- SUBROUTINE SGSVJ0( JOBV, M, N, A, LDA, D, SVA, MV, V, LDV, EPS,
- + SFMIN, TOL, NSWEEP, WORK, LWORK, INFO )
-*
-* -- LAPACK routine (version 3.3.0) --
+*> \brief \b SGSVJ0 pre-processor for the routine sgesvj.
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download SGSVJ0 + dependencies
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sgsvj0.f">
+*> [TGZ]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sgsvj0.f">
+*> [ZIP]</a>
+*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sgsvj0.f">
+*> [TXT]</a>
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE SGSVJ0( JOBV, M, N, A, LDA, D, SVA, MV, V, LDV, EPS,
+* SFMIN, TOL, NSWEEP, WORK, LWORK, INFO )
+*
+* .. Scalar Arguments ..
+* INTEGER INFO, LDA, LDV, LWORK, M, MV, N, NSWEEP
+* REAL EPS, SFMIN, TOL
+* CHARACTER*1 JOBV
+* ..
+* .. Array Arguments ..
+* REAL A( LDA, * ), SVA( N ), D( N ), V( LDV, * ),
+* $ WORK( LWORK )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> SGSVJ0 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 does not check convergence (stopping criterion). Few tuning
+*> parameters (marked by [TP]) are available for the implementer.
+*> \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 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.
+*> \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,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 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 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 .EQ. 'A', then MV rows of V are post-multipled 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 .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.
+*> \endverbatim
+*>
+*> \param[in] LDV
+*> \verbatim
+*> LDV is INTEGER
+*> The leading dimension of the array V, LDV >= 1.
+*> If JOBV = 'V', LDV .GE. N.
+*> If JOBV = 'A', LDV .GE. 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)))) .GT. 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 .GE. 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.
+*
+*> \date December 2016
+*
+*> \ingroup realOTHERcomputational
+*
+*> \par Further Details:
+* =====================
+*>
+*> SGSVJ0 is used just to enable SGESVJ to call a simplified version of
+*> itself to work on a submatrix of the original matrix.
+*>
+*> \par Contributors:
+* ==================
+*>
+*> Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany)
+*>
+*> \par Bugs, Examples and Comments:
+* =================================
+*>
+*> Please report all bugs and send interesting test examples and comments to
+*> drmac@math.hr. Thank you.
*
-* -- Contributed by Zlatko Drmac of the University of Zagreb and --
-* -- Kresimir Veselic of the Fernuniversitaet Hagen --
-* November 2010
+* =====================================================================
+ SUBROUTINE SGSVJ0( JOBV, M, N, A, LDA, D, SVA, MV, V, LDV, EPS,
+ $ SFMIN, TOL, NSWEEP, WORK, LWORK, INFO )
*
+* -- 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..--
+* December 2016
*
-* 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.
-*
- IMPLICIT NONE
-* ..
* .. Scalar Arguments ..
INTEGER INFO, LDA, LDV, LWORK, M, MV, N, NSWEEP
REAL EPS, SFMIN, TOL
* ..
* .. Array Arguments ..
REAL A( LDA, * ), SVA( N ), D( N ), V( LDV, * ),
- + WORK( LWORK )
+ $ WORK( LWORK )
* ..
*
-* Purpose
-* =======
-*
-* SGSVJ0 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 does not check convergence (stopping criterion). Few tuning
-* parameters (marked by [TP]) are available for the implementer.
-*
-* Further Details
-* ~~~~~~~~~~~~~~~
-* SGSVJ0 is used just to enable SGESVJ to call a simplified version of
-* itself to work on a submatrix of the original matrix.
-*
-* Contributors
-* ~~~~~~~~~~~~
-* Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany)
-*
-* Bugs, Examples and Comments
-* ~~~~~~~~~~~~~~~~~~~~~~~~~~~
-* Please report all bugs and send interesting test examples and comments to
-* drmac@math.hr. Thank you.
-*
-* 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.
-*
-* 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 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 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 ABS(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 ..
- REAL ZERO, HALF, ONE, TWO
- PARAMETER ( ZERO = 0.0E0, HALF = 0.5E0, ONE = 1.0E0,
- + TWO = 2.0E0 )
+ 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, MXAAPQ, MXSINJ, ROOTBIG, ROOTEPS,
- + ROOTSFMIN, ROOTTOL, SMALL, SN, T, TEMP1, THETA,
- + THSIGN
+ $ BIGTHETA, CS, MXAAPQ, MXSINJ, ROOTBIG, ROOTEPS,
+ $ ROOTSFMIN, ROOTTOL, SMALL, SN, T, TEMP1, THETA,
+ $ THSIGN
INTEGER BLSKIP, EMPTSW, i, ibr, IERR, igl, IJBLSK, ir1,
- + ISWROT, jbc, jgl, KBL, LKAHEAD, MVL, NBL,
- + NOTROT, p, PSKIPPED, q, ROWSKIP, SWBAND
+ $ ISWROT, jbc, jgl, KBL, LKAHEAD, MVL, NBL,
+ $ NOTROT, p, PSKIPPED, q, ROWSKIP, SWBAND
LOGICAL APPLV, ROTOK, RSVEC
* ..
* .. Local Arrays ..
REAL FASTR( 5 )
* ..
* .. Intrinsic Functions ..
- INTRINSIC ABS, AMAX1, AMIN1, FLOAT, MIN0, SIGN, SQRT
+ INTRINSIC ABS, MAX, FLOAT, MIN, SIGN, SQRT
* ..
* .. External Functions ..
REAL SDOT, SNRM2
INFO = -5
ELSE IF( ( RSVEC.OR.APPLV ) .AND. ( MV.LT.0 ) ) THEN
INFO = -8
- ELSE IF( ( RSVEC.AND.( LDV.LT.N ) ).OR.
- & ( APPLV.AND.( LDV.LT.MV ) ) ) THEN
+ ELSE IF( ( RSVEC.AND.( LDV.LT.N ) ).OR.
+ $ ( APPLV.AND.( LDV.LT.MV ) ) ) THEN
INFO = -10
ELSE IF( TOL.LE.EPS ) THEN
INFO = -13
BIGTHETA = ONE / ROOTEPS
ROOTTOL = SQRT( TOL )
*
-*
* .. Row-cyclic Jacobi SVD algorithm with column pivoting ..
*
EMPTSW = ( N*( N-1 ) ) / 2
* Jacobi SVD algorithm SGESVJ. For sweeps i=1:SWBAND the procedure
* ......
- KBL = MIN0( 8, N )
+ KBL = MIN( 8, N )
*[TP] KBL is a tuning parameter that defines the tile size in the
* tiling of the p-q loops of pivot pairs. In general, an optimal
* value of KBL depends on the matrix dimensions and on the
BLSKIP = ( KBL**2 ) + 1
*[TP] BLKSKIP is a tuning parameter that depends on SWBAND and KBL.
- ROWSKIP = MIN0( 5, KBL )
+ ROWSKIP = MIN( 5, KBL )
*[TP] ROWSKIP is a tuning parameter.
LKAHEAD = 1
igl = ( ibr-1 )*KBL + 1
*
- DO 1002 ir1 = 0, MIN0( LKAHEAD, NBL-ibr )
+ DO 1002 ir1 = 0, MIN( LKAHEAD, NBL-ibr )
*
igl = igl + ir1*KBL
*
- DO 2001 p = igl, MIN0( igl+KBL-1, N-1 )
+ DO 2001 p = igl, MIN( igl+KBL-1, N-1 )
* .. de Rijk's pivoting
q = ISAMAX( N-p+1, SVA( p ), 1 ) + p - 1
IF( p.NE.q ) THEN
CALL SSWAP( M, A( 1, p ), 1, A( 1, q ), 1 )
IF( RSVEC )CALL SSWAP( MVL, V( 1, p ), 1,
- + V( 1, q ), 1 )
+ $ V( 1, q ), 1 )
TEMP1 = SVA( p )
SVA( p ) = SVA( q )
SVA( q ) = TEMP1
* below should read "AAPP = SNRM2( M, A(1,p), 1 ) * D(p)".
*
IF( ( SVA( p ).LT.ROOTBIG ) .AND.
- + ( SVA( p ).GT.ROOTSFMIN ) ) THEN
+ $ ( SVA( p ).GT.ROOTSFMIN ) ) THEN
SVA( p ) = SNRM2( M, A( 1, p ), 1 )*D( p )
ELSE
TEMP1 = ZERO
*
PSKIPPED = 0
*
- DO 2002 q = p + 1, MIN0( igl+KBL-1, N )
+ DO 2002 q = p + 1, MIN( igl+KBL-1, N )
*
AAQQ = SVA( q )
ROTOK = ( SMALL*AAPP ).LE.AAQQ
IF( AAPP.LT.( BIG / AAQQ ) ) THEN
AAPQ = ( SDOT( M, A( 1, p ), 1, A( 1,
- + q ), 1 )*D( p )*D( q ) / AAQQ )
- + / AAPP
+ $ 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 )
+ $ M, 1, WORK, LDA, IERR )
AAPQ = SDOT( M, WORK, 1, A( 1, q ),
- + 1 )*D( q ) / AAQQ
+ $ 1 )*D( q ) / AAQQ
END IF
ELSE
ROTOK = AAPP.LE.( AAQQ / SMALL )
IF( AAPP.GT.( SMALL / AAQQ ) ) THEN
AAPQ = ( SDOT( M, A( 1, p ), 1, A( 1,
- + q ), 1 )*D( p )*D( q ) / AAQQ )
- + / AAPP
+ $ 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 )
+ $ M, 1, WORK, LDA, IERR )
AAPQ = SDOT( M, WORK, 1, A( 1, p ),
- + 1 )*D( p ) / AAPP
+ $ 1 )*D( p ) / AAPP
END IF
END IF
*
- MXAAPQ = AMAX1( MXAAPQ, ABS( AAPQ ) )
+ MXAAPQ = MAX( MXAAPQ, ABS( AAPQ ) )
*
* TO rotate or NOT to rotate, THAT is the question ...
*
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 )
+ $ A( 1, q ), 1, FASTR )
IF( RSVEC )CALL SROTM( MVL,
- + V( 1, p ), 1,
- + V( 1, q ), 1,
- + FASTR )
- SVA( q ) = AAQQ*SQRT( AMAX1( ZERO,
- + ONE+T*APOAQ*AAPQ ) )
- AAPP = AAPP*SQRT( AMAX1( ZERO,
- + ONE-T*AQOAP*AAPQ ) )
- MXSINJ = AMAX1( MXSINJ, ABS( T ) )
+ $ 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
*
*
THSIGN = -SIGN( ONE, AAPQ )
T = ONE / ( THETA+THSIGN*
- + SQRT( ONE+THETA*THETA ) )
+ $ SQRT( ONE+THETA*THETA ) )
CS = SQRT( ONE / ( ONE+T*T ) )
SN = T*CS
*
- MXSINJ = AMAX1( MXSINJ, ABS( SN ) )
- SVA( q ) = AAQQ*SQRT( AMAX1( ZERO,
- + ONE+T*APOAQ*AAPQ ) )
- AAPP = AAPP*SQRT( AMAX1( ZERO,
- + ONE-T*AQOAP*AAPQ ) )
+ 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 )
D( p ) = D( p )*CS
D( q ) = D( q )*CS
CALL SROTM( M, A( 1, p ), 1,
- + A( 1, q ), 1,
- + FASTR )
+ $ A( 1, q ), 1,
+ $ FASTR )
IF( RSVEC )CALL SROTM( MVL,
- + V( 1, p ), 1, V( 1, q ),
- + 1, FASTR )
+ $ V( 1, p ), 1, V( 1, q ),
+ $ 1, FASTR )
ELSE
CALL SAXPY( M, -T*AQOAP,
- + A( 1, q ), 1,
- + A( 1, p ), 1 )
+ $ A( 1, q ), 1,
+ $ A( 1, p ), 1 )
CALL SAXPY( M, CS*SN*APOAQ,
- + A( 1, p ), 1,
- + A( 1, q ), 1 )
+ $ 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 )
+ $ V( 1, q ), 1,
+ $ V( 1, p ), 1 )
CALL SAXPY( MVL,
- + CS*SN*APOAQ,
- + V( 1, p ), 1,
- + V( 1, q ), 1 )
+ $ CS*SN*APOAQ,
+ $ V( 1, p ), 1,
+ $ V( 1, q ), 1 )
END IF
END IF
ELSE
IF( D( q ).GE.ONE ) THEN
CALL SAXPY( M, T*APOAQ,
- + A( 1, p ), 1,
- + A( 1, q ), 1 )
+ $ A( 1, p ), 1,
+ $ A( 1, q ), 1 )
CALL SAXPY( M, -CS*SN*AQOAP,
- + A( 1, q ), 1,
- + A( 1, p ), 1 )
+ $ 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 )
+ $ V( 1, p ), 1,
+ $ V( 1, q ), 1 )
CALL SAXPY( MVL,
- + -CS*SN*AQOAP,
- + V( 1, q ), 1,
- + V( 1, p ), 1 )
+ $ -CS*SN*AQOAP,
+ $ V( 1, q ), 1,
+ $ V( 1, p ), 1 )
END IF
ELSE
IF( D( p ).GE.D( q ) ) THEN
CALL SAXPY( M, -T*AQOAP,
- + A( 1, q ), 1,
- + A( 1, p ), 1 )
+ $ A( 1, q ), 1,
+ $ A( 1, p ), 1 )
CALL SAXPY( M, CS*SN*APOAQ,
- + A( 1, p ), 1,
- + A( 1, q ), 1 )
+ $ 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 )
+ $ -T*AQOAP,
+ $ V( 1, q ), 1,
+ $ V( 1, p ), 1 )
CALL SAXPY( MVL,
- + CS*SN*APOAQ,
- + V( 1, p ), 1,
- + V( 1, q ), 1 )
+ $ 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 )
+ $ A( 1, p ), 1,
+ $ A( 1, q ), 1 )
CALL SAXPY( M,
- + -CS*SN*AQOAP,
- + A( 1, q ), 1,
- + A( 1, p ), 1 )
+ $ -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 )
+ $ T*APOAQ, V( 1, p ),
+ $ 1, V( 1, q ), 1 )
CALL SAXPY( MVL,
- + -CS*SN*AQOAP,
- + V( 1, q ), 1,
- + V( 1, p ), 1 )
+ $ -CS*SN*AQOAP,
+ $ V( 1, q ), 1,
+ $ V( 1, p ), 1 )
END IF
END IF
END IF
* .. have to use modified Gram-Schmidt like transformation
CALL SCOPY( M, A( 1, p ), 1, WORK, 1 )
CALL SLASCL( 'G', 0, 0, AAPP, ONE, M,
- + 1, WORK, LDA, IERR )
+ $ 1, WORK, LDA, IERR )
CALL SLASCL( 'G', 0, 0, AAQQ, ONE, M,
- + 1, A( 1, q ), LDA, IERR )
+ $ 1, A( 1, q ), LDA, IERR )
TEMP1 = -AAPQ*D( p ) / D( q )
CALL SAXPY( M, TEMP1, WORK, 1,
- + A( 1, q ), 1 )
+ $ A( 1, q ), 1 )
CALL SLASCL( 'G', 0, 0, ONE, AAQQ, M,
- + 1, A( 1, q ), LDA, IERR )
- SVA( q ) = AAQQ*SQRT( AMAX1( ZERO,
- + ONE-AAPQ*AAPQ ) )
- MXSINJ = AMAX1( MXSINJ, SFMIN )
+ $ 1, A( 1, q ), LDA, IERR )
+ SVA( q ) = AAQQ*SQRT( MAX( ZERO,
+ $ ONE-AAPQ*AAPQ ) )
+ MXSINJ = MAX( MXSINJ, SFMIN )
END IF
* END IF ROTOK THEN ... ELSE
*
* In the case of cancellation in updating SVA(q), SVA(p)
* recompute SVA(q), SVA(p).
IF( ( SVA( q ) / AAQQ )**2.LE.ROOTEPS )
- + THEN
+ $ THEN
IF( ( AAQQ.LT.ROOTBIG ) .AND.
- + ( AAQQ.GT.ROOTSFMIN ) ) THEN
+ $ ( AAQQ.GT.ROOTSFMIN ) ) THEN
SVA( q ) = SNRM2( M, A( 1, q ), 1 )*
- + D( q )
+ $ D( q )
ELSE
T = ZERO
AAQQ = ONE
CALL SLASSQ( M, A( 1, q ), 1, T,
- + AAQQ )
+ $ AAQQ )
SVA( q ) = T*SQRT( AAQQ )*D( q )
END IF
END IF
IF( ( AAPP / AAPP0 ).LE.ROOTEPS ) THEN
IF( ( AAPP.LT.ROOTBIG ) .AND.
- + ( AAPP.GT.ROOTSFMIN ) ) THEN
+ $ ( AAPP.GT.ROOTSFMIN ) ) THEN
AAPP = SNRM2( M, A( 1, p ), 1 )*
- + D( p )
+ $ D( p )
ELSE
T = ZERO
AAPP = ONE
CALL SLASSQ( M, A( 1, p ), 1, T,
- + AAPP )
+ $ AAPP )
AAPP = T*SQRT( AAPP )*D( p )
END IF
SVA( p ) = AAPP
END IF
*
IF( ( i.LE.SWBAND ) .AND.
- + ( PSKIPPED.GT.ROWSKIP ) ) THEN
+ $ ( PSKIPPED.GT.ROWSKIP ) ) THEN
IF( ir1.EQ.0 )AAPP = -AAPP
NOTROT = 0
GO TO 2103
ELSE
SVA( p ) = AAPP
IF( ( ir1.EQ.0 ) .AND. ( AAPP.EQ.ZERO ) )
- + NOTROT = NOTROT + MIN0( igl+KBL-1, N ) - p
+ $ NOTROT = NOTROT + MIN( igl+KBL-1, N ) - p
END IF
*
2001 CONTINUE
* doing the block at ( ibr, jbc )
*
IJBLSK = 0
- DO 2100 p = igl, MIN0( igl+KBL-1, N )
+ DO 2100 p = igl, MIN( igl+KBL-1, N )
*
AAPP = SVA( p )
*
*
PSKIPPED = 0
*
- DO 2200 q = jgl, MIN0( jgl+KBL-1, N )
+ DO 2200 q = jgl, MIN( jgl+KBL-1, N )
*
AAQQ = SVA( q )
*
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
+ $ 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 )
+ $ M, 1, WORK, LDA, IERR )
AAPQ = SDOT( M, WORK, 1, A( 1, q ),
- + 1 )*D( q ) / AAQQ
+ $ 1 )*D( q ) / AAQQ
END IF
ELSE
IF( AAPP.GE.AAQQ ) THEN
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
+ $ 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 )
+ $ M, 1, WORK, LDA, IERR )
AAPQ = SDOT( M, WORK, 1, A( 1, p ),
- + 1 )*D( p ) / AAPP
+ $ 1 )*D( p ) / AAPP
END IF
END IF
*
- MXAAPQ = AMAX1( MXAAPQ, ABS( AAPQ ) )
+ MXAAPQ = MAX( MXAAPQ, ABS( AAPQ ) )
*
* TO rotate or NOT to rotate, THAT is the question ...
*
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 )
+ $ A( 1, q ), 1, FASTR )
IF( RSVEC )CALL SROTM( MVL,
- + V( 1, p ), 1,
- + V( 1, q ), 1,
- + FASTR )
- SVA( q ) = AAQQ*SQRT( AMAX1( ZERO,
- + ONE+T*APOAQ*AAPQ ) )
- AAPP = AAPP*SQRT( AMAX1( ZERO,
- + ONE-T*AQOAP*AAPQ ) )
- MXSINJ = AMAX1( MXSINJ, ABS( T ) )
+ $ 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 ) )
+ $ SQRT( ONE+THETA*THETA ) )
CS = SQRT( ONE / ( ONE+T*T ) )
SN = T*CS
- MXSINJ = AMAX1( MXSINJ, ABS( SN ) )
- SVA( q ) = AAQQ*SQRT( AMAX1( ZERO,
- + ONE+T*APOAQ*AAPQ ) )
- AAPP = AAPP*SQRT( AMAX1( ZERO,
- + ONE-T*AQOAP*AAPQ ) )
+ 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 )
D( p ) = D( p )*CS
D( q ) = D( q )*CS
CALL SROTM( M, A( 1, p ), 1,
- + A( 1, q ), 1,
- + FASTR )
+ $ A( 1, q ), 1,
+ $ FASTR )
IF( RSVEC )CALL SROTM( MVL,
- + V( 1, p ), 1, V( 1, q ),
- + 1, FASTR )
+ $ V( 1, p ), 1, V( 1, q ),
+ $ 1, FASTR )
ELSE
CALL SAXPY( M, -T*AQOAP,
- + A( 1, q ), 1,
- + A( 1, p ), 1 )
+ $ A( 1, q ), 1,
+ $ A( 1, p ), 1 )
CALL SAXPY( M, CS*SN*APOAQ,
- + A( 1, p ), 1,
- + A( 1, q ), 1 )
+ $ A( 1, p ), 1,
+ $ A( 1, q ), 1 )
IF( RSVEC ) THEN
CALL SAXPY( MVL, -T*AQOAP,
- + V( 1, q ), 1,
- + V( 1, p ), 1 )
+ $ V( 1, q ), 1,
+ $ V( 1, p ), 1 )
CALL SAXPY( MVL,
- + CS*SN*APOAQ,
- + V( 1, p ), 1,
- + V( 1, q ), 1 )
+ $ CS*SN*APOAQ,
+ $ V( 1, p ), 1,
+ $ V( 1, q ), 1 )
END IF
D( p ) = D( p )*CS
D( q ) = D( q ) / CS
ELSE
IF( D( q ).GE.ONE ) THEN
CALL SAXPY( M, T*APOAQ,
- + A( 1, p ), 1,
- + A( 1, q ), 1 )
+ $ A( 1, p ), 1,
+ $ A( 1, q ), 1 )
CALL SAXPY( M, -CS*SN*AQOAP,
- + A( 1, q ), 1,
- + A( 1, p ), 1 )
+ $ A( 1, q ), 1,
+ $ A( 1, p ), 1 )
IF( RSVEC ) THEN
CALL SAXPY( MVL, T*APOAQ,
- + V( 1, p ), 1,
- + V( 1, q ), 1 )
+ $ V( 1, p ), 1,
+ $ V( 1, q ), 1 )
CALL SAXPY( MVL,
- + -CS*SN*AQOAP,
- + V( 1, q ), 1,
- + V( 1, p ), 1 )
+ $ -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 )
+ $ A( 1, q ), 1,
+ $ A( 1, p ), 1 )
CALL SAXPY( M, CS*SN*APOAQ,
- + A( 1, p ), 1,
- + A( 1, q ), 1 )
+ $ 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 )
+ $ -T*AQOAP,
+ $ V( 1, q ), 1,
+ $ V( 1, p ), 1 )
CALL SAXPY( MVL,
- + CS*SN*APOAQ,
- + V( 1, p ), 1,
- + V( 1, q ), 1 )
+ $ 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 )
+ $ A( 1, p ), 1,
+ $ A( 1, q ), 1 )
CALL SAXPY( M,
- + -CS*SN*AQOAP,
- + A( 1, q ), 1,
- + A( 1, p ), 1 )
+ $ -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 )
+ $ T*APOAQ, V( 1, p ),
+ $ 1, V( 1, q ), 1 )
CALL SAXPY( MVL,
- + -CS*SN*AQOAP,
- + V( 1, q ), 1,
- + V( 1, p ), 1 )
+ $ -CS*SN*AQOAP,
+ $ V( 1, q ), 1,
+ $ V( 1, p ), 1 )
END IF
END IF
END IF
ELSE
IF( AAPP.GT.AAQQ ) THEN
CALL SCOPY( M, A( 1, p ), 1, WORK,
- + 1 )
+ $ 1 )
CALL SLASCL( 'G', 0, 0, AAPP, ONE,
- + M, 1, WORK, LDA, IERR )
+ $ M, 1, WORK, LDA, IERR )
CALL SLASCL( 'G', 0, 0, AAQQ, ONE,
- + M, 1, A( 1, q ), LDA,
- + IERR )
+ $ M, 1, A( 1, q ), LDA,
+ $ IERR )
TEMP1 = -AAPQ*D( p ) / D( q )
CALL SAXPY( M, TEMP1, WORK, 1,
- + A( 1, q ), 1 )
+ $ A( 1, q ), 1 )
CALL SLASCL( 'G', 0, 0, ONE, AAQQ,
- + M, 1, A( 1, q ), LDA,
- + IERR )
- SVA( q ) = AAQQ*SQRT( AMAX1( ZERO,
- + ONE-AAPQ*AAPQ ) )
- MXSINJ = AMAX1( MXSINJ, SFMIN )
+ $ 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 )
+ $ 1 )
CALL SLASCL( 'G', 0, 0, AAQQ, ONE,
- + M, 1, WORK, LDA, IERR )
+ $ M, 1, WORK, LDA, IERR )
CALL SLASCL( 'G', 0, 0, AAPP, ONE,
- + M, 1, A( 1, p ), LDA,
- + IERR )
+ $ M, 1, A( 1, p ), LDA,
+ $ IERR )
TEMP1 = -AAPQ*D( q ) / D( p )
CALL SAXPY( M, TEMP1, WORK, 1,
- + A( 1, p ), 1 )
+ $ A( 1, p ), 1 )
CALL SLASCL( 'G', 0, 0, ONE, AAPP,
- + M, 1, A( 1, p ), LDA,
- + IERR )
- SVA( p ) = AAPP*SQRT( AMAX1( ZERO,
- + ONE-AAPQ*AAPQ ) )
- MXSINJ = AMAX1( MXSINJ, SFMIN )
+ $ 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
+ $ THEN
IF( ( AAQQ.LT.ROOTBIG ) .AND.
- + ( AAQQ.GT.ROOTSFMIN ) ) THEN
+ $ ( AAQQ.GT.ROOTSFMIN ) ) THEN
SVA( q ) = SNRM2( M, A( 1, q ), 1 )*
- + D( q )
+ $ D( q )
ELSE
T = ZERO
AAQQ = ONE
CALL SLASSQ( M, A( 1, q ), 1, T,
- + AAQQ )
+ $ 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.GT.ROOTSFMIN ) ) THEN
AAPP = SNRM2( M, A( 1, p ), 1 )*
- + D( p )
+ $ D( p )
ELSE
T = ZERO
AAPP = ONE
CALL SLASSQ( M, A( 1, p ), 1, T,
- + AAPP )
+ $ AAPP )
AAPP = T*SQRT( AAPP )*D( p )
END IF
SVA( p ) = AAPP
END IF
*
IF( ( i.LE.SWBAND ) .AND. ( IJBLSK.GE.BLSKIP ) )
- + THEN
+ $ THEN
SVA( p ) = AAPP
NOTROT = 0
GO TO 2011
END IF
IF( ( i.LE.SWBAND ) .AND.
- + ( PSKIPPED.GT.ROWSKIP ) ) THEN
+ $ ( PSKIPPED.GT.ROWSKIP ) ) THEN
AAPP = -AAPP
NOTROT = 0
GO TO 2203
*
ELSE
IF( AAPP.EQ.ZERO )NOTROT = NOTROT +
- + MIN0( jgl+KBL-1, N ) - jgl + 1
+ $ MIN( jgl+KBL-1, N ) - jgl + 1
IF( AAPP.LT.ZERO )NOTROT = 0
END IF
* end of the jbc-loop
2011 CONTINUE
*2011 bailed out of the jbc-loop
- DO 2012 p = igl, MIN0( igl+KBL-1, N )
+ DO 2012 p = igl, MIN( igl+KBL-1, N )
SVA( p ) = ABS( SVA( p ) )
2012 CONTINUE
*
*
* .. update SVA(N)
IF( ( SVA( N ).LT.ROOTBIG ) .AND. ( SVA( N ).GT.ROOTSFMIN ) )
- + THEN
+ $ THEN
SVA( N ) = SNRM2( M, A( 1, N ), 1 )*D( N )
ELSE
T = ZERO
* Additional steering devices
*
IF( ( i.LT.SWBAND ) .AND. ( ( MXAAPQ.LE.ROOTTOL ) .OR.
- + ( ISWROT.LE.N ) ) )SWBAND = i
+ $ ( ISWROT.LE.N ) ) )SWBAND = i
*
IF( ( i.GT.SWBAND+1 ) .AND. ( MXAAPQ.LT.FLOAT( N )*TOL ) .AND.
- + ( FLOAT( N )*MXAAPQ*MXSINJ.LT.TOL ) ) THEN
+ $ ( FLOAT( N )*MXAAPQ*MXSINJ.LT.TOL ) ) THEN
GO TO 1994
END IF
*
projects / platform / upstream / lapack.git / blobdiff