ), * $ WORK( LWORK ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> SGSVJ1 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 tuning parameters (marked by [TP]) are *> available for the implementer. *> *> Further Details *> ~~~~~~~~~~~~~~~ *> SGSVJ1 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 tuning parameter. *> The number of sweeps is given in NSWEEP and the orthogonality threshold *> is given in TOL. *> \endverbatim * * Arguments: * ========== * *> \param[in] JOBV *> \verbatim *> JOBV is 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 postmultiplying the N-by-N array V. *> (See the description of V.) *> = 'A': the product of the Jacobi rotations is accumulated *> by postmultiplying the MV-by-N array V. *> (See the descriptions of MV and V.) *> = 'N': the Jacobi rotations are not accumulated. *> \endverbatim *> *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the input matrix A. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the input matrix A. *> M >= N >= 0. *> \endverbatim *> *> \param[in] N1 *> \verbatim *> N1 is INTEGER *> N1 specifies the 2 x 2 block partition, the first N1 columns are *> rotated 'against' the remaining N-N1 columns of A. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is 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.) *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,M). *> \endverbatim *> *> \param[in,out] D *> \verbatim *> D is 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.) *> \endverbatim *> *> \param[in,out] SVA *> \verbatim *> SVA is 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). *> \endverbatim *> *> \param[in] MV *> \verbatim *> MV is INTEGER *> If JOBV = 'A', then MV rows of V are post-multiplied by a *> sequence of Jacobi rotations. *> If JOBV = 'N', then MV is not referenced. *> \endverbatim *> *> \param[in,out] V *> \verbatim *> V is REAL array, dimension (LDV,N) *> If JOBV = 'V' then N rows of V are post-multiplied by a *> sequence of Jacobi rotations. *> If JOBV = 'A' then MV rows of V are post-multiplied by a *> sequence of Jacobi rotations. *> If JOBV = 'N', then V is not referenced. *> \endverbatim *> *> \param[in] LDV *> \verbatim *> LDV is INTEGER *> The leading dimension of the array V, LDV >= 1. *> If JOBV = 'V', LDV >= N. *> If JOBV = 'A', LDV >= MV. *> \endverbatim *> *> \param[in] EPS *> \verbatim *> EPS is REAL *> EPS = SLAMCH('Epsilon') *> \endverbatim *> *> \param[in] SFMIN *> \verbatim *> SFMIN is REAL *> SFMIN = SLAMCH('Safe Minimum') *> \endverbatim *> *> \param[in] TOL *> \verbatim *> TOL is 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 ABS(COS(angle(A(:,p),A(:,q)))) > TOL. *> \endverbatim *> *> \param[in] NSWEEP *> \verbatim *> NSWEEP is INTEGER *> NSWEEP is the number of sweeps of Jacobi rotations to be *> performed. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is REAL array, dimension (LWORK) *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> LWORK is the dimension of WORK. LWORK >= M. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit. *> < 0: if INFO = -i, then the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup gsvj1 * *> \par Contributors: * ================== *> *> Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany) * * ===================================================================== SUBROUTINE SGSVJ1( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV, $ EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO ) * * -- LAPACK computational routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. REAL EPS, SFMIN, TOL INTEGER INFO, LDA, LDV, LWORK, M, MV, N, N1, NSWEEP CHARACTER*1 JOBV * .. * .. Array Arguments .. REAL A( LDA, * ), D( N ), SVA( N ), V( LDV, * ), $ WORK( LWORK ) * .. * * ===================================================================== * * .. Local Parameters .. REAL ZERO, HALF, ONE PARAMETER ( ZERO = 0.0E0, HALF = 0.5E0, ONE = 1.0E0) * .. * .. Local Scalars .. REAL 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 .. REAL FASTR( 5 ) * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, FLOAT, MIN, SIGN, SQRT * .. * .. External Functions .. REAL SDOT, SNRM2 INTEGER ISAMAX LOGICAL LSAME EXTERNAL ISAMAX, LSAME, SDOT, SNRM2 * .. * .. External Subroutines .. EXTERNAL SAXPY, SCOPY, SLASCL, SLASSQ, SROTM, $ SSWAP, $ XERBLA * .. * .. Executable Statements .. * * Test the input parameters. * 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( ( RSVEC.OR.APPLV ) .AND. ( MV.LT.0 ) ) THEN INFO = -9 ELSE IF( ( RSVEC.AND.( LDV.LT.N ) ).OR. $ ( APPLV.AND.( LDV.LT.MV ) ) ) 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( 'SGSVJ1', -INFO ) RETURN END IF * IF( RSVEC ) THEN MVL = N ELSE IF( APPLV ) THEN MVL = MV END IF RSVEC = RSVEC .OR. APPLV ROOTEPS = SQRT( EPS ) ROOTSFMIN = SQRT( SFMIN ) SMALL = SFMIN / EPS BIG = ONE / SFMIN ROOTBIG = ONE / ROOTSFMIN LARGE = BIG / SQRT( FLOAT( M*N ) ) BIGTHETA = ONE / ROOTEPS ROOTTOL = SQRT( 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 = MIN( 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 = MIN( 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, MIN( igl+KBL-1, N1 ) AAPP = SVA( p ) IF( AAPP.GT.ZERO ) THEN PSKIPPED = 0 DO 2200 q = jgl, MIN( 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 = ( SDOT( M, A( 1, p ), 1, $ A( 1, $ q ), 1 )*D( p )*D( q ) / AAQQ ) $ / AAPP ELSE CALL SCOPY( M, A( 1, p ), 1, WORK, $ 1 ) CALL SLASCL( 'G', 0, 0, AAPP, $ D( p ), $ M, 1, WORK, LDA, IERR ) AAPQ = SDOT( 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 = ( SDOT( M, A( 1, p ), 1, $ A( 1, $ q ), 1 )*D( p )*D( q ) / AAQQ ) $ / AAPP ELSE CALL SCOPY( M, A( 1, q ), 1, WORK, $ 1 ) CALL SLASCL( 'G', 0, 0, AAQQ, $ D( q ), $ M, 1, WORK, LDA, IERR ) AAPQ = SDOT( M, WORK, 1, A( 1, p ), $ 1 )*D( p ) / AAPP END IF END IF MXAAPQ = MAX( MXAAPQ, ABS( AAPQ ) ) * TO rotate or NOT to rotate, THAT is the question ... * IF( ABS( 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*ABS( AQOAP-APOAQ ) / AAPQ IF( AAQQ.GT.AAPP0 )THETA = -THETA IF( ABS( THETA ).GT.BIGTHETA ) THEN T = HALF / THETA FASTR( 3 ) = T*D( p ) / D( q ) FASTR( 4 ) = -T*D( q ) / D( p ) CALL SROTM( M, A( 1, p ), 1, $ A( 1, q ), 1, FASTR ) IF( RSVEC )CALL SROTM( MVL, $ V( 1, p ), 1, $ V( 1, q ), 1, $ FASTR ) SVA( q ) = AAQQ*SQRT( MAX( ZERO, $ ONE+T*APOAQ*AAPQ ) ) AAPP = AAPP*SQRT( MAX( ZERO, $ ONE-T*AQOAP*AAPQ ) ) MXSINJ = MAX( MXSINJ, ABS( T ) ) ELSE * * .. choose correct signum for THETA and rotate * THSIGN = -SIGN( ONE, AAPQ ) IF( AAQQ.GT.AAPP0 )THSIGN = -THSIGN T = ONE / ( THETA+THSIGN* $ SQRT( ONE+THETA*THETA ) ) CS = SQRT( ONE / ( ONE+T*T ) ) SN = T*CS MXSINJ = MAX( MXSINJ, ABS( SN ) ) SVA( q ) = AAQQ*SQRT( MAX( ZERO, $ ONE+T*APOAQ*AAPQ ) ) AAPP = AAPP*SQRT( MAX( ZERO, $ 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 SROTM( M, A( 1, p ), $ 1, $ A( 1, q ), 1, $ FASTR ) IF( RSVEC )CALL SROTM( MVL, $ V( 1, p ), 1, V( 1, q ), $ 1, FASTR ) ELSE CALL SAXPY( M, -T*AQOAP, $ A( 1, q ), 1, $ A( 1, p ), 1 ) CALL SAXPY( M, CS*SN*APOAQ, $ A( 1, p ), 1, $ A( 1, q ), 1 ) IF( RSVEC ) THEN CALL SAXPY( MVL, $ -T*AQOAP, $ V( 1, q ), 1, $ V( 1, p ), 1 ) CALL SAXPY( 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 SAXPY( M, T*APOAQ, $ A( 1, p ), 1, $ A( 1, q ), 1 ) CALL SAXPY( M, $ -CS*SN*AQOAP, $ A( 1, q ), 1, $ A( 1, p ), 1 ) IF( RSVEC ) THEN CALL SAXPY( MVL, $ T*APOAQ, $ V( 1, p ), 1, $ V( 1, q ), 1 ) CALL SAXPY( 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 SAXPY( M, -T*AQOAP, $ A( 1, q ), 1, $ A( 1, p ), 1 ) CALL SAXPY( 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 SAXPY( MVL, $ -T*AQOAP, $ V( 1, q ), 1, $ V( 1, p ), 1 ) CALL SAXPY( MVL, $ CS*SN*APOAQ, $ V( 1, p ), 1, $ V( 1, q ), 1 ) END IF ELSE CALL SAXPY( M, T*APOAQ, $ A( 1, p ), 1, $ A( 1, q ), 1 ) CALL SAXPY( 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 SAXPY( MVL, $ T*APOAQ, V( 1, p ), $ 1, V( 1, q ), 1 ) CALL SAXPY( MVL, $ -CS*SN*AQOAP, $ V( 1, q ), 1, $ V( 1, p ), 1 ) END IF END IF END IF END IF END IF ELSE IF( AAPP.GT.AAQQ ) THEN CALL SCOPY( M, A( 1, p ), 1, $ WORK, $ 1 ) CALL SLASCL( 'G', 0, 0, AAPP, $ ONE, $ M, 1, WORK, LDA, IERR ) CALL SLASCL( 'G', 0, 0, AAQQ, $ ONE, $ M, 1, A( 1, q ), LDA, $ IERR ) TEMP1 = -AAPQ*D( p ) / D( q ) CALL SAXPY( M, TEMP1, WORK, 1, $ A( 1, q ), 1 ) CALL SLASCL( 'G', 0, 0, ONE, $ AAQQ, $ M, 1, A( 1, q ), LDA, $ IERR ) SVA( q ) = AAQQ*SQRT( MAX( ZERO, $ ONE-AAPQ*AAPQ ) ) MXSINJ = MAX( MXSINJ, SFMIN ) ELSE CALL SCOPY( M, A( 1, q ), 1, $ WORK, $ 1 ) CALL SLASCL( 'G', 0, 0, AAQQ, $ ONE, $ M, 1, WORK, LDA, IERR ) CALL SLASCL( 'G', 0, 0, AAPP, $ ONE, $ M, 1, A( 1, p ), LDA, $ IERR ) TEMP1 = -AAPQ*D( q ) / D( p ) CALL SAXPY( M, TEMP1, WORK, 1, $ A( 1, p ), 1 ) CALL SLASCL( 'G', 0, 0, ONE, $ AAPP, $ M, 1, A( 1, p ), LDA, $ IERR ) SVA( p ) = AAPP*SQRT( MAX( ZERO, $ ONE-AAPQ*AAPQ ) ) MXSINJ = MAX( 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 ) = SNRM2( M, A( 1, q ), $ 1 )* $ D( q ) ELSE T = ZERO AAQQ = ONE CALL SLASSQ( M, A( 1, q ), 1, T, $ AAQQ ) SVA( q ) = T*SQRT( AAQQ )*D( q ) END IF END IF IF( ( AAPP / AAPP0 )**2.LE.ROOTEPS ) THEN IF( ( AAPP.LT.ROOTBIG ) .AND. $ ( AAPP.GT.ROOTSFMIN ) ) THEN AAPP = SNRM2( M, A( 1, p ), 1 )* $ D( p ) ELSE T = ZERO AAPP = ONE CALL SLASSQ( M, A( 1, p ), 1, T, $ AAPP ) AAPP = T*SQRT( 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 + $ MIN( 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, MIN( igl+KBL-1, N ) SVA( p ) = ABS( 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 ) = SNRM2( M, A( 1, N ), 1 )*D( N ) ELSE T = ZERO AAPP = ONE CALL SLASSQ( M, A( 1, N ), 1, T, AAPP ) SVA( N ) = T*SQRT( 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.FLOAT( N )*TOL ) .AND. $ ( FLOAT( 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 = ISAMAX( 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 SSWAP( M, A( 1, p ), 1, A( 1, q ), 1 ) IF( RSVEC )CALL SSWAP( MVL, V( 1, p ), 1, V( 1, q ), 1 ) END IF 5991 CONTINUE * RETURN * .. * .. END OF SGSVJ1 * .. END