version 1.1, 2010/08/07 13:21:03
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version 1.6, 2011/07/22 07:38:05
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SUBROUTINE DGESVJ( JOBA, JOBU, JOBV, M, N, A, LDA, SVA, MV, V, |
SUBROUTINE DGESVJ( JOBA, JOBU, JOBV, M, N, A, LDA, SVA, MV, V, |
+ LDV, WORK, LWORK, INFO ) |
$ LDV, WORK, LWORK, INFO ) |
* |
* |
* -- LAPACK routine (version 3.2.2) -- |
* -- LAPACK routine (version 3.3.1) -- |
* |
* |
* -- Contributed by Zlatko Drmac of the University of Zagreb and -- |
* -- Contributed by Zlatko Drmac of the University of Zagreb and -- |
* -- Kresimir Veselic of the Fernuniversitaet Hagen -- |
* -- Kresimir Veselic of the Fernuniversitaet Hagen -- |
* -- June 2010 -- |
* -- April 2011 -- |
* |
* |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
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* .. |
* .. |
* .. Array Arguments .. |
* .. Array Arguments .. |
DOUBLE PRECISION A( LDA, * ), SVA( N ), V( LDV, * ), |
DOUBLE PRECISION A( LDA, * ), SVA( N ), V( LDV, * ), |
+ WORK( LWORK ) |
$ WORK( LWORK ) |
* .. |
* .. |
* |
* |
* Purpose |
* Purpose |
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* referenced |
* referenced |
* |
* |
* M (input) INTEGER |
* M (input) INTEGER |
* The number of rows of the input matrix A. M >= 0. |
* The number of rows of the input matrix A. 1/DLAMCH('E') > M >= 0. |
* |
* |
* N (input) INTEGER |
* N (input) INTEGER |
* The number of columns of the input matrix A. |
* The number of columns of the input matrix A. |
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* orthogonal up to CTOL*EPS, EPS=DLAMCH('E'). |
* orthogonal up to CTOL*EPS, EPS=DLAMCH('E'). |
* It is required that CTOL >= ONE, i.e. it is not |
* It is required that CTOL >= ONE, i.e. it is not |
* allowed to force the routine to obtain orthogonality |
* allowed to force the routine to obtain orthogonality |
* below EPSILON. |
* below EPS. |
* On exit : |
* On exit : |
* WORK(1) = SCALE is the scaling factor such that SCALE*SVA(1:N) |
* WORK(1) = SCALE is the scaling factor such that SCALE*SVA(1:N) |
* are the computed singular values of A. |
* are the computed singular values of A. |
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* .. Local Parameters .. |
* .. Local Parameters .. |
DOUBLE PRECISION ZERO, HALF, ONE, TWO |
DOUBLE PRECISION ZERO, HALF, ONE, TWO |
PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0, |
PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0, |
+ TWO = 2.0D0 ) |
$ TWO = 2.0D0 ) |
INTEGER NSWEEP |
INTEGER NSWEEP |
PARAMETER ( NSWEEP = 30 ) |
PARAMETER ( NSWEEP = 30 ) |
* .. |
* .. |
* .. Local Scalars .. |
* .. Local Scalars .. |
DOUBLE PRECISION AAPP, AAPP0, AAPQ, AAQQ, APOAQ, AQOAP, BIG, |
DOUBLE PRECISION AAPP, AAPP0, AAPQ, AAQQ, APOAQ, AQOAP, BIG, |
+ BIGTHETA, CS, CTOL, EPSILON, LARGE, MXAAPQ, |
$ BIGTHETA, CS, CTOL, EPSLN, LARGE, MXAAPQ, |
+ MXSINJ, ROOTBIG, ROOTEPS, ROOTSFMIN, ROOTTOL, |
$ MXSINJ, ROOTBIG, ROOTEPS, ROOTSFMIN, ROOTTOL, |
+ SCALE, SFMIN, SMALL, SN, T, TEMP1, THETA, |
$ SKL, SFMIN, SMALL, SN, T, TEMP1, THETA, |
+ THSIGN, TOL |
$ THSIGN, TOL |
INTEGER BLSKIP, EMPTSW, i, ibr, IERR, igl, IJBLSK, ir1, |
INTEGER BLSKIP, EMPTSW, i, ibr, IERR, igl, IJBLSK, ir1, |
+ ISWROT, jbc, jgl, KBL, LKAHEAD, MVL, N2, N34, |
$ ISWROT, jbc, jgl, KBL, LKAHEAD, MVL, N2, N34, |
+ N4, NBL, NOTROT, p, PSKIPPED, q, ROWSKIP, |
$ N4, NBL, NOTROT, p, PSKIPPED, q, ROWSKIP, |
+ SWBAND |
$ SWBAND |
LOGICAL APPLV, GOSCALE, LOWER, LSVEC, NOSCALE, ROTOK, |
LOGICAL APPLV, GOSCALE, LOWER, LSVEC, NOSCALE, ROTOK, |
+ RSVEC, UCTOL, UPPER |
$ RSVEC, UCTOL, UPPER |
* .. |
* .. |
* .. Local Arrays .. |
* .. Local Arrays .. |
DOUBLE PRECISION FASTR( 5 ) |
DOUBLE PRECISION FASTR( 5 ) |
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ELSE IF( MV.LT.0 ) THEN |
ELSE IF( MV.LT.0 ) THEN |
INFO = -9 |
INFO = -9 |
ELSE IF( ( RSVEC .AND. ( LDV.LT.N ) ) .OR. |
ELSE IF( ( RSVEC .AND. ( LDV.LT.N ) ) .OR. |
+ ( APPLV .AND. ( LDV.LT.MV ) ) ) THEN |
$ ( APPLV .AND. ( LDV.LT.MV ) ) ) THEN |
INFO = -11 |
INFO = -11 |
ELSE IF( UCTOL .AND. ( WORK( 1 ).LE.ONE ) ) THEN |
ELSE IF( UCTOL .AND. ( WORK( 1 ).LE.ONE ) ) THEN |
INFO = -12 |
INFO = -12 |
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* ... and the machine dependent parameters are |
* ... and the machine dependent parameters are |
*[!] (Make sure that DLAMCH() works properly on the target machine.) |
*[!] (Make sure that DLAMCH() works properly on the target machine.) |
* |
* |
EPSILON = DLAMCH( 'Epsilon' ) |
EPSLN = DLAMCH( 'Epsilon' ) |
ROOTEPS = DSQRT( EPSILON ) |
ROOTEPS = DSQRT( EPSLN ) |
SFMIN = DLAMCH( 'SafeMinimum' ) |
SFMIN = DLAMCH( 'SafeMinimum' ) |
ROOTSFMIN = DSQRT( SFMIN ) |
ROOTSFMIN = DSQRT( SFMIN ) |
SMALL = SFMIN / EPSILON |
SMALL = SFMIN / EPSLN |
BIG = DLAMCH( 'Overflow' ) |
BIG = DLAMCH( 'Overflow' ) |
* BIG = ONE / SFMIN |
* BIG = ONE / SFMIN |
ROOTBIG = ONE / ROOTSFMIN |
ROOTBIG = ONE / ROOTSFMIN |
LARGE = BIG / DSQRT( DBLE( M*N ) ) |
LARGE = BIG / DSQRT( DBLE( M*N ) ) |
BIGTHETA = ONE / ROOTEPS |
BIGTHETA = ONE / ROOTEPS |
* |
* |
TOL = CTOL*EPSILON |
TOL = CTOL*EPSLN |
ROOTTOL = DSQRT( TOL ) |
ROOTTOL = DSQRT( TOL ) |
* |
* |
IF( DBLE( M )*EPSILON.GE.ONE ) THEN |
IF( DBLE( M )*EPSLN.GE.ONE ) THEN |
INFO = -5 |
INFO = -4 |
CALL XERBLA( 'DGESVJ', -INFO ) |
CALL XERBLA( 'DGESVJ', -INFO ) |
RETURN |
RETURN |
END IF |
END IF |
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* DSQRT(N)*max_i SVA(i) does not overflow. If INFinite entries |
* DSQRT(N)*max_i SVA(i) does not overflow. If INFinite entries |
* in A are detected, the procedure returns with INFO=-6. |
* in A are detected, the procedure returns with INFO=-6. |
* |
* |
SCALE = ONE / DSQRT( DBLE( M )*DBLE( N ) ) |
SKL= ONE / DSQRT( DBLE( M )*DBLE( N ) ) |
NOSCALE = .TRUE. |
NOSCALE = .TRUE. |
GOSCALE = .TRUE. |
GOSCALE = .TRUE. |
* |
* |
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* the input matrix is M-by-N lower triangular (trapezoidal) |
* the input matrix is M-by-N lower triangular (trapezoidal) |
DO 1874 p = 1, N |
DO 1874 p = 1, N |
AAPP = ZERO |
AAPP = ZERO |
AAQQ = ZERO |
AAQQ = ONE |
CALL DLASSQ( M-p+1, A( p, p ), 1, AAPP, AAQQ ) |
CALL DLASSQ( M-p+1, A( p, p ), 1, AAPP, AAQQ ) |
IF( AAPP.GT.BIG ) THEN |
IF( AAPP.GT.BIG ) THEN |
INFO = -6 |
INFO = -6 |
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SVA( p ) = AAPP*AAQQ |
SVA( p ) = AAPP*AAQQ |
ELSE |
ELSE |
NOSCALE = .FALSE. |
NOSCALE = .FALSE. |
SVA( p ) = AAPP*( AAQQ*SCALE ) |
SVA( p ) = AAPP*( AAQQ*SKL) |
IF( GOSCALE ) THEN |
IF( GOSCALE ) THEN |
GOSCALE = .FALSE. |
GOSCALE = .FALSE. |
DO 1873 q = 1, p - 1 |
DO 1873 q = 1, p - 1 |
SVA( q ) = SVA( q )*SCALE |
SVA( q ) = SVA( q )*SKL |
1873 CONTINUE |
1873 CONTINUE |
END IF |
END IF |
END IF |
END IF |
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* the input matrix is M-by-N upper triangular (trapezoidal) |
* the input matrix is M-by-N upper triangular (trapezoidal) |
DO 2874 p = 1, N |
DO 2874 p = 1, N |
AAPP = ZERO |
AAPP = ZERO |
AAQQ = ZERO |
AAQQ = ONE |
CALL DLASSQ( p, A( 1, p ), 1, AAPP, AAQQ ) |
CALL DLASSQ( p, A( 1, p ), 1, AAPP, AAQQ ) |
IF( AAPP.GT.BIG ) THEN |
IF( AAPP.GT.BIG ) THEN |
INFO = -6 |
INFO = -6 |
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SVA( p ) = AAPP*AAQQ |
SVA( p ) = AAPP*AAQQ |
ELSE |
ELSE |
NOSCALE = .FALSE. |
NOSCALE = .FALSE. |
SVA( p ) = AAPP*( AAQQ*SCALE ) |
SVA( p ) = AAPP*( AAQQ*SKL) |
IF( GOSCALE ) THEN |
IF( GOSCALE ) THEN |
GOSCALE = .FALSE. |
GOSCALE = .FALSE. |
DO 2873 q = 1, p - 1 |
DO 2873 q = 1, p - 1 |
SVA( q ) = SVA( q )*SCALE |
SVA( q ) = SVA( q )*SKL |
2873 CONTINUE |
2873 CONTINUE |
END IF |
END IF |
END IF |
END IF |
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* the input matrix is M-by-N general dense |
* the input matrix is M-by-N general dense |
DO 3874 p = 1, N |
DO 3874 p = 1, N |
AAPP = ZERO |
AAPP = ZERO |
AAQQ = ZERO |
AAQQ = ONE |
CALL DLASSQ( M, A( 1, p ), 1, AAPP, AAQQ ) |
CALL DLASSQ( M, A( 1, p ), 1, AAPP, AAQQ ) |
IF( AAPP.GT.BIG ) THEN |
IF( AAPP.GT.BIG ) THEN |
INFO = -6 |
INFO = -6 |
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SVA( p ) = AAPP*AAQQ |
SVA( p ) = AAPP*AAQQ |
ELSE |
ELSE |
NOSCALE = .FALSE. |
NOSCALE = .FALSE. |
SVA( p ) = AAPP*( AAQQ*SCALE ) |
SVA( p ) = AAPP*( AAQQ*SKL) |
IF( GOSCALE ) THEN |
IF( GOSCALE ) THEN |
GOSCALE = .FALSE. |
GOSCALE = .FALSE. |
DO 3873 q = 1, p - 1 |
DO 3873 q = 1, p - 1 |
SVA( q ) = SVA( q )*SCALE |
SVA( q ) = SVA( q )*SKL |
3873 CONTINUE |
3873 CONTINUE |
END IF |
END IF |
END IF |
END IF |
3874 CONTINUE |
3874 CONTINUE |
END IF |
END IF |
* |
* |
IF( NOSCALE )SCALE = ONE |
IF( NOSCALE )SKL= ONE |
* |
* |
* Move the smaller part of the spectrum from the underflow threshold |
* Move the smaller part of the spectrum from the underflow threshold |
*(!) Start by determining the position of the nonzero entries of the |
*(!) Start by determining the position of the nonzero entries of the |
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* #:) Quick return for one-column matrix |
* #:) Quick return for one-column matrix |
* |
* |
IF( N.EQ.1 ) THEN |
IF( N.EQ.1 ) THEN |
IF( LSVEC )CALL DLASCL( 'G', 0, 0, SVA( 1 ), SCALE, M, 1, |
IF( LSVEC )CALL DLASCL( 'G', 0, 0, SVA( 1 ), SKL, M, 1, |
+ A( 1, 1 ), LDA, IERR ) |
$ A( 1, 1 ), LDA, IERR ) |
WORK( 1 ) = ONE / SCALE |
WORK( 1 ) = ONE / SKL |
IF( SVA( 1 ).GE.SFMIN ) THEN |
IF( SVA( 1 ).GE.SFMIN ) THEN |
WORK( 2 ) = ONE |
WORK( 2 ) = ONE |
ELSE |
ELSE |
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* Protect small singular values from underflow, and try to |
* Protect small singular values from underflow, and try to |
* avoid underflows/overflows in computing Jacobi rotations. |
* avoid underflows/overflows in computing Jacobi rotations. |
* |
* |
SN = DSQRT( SFMIN / EPSILON ) |
SN = DSQRT( SFMIN / EPSLN ) |
TEMP1 = DSQRT( BIG / DBLE( N ) ) |
TEMP1 = DSQRT( BIG / DBLE( N ) ) |
IF( ( AAPP.LE.SN ) .OR. ( AAQQ.GE.TEMP1 ) .OR. |
IF( ( AAPP.LE.SN ) .OR. ( AAQQ.GE.TEMP1 ) .OR. |
+ ( ( SN.LE.AAQQ ) .AND. ( AAPP.LE.TEMP1 ) ) ) THEN |
$ ( ( SN.LE.AAQQ ) .AND. ( AAPP.LE.TEMP1 ) ) ) THEN |
TEMP1 = DMIN1( BIG, TEMP1 / AAPP ) |
TEMP1 = DMIN1( BIG, TEMP1 / AAPP ) |
* AAQQ = AAQQ*TEMP1 |
* AAQQ = AAQQ*TEMP1 |
* AAPP = AAPP*TEMP1 |
* AAPP = AAPP*TEMP1 |
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IF( TEMP1.NE.ONE ) THEN |
IF( TEMP1.NE.ONE ) THEN |
CALL DLASCL( 'G', 0, 0, ONE, TEMP1, N, 1, SVA, N, IERR ) |
CALL DLASCL( 'G', 0, 0, ONE, TEMP1, N, 1, SVA, N, IERR ) |
END IF |
END IF |
SCALE = TEMP1*SCALE |
SKL= TEMP1*SKL |
IF( SCALE.NE.ONE ) THEN |
IF( SKL.NE.ONE ) THEN |
CALL DLASCL( JOBA, 0, 0, ONE, SCALE, M, N, A, LDA, IERR ) |
CALL DLASCL( JOBA, 0, 0, ONE, SKL, M, N, A, LDA, IERR ) |
SCALE = ONE / SCALE |
SKL= ONE / SKL |
END IF |
END IF |
* |
* |
* Row-cyclic Jacobi SVD algorithm with column pivoting |
* Row-cyclic Jacobi SVD algorithm with column pivoting |
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* [+ + x x] [x x]. [x x] |
* [+ + x x] [x x]. [x x] |
* |
* |
CALL DGSVJ0( JOBV, M-N34, N-N34, A( N34+1, N34+1 ), LDA, |
CALL DGSVJ0( JOBV, M-N34, N-N34, A( N34+1, N34+1 ), LDA, |
+ WORK( N34+1 ), SVA( N34+1 ), MVL, |
$ WORK( N34+1 ), SVA( N34+1 ), MVL, |
+ V( N34*q+1, N34+1 ), LDV, EPSILON, SFMIN, TOL, |
$ V( N34*q+1, N34+1 ), LDV, EPSLN, SFMIN, TOL, |
+ 2, WORK( N+1 ), LWORK-N, IERR ) |
$ 2, WORK( N+1 ), LWORK-N, IERR ) |
* |
* |
CALL DGSVJ0( JOBV, M-N2, N34-N2, A( N2+1, N2+1 ), LDA, |
CALL DGSVJ0( JOBV, M-N2, N34-N2, A( N2+1, N2+1 ), LDA, |
+ WORK( N2+1 ), SVA( N2+1 ), MVL, |
$ WORK( N2+1 ), SVA( N2+1 ), MVL, |
+ V( N2*q+1, N2+1 ), LDV, EPSILON, SFMIN, TOL, 2, |
$ V( N2*q+1, N2+1 ), LDV, EPSLN, SFMIN, TOL, 2, |
+ WORK( N+1 ), LWORK-N, IERR ) |
$ WORK( N+1 ), LWORK-N, IERR ) |
* |
* |
CALL DGSVJ1( JOBV, M-N2, N-N2, N4, A( N2+1, N2+1 ), LDA, |
CALL DGSVJ1( JOBV, M-N2, N-N2, N4, A( N2+1, N2+1 ), LDA, |
+ WORK( N2+1 ), SVA( N2+1 ), MVL, |
$ WORK( N2+1 ), SVA( N2+1 ), MVL, |
+ V( N2*q+1, N2+1 ), LDV, EPSILON, SFMIN, TOL, 1, |
$ V( N2*q+1, N2+1 ), LDV, EPSLN, SFMIN, TOL, 1, |
+ WORK( N+1 ), LWORK-N, IERR ) |
$ WORK( N+1 ), LWORK-N, IERR ) |
* |
* |
CALL DGSVJ0( JOBV, M-N4, N2-N4, A( N4+1, N4+1 ), LDA, |
CALL DGSVJ0( JOBV, M-N4, N2-N4, A( N4+1, N4+1 ), LDA, |
+ WORK( N4+1 ), SVA( N4+1 ), MVL, |
$ WORK( N4+1 ), SVA( N4+1 ), MVL, |
+ V( N4*q+1, N4+1 ), LDV, EPSILON, SFMIN, TOL, 1, |
$ V( N4*q+1, N4+1 ), LDV, EPSLN, SFMIN, TOL, 1, |
+ WORK( N+1 ), LWORK-N, IERR ) |
$ WORK( N+1 ), LWORK-N, IERR ) |
* |
* |
CALL DGSVJ0( JOBV, M, N4, A, LDA, WORK, SVA, MVL, V, LDV, |
CALL DGSVJ0( JOBV, M, N4, A, LDA, WORK, SVA, MVL, V, LDV, |
+ EPSILON, SFMIN, TOL, 1, WORK( N+1 ), LWORK-N, |
$ EPSLN, SFMIN, TOL, 1, WORK( N+1 ), LWORK-N, |
+ IERR ) |
$ IERR ) |
* |
* |
CALL DGSVJ1( JOBV, M, N2, N4, A, LDA, WORK, SVA, MVL, V, |
CALL DGSVJ1( JOBV, M, N2, N4, A, LDA, WORK, SVA, MVL, V, |
+ LDV, EPSILON, SFMIN, TOL, 1, WORK( N+1 ), |
$ LDV, EPSLN, SFMIN, TOL, 1, WORK( N+1 ), |
+ LWORK-N, IERR ) |
$ LWORK-N, IERR ) |
* |
* |
* |
* |
ELSE IF( UPPER ) THEN |
ELSE IF( UPPER ) THEN |
* |
* |
* |
* |
CALL DGSVJ0( JOBV, N4, N4, A, LDA, WORK, SVA, MVL, V, LDV, |
CALL DGSVJ0( JOBV, N4, N4, A, LDA, WORK, SVA, MVL, V, LDV, |
+ EPSILON, SFMIN, TOL, 2, WORK( N+1 ), LWORK-N, |
$ EPSLN, SFMIN, TOL, 2, WORK( N+1 ), LWORK-N, |
+ IERR ) |
$ IERR ) |
* |
* |
CALL DGSVJ0( JOBV, N2, N4, A( 1, N4+1 ), LDA, WORK( N4+1 ), |
CALL DGSVJ0( JOBV, N2, N4, A( 1, N4+1 ), LDA, WORK( N4+1 ), |
+ SVA( N4+1 ), MVL, V( N4*q+1, N4+1 ), LDV, |
$ SVA( N4+1 ), MVL, V( N4*q+1, N4+1 ), LDV, |
+ EPSILON, SFMIN, TOL, 1, WORK( N+1 ), LWORK-N, |
$ EPSLN, SFMIN, TOL, 1, WORK( N+1 ), LWORK-N, |
+ IERR ) |
$ IERR ) |
* |
* |
CALL DGSVJ1( JOBV, N2, N2, N4, A, LDA, WORK, SVA, MVL, V, |
CALL DGSVJ1( JOBV, N2, N2, N4, A, LDA, WORK, SVA, MVL, V, |
+ LDV, EPSILON, SFMIN, TOL, 1, WORK( N+1 ), |
$ LDV, EPSLN, SFMIN, TOL, 1, WORK( N+1 ), |
+ LWORK-N, IERR ) |
$ LWORK-N, IERR ) |
* |
* |
CALL DGSVJ0( JOBV, N2+N4, N4, A( 1, N2+1 ), LDA, |
CALL DGSVJ0( JOBV, N2+N4, N4, A( 1, N2+1 ), LDA, |
+ WORK( N2+1 ), SVA( N2+1 ), MVL, |
$ WORK( N2+1 ), SVA( N2+1 ), MVL, |
+ V( N2*q+1, N2+1 ), LDV, EPSILON, SFMIN, TOL, 1, |
$ V( N2*q+1, N2+1 ), LDV, EPSLN, SFMIN, TOL, 1, |
+ WORK( N+1 ), LWORK-N, IERR ) |
$ WORK( N+1 ), LWORK-N, IERR ) |
|
|
END IF |
END IF |
* |
* |
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IF( p.NE.q ) THEN |
IF( p.NE.q ) THEN |
CALL DSWAP( M, A( 1, p ), 1, A( 1, q ), 1 ) |
CALL DSWAP( M, A( 1, p ), 1, A( 1, q ), 1 ) |
IF( RSVEC )CALL DSWAP( MVL, V( 1, p ), 1, |
IF( RSVEC )CALL DSWAP( MVL, V( 1, p ), 1, |
+ V( 1, q ), 1 ) |
$ V( 1, q ), 1 ) |
TEMP1 = SVA( p ) |
TEMP1 = SVA( p ) |
SVA( p ) = SVA( q ) |
SVA( p ) = SVA( q ) |
SVA( q ) = TEMP1 |
SVA( q ) = TEMP1 |
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* below should read "AAPP = DNRM2( M, A(1,p), 1 ) * WORK(p)". |
* below should read "AAPP = DNRM2( M, A(1,p), 1 ) * WORK(p)". |
* |
* |
IF( ( SVA( p ).LT.ROOTBIG ) .AND. |
IF( ( SVA( p ).LT.ROOTBIG ) .AND. |
+ ( SVA( p ).GT.ROOTSFMIN ) ) THEN |
$ ( SVA( p ).GT.ROOTSFMIN ) ) THEN |
SVA( p ) = DNRM2( M, A( 1, p ), 1 )*WORK( p ) |
SVA( p ) = DNRM2( M, A( 1, p ), 1 )*WORK( p ) |
ELSE |
ELSE |
TEMP1 = ZERO |
TEMP1 = ZERO |
AAPP = ZERO |
AAPP = ONE |
CALL DLASSQ( M, A( 1, p ), 1, TEMP1, AAPP ) |
CALL DLASSQ( M, A( 1, p ), 1, TEMP1, AAPP ) |
SVA( p ) = TEMP1*DSQRT( AAPP )*WORK( p ) |
SVA( p ) = TEMP1*DSQRT( AAPP )*WORK( p ) |
END IF |
END IF |
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ROTOK = ( SMALL*AAPP ).LE.AAQQ |
ROTOK = ( SMALL*AAPP ).LE.AAQQ |
IF( AAPP.LT.( BIG / AAQQ ) ) THEN |
IF( AAPP.LT.( BIG / AAQQ ) ) THEN |
AAPQ = ( DDOT( M, A( 1, p ), 1, A( 1, |
AAPQ = ( DDOT( M, A( 1, p ), 1, A( 1, |
+ q ), 1 )*WORK( p )*WORK( q ) / |
$ q ), 1 )*WORK( p )*WORK( q ) / |
+ AAQQ ) / AAPP |
$ AAQQ ) / AAPP |
ELSE |
ELSE |
CALL DCOPY( M, A( 1, p ), 1, |
CALL DCOPY( M, A( 1, p ), 1, |
+ WORK( N+1 ), 1 ) |
$ WORK( N+1 ), 1 ) |
CALL DLASCL( 'G', 0, 0, AAPP, |
CALL DLASCL( 'G', 0, 0, AAPP, |
+ WORK( p ), M, 1, |
$ WORK( p ), M, 1, |
+ WORK( N+1 ), LDA, IERR ) |
$ WORK( N+1 ), LDA, IERR ) |
AAPQ = DDOT( M, WORK( N+1 ), 1, |
AAPQ = DDOT( M, WORK( N+1 ), 1, |
+ A( 1, q ), 1 )*WORK( q ) / AAQQ |
$ A( 1, q ), 1 )*WORK( q ) / AAQQ |
END IF |
END IF |
ELSE |
ELSE |
ROTOK = AAPP.LE.( AAQQ / SMALL ) |
ROTOK = AAPP.LE.( AAQQ / SMALL ) |
IF( AAPP.GT.( SMALL / AAQQ ) ) THEN |
IF( AAPP.GT.( SMALL / AAQQ ) ) THEN |
AAPQ = ( DDOT( M, A( 1, p ), 1, A( 1, |
AAPQ = ( DDOT( M, A( 1, p ), 1, A( 1, |
+ q ), 1 )*WORK( p )*WORK( q ) / |
$ q ), 1 )*WORK( p )*WORK( q ) / |
+ AAQQ ) / AAPP |
$ AAQQ ) / AAPP |
ELSE |
ELSE |
CALL DCOPY( M, A( 1, q ), 1, |
CALL DCOPY( M, A( 1, q ), 1, |
+ WORK( N+1 ), 1 ) |
$ WORK( N+1 ), 1 ) |
CALL DLASCL( 'G', 0, 0, AAQQ, |
CALL DLASCL( 'G', 0, 0, AAQQ, |
+ WORK( q ), M, 1, |
$ WORK( q ), M, 1, |
+ WORK( N+1 ), LDA, IERR ) |
$ WORK( N+1 ), LDA, IERR ) |
AAPQ = DDOT( M, WORK( N+1 ), 1, |
AAPQ = DDOT( M, WORK( N+1 ), 1, |
+ A( 1, p ), 1 )*WORK( p ) / AAPP |
$ A( 1, p ), 1 )*WORK( p ) / AAPP |
END IF |
END IF |
END IF |
END IF |
* |
* |
Line 824
|
Line 824
|
* |
* |
AQOAP = AAQQ / AAPP |
AQOAP = AAQQ / AAPP |
APOAQ = AAPP / AAQQ |
APOAQ = AAPP / AAQQ |
THETA = -HALF*DABS( AQOAP-APOAQ ) / |
THETA = -HALF*DABS(AQOAP-APOAQ)/AAPQ |
+ AAPQ |
|
* |
* |
IF( DABS( THETA ).GT.BIGTHETA ) THEN |
IF( DABS( THETA ).GT.BIGTHETA ) THEN |
* |
* |
T = HALF / THETA |
T = HALF / THETA |
FASTR( 3 ) = T*WORK( p ) / WORK( q ) |
FASTR( 3 ) = T*WORK( p ) / WORK( q ) |
FASTR( 4 ) = -T*WORK( q ) / |
FASTR( 4 ) = -T*WORK( q ) / |
+ WORK( p ) |
$ WORK( p ) |
CALL DROTM( M, A( 1, p ), 1, |
CALL DROTM( M, A( 1, p ), 1, |
+ A( 1, q ), 1, FASTR ) |
$ A( 1, q ), 1, FASTR ) |
IF( RSVEC )CALL DROTM( MVL, |
IF( RSVEC )CALL DROTM( MVL, |
+ V( 1, p ), 1, |
$ V( 1, p ), 1, |
+ V( 1, q ), 1, |
$ V( 1, q ), 1, |
+ FASTR ) |
$ FASTR ) |
SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO, |
SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO, |
+ ONE+T*APOAQ*AAPQ ) ) |
$ ONE+T*APOAQ*AAPQ ) ) |
AAPP = AAPP*DSQRT( ONE-T*AQOAP* |
AAPP = AAPP*DSQRT( DMAX1( ZERO, |
+ AAPQ ) |
$ ONE-T*AQOAP*AAPQ ) ) |
MXSINJ = DMAX1( MXSINJ, DABS( T ) ) |
MXSINJ = DMAX1( MXSINJ, DABS( T ) ) |
* |
* |
ELSE |
ELSE |
Line 851
|
Line 850
|
* |
* |
THSIGN = -DSIGN( ONE, AAPQ ) |
THSIGN = -DSIGN( ONE, AAPQ ) |
T = ONE / ( THETA+THSIGN* |
T = ONE / ( THETA+THSIGN* |
+ DSQRT( ONE+THETA*THETA ) ) |
$ DSQRT( ONE+THETA*THETA ) ) |
CS = DSQRT( ONE / ( ONE+T*T ) ) |
CS = DSQRT( ONE / ( ONE+T*T ) ) |
SN = T*CS |
SN = T*CS |
* |
* |
MXSINJ = DMAX1( MXSINJ, DABS( SN ) ) |
MXSINJ = DMAX1( MXSINJ, DABS( SN ) ) |
SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO, |
SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO, |
+ ONE+T*APOAQ*AAPQ ) ) |
$ ONE+T*APOAQ*AAPQ ) ) |
AAPP = AAPP*DSQRT( DMAX1( ZERO, |
AAPP = AAPP*DSQRT( DMAX1( ZERO, |
+ ONE-T*AQOAP*AAPQ ) ) |
$ ONE-T*AQOAP*AAPQ ) ) |
* |
* |
APOAQ = WORK( p ) / WORK( q ) |
APOAQ = WORK( p ) / WORK( q ) |
AQOAP = WORK( q ) / WORK( p ) |
AQOAP = WORK( q ) / WORK( p ) |
Line 870
|
Line 869
|
WORK( p ) = WORK( p )*CS |
WORK( p ) = WORK( p )*CS |
WORK( q ) = WORK( q )*CS |
WORK( q ) = WORK( q )*CS |
CALL DROTM( M, A( 1, p ), 1, |
CALL DROTM( M, A( 1, p ), 1, |
+ A( 1, q ), 1, |
$ A( 1, q ), 1, |
+ FASTR ) |
$ FASTR ) |
IF( RSVEC )CALL DROTM( MVL, |
IF( RSVEC )CALL DROTM( MVL, |
+ V( 1, p ), 1, V( 1, q ), |
$ V( 1, p ), 1, V( 1, q ), |
+ 1, FASTR ) |
$ 1, FASTR ) |
ELSE |
ELSE |
CALL DAXPY( M, -T*AQOAP, |
CALL DAXPY( M, -T*AQOAP, |
+ A( 1, q ), 1, |
$ A( 1, q ), 1, |
+ A( 1, p ), 1 ) |
$ A( 1, p ), 1 ) |
CALL DAXPY( M, CS*SN*APOAQ, |
CALL DAXPY( M, CS*SN*APOAQ, |
+ A( 1, p ), 1, |
$ A( 1, p ), 1, |
+ A( 1, q ), 1 ) |
$ A( 1, q ), 1 ) |
WORK( p ) = WORK( p )*CS |
WORK( p ) = WORK( p )*CS |
WORK( q ) = WORK( q ) / CS |
WORK( q ) = WORK( q ) / CS |
IF( RSVEC ) THEN |
IF( RSVEC ) THEN |
CALL DAXPY( MVL, -T*AQOAP, |
CALL DAXPY( MVL, -T*AQOAP, |
+ V( 1, q ), 1, |
$ V( 1, q ), 1, |
+ V( 1, p ), 1 ) |
$ V( 1, p ), 1 ) |
CALL DAXPY( MVL, |
CALL DAXPY( MVL, |
+ CS*SN*APOAQ, |
$ CS*SN*APOAQ, |
+ V( 1, p ), 1, |
$ V( 1, p ), 1, |
+ V( 1, q ), 1 ) |
$ V( 1, q ), 1 ) |
END IF |
END IF |
END IF |
END IF |
ELSE |
ELSE |
IF( WORK( q ).GE.ONE ) THEN |
IF( WORK( q ).GE.ONE ) THEN |
CALL DAXPY( M, T*APOAQ, |
CALL DAXPY( M, T*APOAQ, |
+ A( 1, p ), 1, |
$ A( 1, p ), 1, |
+ A( 1, q ), 1 ) |
$ A( 1, q ), 1 ) |
CALL DAXPY( M, -CS*SN*AQOAP, |
CALL DAXPY( M, -CS*SN*AQOAP, |
+ A( 1, q ), 1, |
$ A( 1, q ), 1, |
+ A( 1, p ), 1 ) |
$ A( 1, p ), 1 ) |
WORK( p ) = WORK( p ) / CS |
WORK( p ) = WORK( p ) / CS |
WORK( q ) = WORK( q )*CS |
WORK( q ) = WORK( q )*CS |
IF( RSVEC ) THEN |
IF( RSVEC ) THEN |
CALL DAXPY( MVL, T*APOAQ, |
CALL DAXPY( MVL, T*APOAQ, |
+ V( 1, p ), 1, |
$ V( 1, p ), 1, |
+ V( 1, q ), 1 ) |
$ V( 1, q ), 1 ) |
CALL DAXPY( MVL, |
CALL DAXPY( MVL, |
+ -CS*SN*AQOAP, |
$ -CS*SN*AQOAP, |
+ V( 1, q ), 1, |
$ V( 1, q ), 1, |
+ V( 1, p ), 1 ) |
$ V( 1, p ), 1 ) |
END IF |
END IF |
ELSE |
ELSE |
IF( WORK( p ).GE.WORK( q ) ) |
IF( WORK( p ).GE.WORK( q ) ) |
+ THEN |
$ THEN |
CALL DAXPY( M, -T*AQOAP, |
CALL DAXPY( M, -T*AQOAP, |
+ A( 1, q ), 1, |
$ A( 1, q ), 1, |
+ A( 1, p ), 1 ) |
$ A( 1, p ), 1 ) |
CALL DAXPY( M, CS*SN*APOAQ, |
CALL DAXPY( M, CS*SN*APOAQ, |
+ A( 1, p ), 1, |
$ A( 1, p ), 1, |
+ A( 1, q ), 1 ) |
$ A( 1, q ), 1 ) |
WORK( p ) = WORK( p )*CS |
WORK( p ) = WORK( p )*CS |
WORK( q ) = WORK( q ) / CS |
WORK( q ) = WORK( q ) / CS |
IF( RSVEC ) THEN |
IF( RSVEC ) THEN |
CALL DAXPY( MVL, |
CALL DAXPY( MVL, |
+ -T*AQOAP, |
$ -T*AQOAP, |
+ V( 1, q ), 1, |
$ V( 1, q ), 1, |
+ V( 1, p ), 1 ) |
$ V( 1, p ), 1 ) |
CALL DAXPY( MVL, |
CALL DAXPY( MVL, |
+ CS*SN*APOAQ, |
$ CS*SN*APOAQ, |
+ V( 1, p ), 1, |
$ V( 1, p ), 1, |
+ V( 1, q ), 1 ) |
$ V( 1, q ), 1 ) |
END IF |
END IF |
ELSE |
ELSE |
CALL DAXPY( M, T*APOAQ, |
CALL DAXPY( M, T*APOAQ, |
+ A( 1, p ), 1, |
$ A( 1, p ), 1, |
+ A( 1, q ), 1 ) |
$ A( 1, q ), 1 ) |
CALL DAXPY( M, |
CALL DAXPY( M, |
+ -CS*SN*AQOAP, |
$ -CS*SN*AQOAP, |
+ A( 1, q ), 1, |
$ A( 1, q ), 1, |
+ A( 1, p ), 1 ) |
$ A( 1, p ), 1 ) |
WORK( p ) = WORK( p ) / CS |
WORK( p ) = WORK( p ) / CS |
WORK( q ) = WORK( q )*CS |
WORK( q ) = WORK( q )*CS |
IF( RSVEC ) THEN |
IF( RSVEC ) THEN |
CALL DAXPY( MVL, |
CALL DAXPY( MVL, |
+ T*APOAQ, V( 1, p ), |
$ T*APOAQ, V( 1, p ), |
+ 1, V( 1, q ), 1 ) |
$ 1, V( 1, q ), 1 ) |
CALL DAXPY( MVL, |
CALL DAXPY( MVL, |
+ -CS*SN*AQOAP, |
$ -CS*SN*AQOAP, |
+ V( 1, q ), 1, |
$ V( 1, q ), 1, |
+ V( 1, p ), 1 ) |
$ V( 1, p ), 1 ) |
END IF |
END IF |
END IF |
END IF |
END IF |
END IF |
Line 961
|
Line 960
|
ELSE |
ELSE |
* .. have to use modified Gram-Schmidt like transformation |
* .. have to use modified Gram-Schmidt like transformation |
CALL DCOPY( M, A( 1, p ), 1, |
CALL DCOPY( M, A( 1, p ), 1, |
+ WORK( N+1 ), 1 ) |
$ WORK( N+1 ), 1 ) |
CALL DLASCL( 'G', 0, 0, AAPP, ONE, M, |
CALL DLASCL( 'G', 0, 0, AAPP, ONE, M, |
+ 1, WORK( N+1 ), LDA, |
$ 1, WORK( N+1 ), LDA, |
+ IERR ) |
$ IERR ) |
CALL DLASCL( 'G', 0, 0, AAQQ, ONE, M, |
CALL DLASCL( 'G', 0, 0, AAQQ, ONE, M, |
+ 1, A( 1, q ), LDA, IERR ) |
$ 1, A( 1, q ), LDA, IERR ) |
TEMP1 = -AAPQ*WORK( p ) / WORK( q ) |
TEMP1 = -AAPQ*WORK( p ) / WORK( q ) |
CALL DAXPY( M, TEMP1, WORK( N+1 ), 1, |
CALL DAXPY( M, TEMP1, WORK( N+1 ), 1, |
+ A( 1, q ), 1 ) |
$ A( 1, q ), 1 ) |
CALL DLASCL( 'G', 0, 0, ONE, AAQQ, M, |
CALL DLASCL( 'G', 0, 0, ONE, AAQQ, M, |
+ 1, A( 1, q ), LDA, IERR ) |
$ 1, A( 1, q ), LDA, IERR ) |
SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO, |
SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO, |
+ ONE-AAPQ*AAPQ ) ) |
$ ONE-AAPQ*AAPQ ) ) |
MXSINJ = DMAX1( MXSINJ, SFMIN ) |
MXSINJ = DMAX1( MXSINJ, SFMIN ) |
END IF |
END IF |
* END IF ROTOK THEN ... ELSE |
* END IF ROTOK THEN ... ELSE |
Line 982
|
Line 981
|
* recompute SVA(q), SVA(p). |
* recompute SVA(q), SVA(p). |
* |
* |
IF( ( SVA( q ) / AAQQ )**2.LE.ROOTEPS ) |
IF( ( SVA( q ) / AAQQ )**2.LE.ROOTEPS ) |
+ THEN |
$ THEN |
IF( ( AAQQ.LT.ROOTBIG ) .AND. |
IF( ( AAQQ.LT.ROOTBIG ) .AND. |
+ ( AAQQ.GT.ROOTSFMIN ) ) THEN |
$ ( AAQQ.GT.ROOTSFMIN ) ) THEN |
SVA( q ) = DNRM2( M, A( 1, q ), 1 )* |
SVA( q ) = DNRM2( M, A( 1, q ), 1 )* |
+ WORK( q ) |
$ WORK( q ) |
ELSE |
ELSE |
T = ZERO |
T = ZERO |
AAQQ = ZERO |
AAQQ = ONE |
CALL DLASSQ( M, A( 1, q ), 1, T, |
CALL DLASSQ( M, A( 1, q ), 1, T, |
+ AAQQ ) |
$ AAQQ ) |
SVA( q ) = T*DSQRT( AAQQ )*WORK( q ) |
SVA( q ) = T*DSQRT( AAQQ )*WORK( q ) |
END IF |
END IF |
END IF |
END IF |
IF( ( AAPP / AAPP0 ).LE.ROOTEPS ) THEN |
IF( ( AAPP / AAPP0 ).LE.ROOTEPS ) THEN |
IF( ( AAPP.LT.ROOTBIG ) .AND. |
IF( ( AAPP.LT.ROOTBIG ) .AND. |
+ ( AAPP.GT.ROOTSFMIN ) ) THEN |
$ ( AAPP.GT.ROOTSFMIN ) ) THEN |
AAPP = DNRM2( M, A( 1, p ), 1 )* |
AAPP = DNRM2( M, A( 1, p ), 1 )* |
+ WORK( p ) |
$ WORK( p ) |
ELSE |
ELSE |
T = ZERO |
T = ZERO |
AAPP = ZERO |
AAPP = ONE |
CALL DLASSQ( M, A( 1, p ), 1, T, |
CALL DLASSQ( M, A( 1, p ), 1, T, |
+ AAPP ) |
$ AAPP ) |
AAPP = T*DSQRT( AAPP )*WORK( p ) |
AAPP = T*DSQRT( AAPP )*WORK( p ) |
END IF |
END IF |
SVA( p ) = AAPP |
SVA( p ) = AAPP |
Line 1023
|
Line 1022
|
END IF |
END IF |
* |
* |
IF( ( i.LE.SWBAND ) .AND. |
IF( ( i.LE.SWBAND ) .AND. |
+ ( PSKIPPED.GT.ROWSKIP ) ) THEN |
$ ( PSKIPPED.GT.ROWSKIP ) ) THEN |
IF( ir1.EQ.0 )AAPP = -AAPP |
IF( ir1.EQ.0 )AAPP = -AAPP |
NOTROT = 0 |
NOTROT = 0 |
GO TO 2103 |
GO TO 2103 |
Line 1040
|
Line 1039
|
ELSE |
ELSE |
SVA( p ) = AAPP |
SVA( p ) = AAPP |
IF( ( ir1.EQ.0 ) .AND. ( AAPP.EQ.ZERO ) ) |
IF( ( ir1.EQ.0 ) .AND. ( AAPP.EQ.ZERO ) ) |
+ NOTROT = NOTROT + MIN0( igl+KBL-1, N ) - p |
$ NOTROT = NOTROT + MIN0( igl+KBL-1, N ) - p |
END IF |
END IF |
* |
* |
2001 CONTINUE |
2001 CONTINUE |
Line 1085
|
Line 1084
|
END IF |
END IF |
IF( AAPP.LT.( BIG / AAQQ ) ) THEN |
IF( AAPP.LT.( BIG / AAQQ ) ) THEN |
AAPQ = ( DDOT( M, A( 1, p ), 1, A( 1, |
AAPQ = ( DDOT( M, A( 1, p ), 1, A( 1, |
+ q ), 1 )*WORK( p )*WORK( q ) / |
$ q ), 1 )*WORK( p )*WORK( q ) / |
+ AAQQ ) / AAPP |
$ AAQQ ) / AAPP |
ELSE |
ELSE |
CALL DCOPY( M, A( 1, p ), 1, |
CALL DCOPY( M, A( 1, p ), 1, |
+ WORK( N+1 ), 1 ) |
$ WORK( N+1 ), 1 ) |
CALL DLASCL( 'G', 0, 0, AAPP, |
CALL DLASCL( 'G', 0, 0, AAPP, |
+ WORK( p ), M, 1, |
$ WORK( p ), M, 1, |
+ WORK( N+1 ), LDA, IERR ) |
$ WORK( N+1 ), LDA, IERR ) |
AAPQ = DDOT( M, WORK( N+1 ), 1, |
AAPQ = DDOT( M, WORK( N+1 ), 1, |
+ A( 1, q ), 1 )*WORK( q ) / AAQQ |
$ A( 1, q ), 1 )*WORK( q ) / AAQQ |
END IF |
END IF |
ELSE |
ELSE |
IF( AAPP.GE.AAQQ ) THEN |
IF( AAPP.GE.AAQQ ) THEN |
Line 1104
|
Line 1103
|
END IF |
END IF |
IF( AAPP.GT.( SMALL / AAQQ ) ) THEN |
IF( AAPP.GT.( SMALL / AAQQ ) ) THEN |
AAPQ = ( DDOT( M, A( 1, p ), 1, A( 1, |
AAPQ = ( DDOT( M, A( 1, p ), 1, A( 1, |
+ q ), 1 )*WORK( p )*WORK( q ) / |
$ q ), 1 )*WORK( p )*WORK( q ) / |
+ AAQQ ) / AAPP |
$ AAQQ ) / AAPP |
ELSE |
ELSE |
CALL DCOPY( M, A( 1, q ), 1, |
CALL DCOPY( M, A( 1, q ), 1, |
+ WORK( N+1 ), 1 ) |
$ WORK( N+1 ), 1 ) |
CALL DLASCL( 'G', 0, 0, AAQQ, |
CALL DLASCL( 'G', 0, 0, AAQQ, |
+ WORK( q ), M, 1, |
$ WORK( q ), M, 1, |
+ WORK( N+1 ), LDA, IERR ) |
$ WORK( N+1 ), LDA, IERR ) |
AAPQ = DDOT( M, WORK( N+1 ), 1, |
AAPQ = DDOT( M, WORK( N+1 ), 1, |
+ A( 1, p ), 1 )*WORK( p ) / AAPP |
$ A( 1, p ), 1 )*WORK( p ) / AAPP |
END IF |
END IF |
END IF |
END IF |
* |
* |
Line 1131
|
Line 1130
|
* |
* |
AQOAP = AAQQ / AAPP |
AQOAP = AAQQ / AAPP |
APOAQ = AAPP / AAQQ |
APOAQ = AAPP / AAQQ |
THETA = -HALF*DABS( AQOAP-APOAQ ) / |
THETA = -HALF*DABS(AQOAP-APOAQ)/AAPQ |
+ AAPQ |
|
IF( AAQQ.GT.AAPP0 )THETA = -THETA |
IF( AAQQ.GT.AAPP0 )THETA = -THETA |
* |
* |
IF( DABS( THETA ).GT.BIGTHETA ) THEN |
IF( DABS( THETA ).GT.BIGTHETA ) THEN |
T = HALF / THETA |
T = HALF / THETA |
FASTR( 3 ) = T*WORK( p ) / WORK( q ) |
FASTR( 3 ) = T*WORK( p ) / WORK( q ) |
FASTR( 4 ) = -T*WORK( q ) / |
FASTR( 4 ) = -T*WORK( q ) / |
+ WORK( p ) |
$ WORK( p ) |
CALL DROTM( M, A( 1, p ), 1, |
CALL DROTM( M, A( 1, p ), 1, |
+ A( 1, q ), 1, FASTR ) |
$ A( 1, q ), 1, FASTR ) |
IF( RSVEC )CALL DROTM( MVL, |
IF( RSVEC )CALL DROTM( MVL, |
+ V( 1, p ), 1, |
$ V( 1, p ), 1, |
+ V( 1, q ), 1, |
$ V( 1, q ), 1, |
+ FASTR ) |
$ FASTR ) |
SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO, |
SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO, |
+ ONE+T*APOAQ*AAPQ ) ) |
$ ONE+T*APOAQ*AAPQ ) ) |
AAPP = AAPP*DSQRT( DMAX1( ZERO, |
AAPP = AAPP*DSQRT( DMAX1( ZERO, |
+ ONE-T*AQOAP*AAPQ ) ) |
$ ONE-T*AQOAP*AAPQ ) ) |
MXSINJ = DMAX1( MXSINJ, DABS( T ) ) |
MXSINJ = DMAX1( MXSINJ, DABS( T ) ) |
ELSE |
ELSE |
* |
* |
Line 1158
|
Line 1156
|
THSIGN = -DSIGN( ONE, AAPQ ) |
THSIGN = -DSIGN( ONE, AAPQ ) |
IF( AAQQ.GT.AAPP0 )THSIGN = -THSIGN |
IF( AAQQ.GT.AAPP0 )THSIGN = -THSIGN |
T = ONE / ( THETA+THSIGN* |
T = ONE / ( THETA+THSIGN* |
+ DSQRT( ONE+THETA*THETA ) ) |
$ DSQRT( ONE+THETA*THETA ) ) |
CS = DSQRT( ONE / ( ONE+T*T ) ) |
CS = DSQRT( ONE / ( ONE+T*T ) ) |
SN = T*CS |
SN = T*CS |
MXSINJ = DMAX1( MXSINJ, DABS( SN ) ) |
MXSINJ = DMAX1( MXSINJ, DABS( SN ) ) |
SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO, |
SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO, |
+ ONE+T*APOAQ*AAPQ ) ) |
$ ONE+T*APOAQ*AAPQ ) ) |
AAPP = AAPP*DSQRT( ONE-T*AQOAP* |
AAPP = AAPP*DSQRT( DMAX1( ZERO, |
+ AAPQ ) |
$ ONE-T*AQOAP*AAPQ ) ) |
* |
* |
APOAQ = WORK( p ) / WORK( q ) |
APOAQ = WORK( p ) / WORK( q ) |
AQOAP = WORK( q ) / WORK( p ) |
AQOAP = WORK( q ) / WORK( p ) |
Line 1177
|
Line 1175
|
WORK( p ) = WORK( p )*CS |
WORK( p ) = WORK( p )*CS |
WORK( q ) = WORK( q )*CS |
WORK( q ) = WORK( q )*CS |
CALL DROTM( M, A( 1, p ), 1, |
CALL DROTM( M, A( 1, p ), 1, |
+ A( 1, q ), 1, |
$ A( 1, q ), 1, |
+ FASTR ) |
$ FASTR ) |
IF( RSVEC )CALL DROTM( MVL, |
IF( RSVEC )CALL DROTM( MVL, |
+ V( 1, p ), 1, V( 1, q ), |
$ V( 1, p ), 1, V( 1, q ), |
+ 1, FASTR ) |
$ 1, FASTR ) |
ELSE |
ELSE |
CALL DAXPY( M, -T*AQOAP, |
CALL DAXPY( M, -T*AQOAP, |
+ A( 1, q ), 1, |
$ A( 1, q ), 1, |
+ A( 1, p ), 1 ) |
$ A( 1, p ), 1 ) |
CALL DAXPY( M, CS*SN*APOAQ, |
CALL DAXPY( M, CS*SN*APOAQ, |
+ A( 1, p ), 1, |
$ A( 1, p ), 1, |
+ A( 1, q ), 1 ) |
$ A( 1, q ), 1 ) |
IF( RSVEC ) THEN |
IF( RSVEC ) THEN |
CALL DAXPY( MVL, -T*AQOAP, |
CALL DAXPY( MVL, -T*AQOAP, |
+ V( 1, q ), 1, |
$ V( 1, q ), 1, |
+ V( 1, p ), 1 ) |
$ V( 1, p ), 1 ) |
CALL DAXPY( MVL, |
CALL DAXPY( MVL, |
+ CS*SN*APOAQ, |
$ CS*SN*APOAQ, |
+ V( 1, p ), 1, |
$ V( 1, p ), 1, |
+ V( 1, q ), 1 ) |
$ V( 1, q ), 1 ) |
END IF |
END IF |
WORK( p ) = WORK( p )*CS |
WORK( p ) = WORK( p )*CS |
WORK( q ) = WORK( q ) / CS |
WORK( q ) = WORK( q ) / CS |
Line 1204
|
Line 1202
|
ELSE |
ELSE |
IF( WORK( q ).GE.ONE ) THEN |
IF( WORK( q ).GE.ONE ) THEN |
CALL DAXPY( M, T*APOAQ, |
CALL DAXPY( M, T*APOAQ, |
+ A( 1, p ), 1, |
$ A( 1, p ), 1, |
+ A( 1, q ), 1 ) |
$ A( 1, q ), 1 ) |
CALL DAXPY( M, -CS*SN*AQOAP, |
CALL DAXPY( M, -CS*SN*AQOAP, |
+ A( 1, q ), 1, |
$ A( 1, q ), 1, |
+ A( 1, p ), 1 ) |
$ A( 1, p ), 1 ) |
IF( RSVEC ) THEN |
IF( RSVEC ) THEN |
CALL DAXPY( MVL, T*APOAQ, |
CALL DAXPY( MVL, T*APOAQ, |
+ V( 1, p ), 1, |
$ V( 1, p ), 1, |
+ V( 1, q ), 1 ) |
$ V( 1, q ), 1 ) |
CALL DAXPY( MVL, |
CALL DAXPY( MVL, |
+ -CS*SN*AQOAP, |
$ -CS*SN*AQOAP, |
+ V( 1, q ), 1, |
$ V( 1, q ), 1, |
+ V( 1, p ), 1 ) |
$ V( 1, p ), 1 ) |
END IF |
END IF |
WORK( p ) = WORK( p ) / CS |
WORK( p ) = WORK( p ) / CS |
WORK( q ) = WORK( q )*CS |
WORK( q ) = WORK( q )*CS |
ELSE |
ELSE |
IF( WORK( p ).GE.WORK( q ) ) |
IF( WORK( p ).GE.WORK( q ) ) |
+ THEN |
$ THEN |
CALL DAXPY( M, -T*AQOAP, |
CALL DAXPY( M, -T*AQOAP, |
+ A( 1, q ), 1, |
$ A( 1, q ), 1, |
+ A( 1, p ), 1 ) |
$ A( 1, p ), 1 ) |
CALL DAXPY( M, CS*SN*APOAQ, |
CALL DAXPY( M, CS*SN*APOAQ, |
+ A( 1, p ), 1, |
$ A( 1, p ), 1, |
+ A( 1, q ), 1 ) |
$ A( 1, q ), 1 ) |
WORK( p ) = WORK( p )*CS |
WORK( p ) = WORK( p )*CS |
WORK( q ) = WORK( q ) / CS |
WORK( q ) = WORK( q ) / CS |
IF( RSVEC ) THEN |
IF( RSVEC ) THEN |
CALL DAXPY( MVL, |
CALL DAXPY( MVL, |
+ -T*AQOAP, |
$ -T*AQOAP, |
+ V( 1, q ), 1, |
$ V( 1, q ), 1, |
+ V( 1, p ), 1 ) |
$ V( 1, p ), 1 ) |
CALL DAXPY( MVL, |
CALL DAXPY( MVL, |
+ CS*SN*APOAQ, |
$ CS*SN*APOAQ, |
+ V( 1, p ), 1, |
$ V( 1, p ), 1, |
+ V( 1, q ), 1 ) |
$ V( 1, q ), 1 ) |
END IF |
END IF |
ELSE |
ELSE |
CALL DAXPY( M, T*APOAQ, |
CALL DAXPY( M, T*APOAQ, |
+ A( 1, p ), 1, |
$ A( 1, p ), 1, |
+ A( 1, q ), 1 ) |
$ A( 1, q ), 1 ) |
CALL DAXPY( M, |
CALL DAXPY( M, |
+ -CS*SN*AQOAP, |
$ -CS*SN*AQOAP, |
+ A( 1, q ), 1, |
$ A( 1, q ), 1, |
+ A( 1, p ), 1 ) |
$ A( 1, p ), 1 ) |
WORK( p ) = WORK( p ) / CS |
WORK( p ) = WORK( p ) / CS |
WORK( q ) = WORK( q )*CS |
WORK( q ) = WORK( q )*CS |
IF( RSVEC ) THEN |
IF( RSVEC ) THEN |
CALL DAXPY( MVL, |
CALL DAXPY( MVL, |
+ T*APOAQ, V( 1, p ), |
$ T*APOAQ, V( 1, p ), |
+ 1, V( 1, q ), 1 ) |
$ 1, V( 1, q ), 1 ) |
CALL DAXPY( MVL, |
CALL DAXPY( MVL, |
+ -CS*SN*AQOAP, |
$ -CS*SN*AQOAP, |
+ V( 1, q ), 1, |
$ V( 1, q ), 1, |
+ V( 1, p ), 1 ) |
$ V( 1, p ), 1 ) |
END IF |
END IF |
END IF |
END IF |
END IF |
END IF |
Line 1268
|
Line 1266
|
ELSE |
ELSE |
IF( AAPP.GT.AAQQ ) THEN |
IF( AAPP.GT.AAQQ ) THEN |
CALL DCOPY( M, A( 1, p ), 1, |
CALL DCOPY( M, A( 1, p ), 1, |
+ WORK( N+1 ), 1 ) |
$ WORK( N+1 ), 1 ) |
CALL DLASCL( 'G', 0, 0, AAPP, ONE, |
CALL DLASCL( 'G', 0, 0, AAPP, ONE, |
+ M, 1, WORK( N+1 ), LDA, |
$ M, 1, WORK( N+1 ), LDA, |
+ IERR ) |
$ IERR ) |
CALL DLASCL( 'G', 0, 0, AAQQ, ONE, |
CALL DLASCL( 'G', 0, 0, AAQQ, ONE, |
+ M, 1, A( 1, q ), LDA, |
$ M, 1, A( 1, q ), LDA, |
+ IERR ) |
$ IERR ) |
TEMP1 = -AAPQ*WORK( p ) / WORK( q ) |
TEMP1 = -AAPQ*WORK( p ) / WORK( q ) |
CALL DAXPY( M, TEMP1, WORK( N+1 ), |
CALL DAXPY( M, TEMP1, WORK( N+1 ), |
+ 1, A( 1, q ), 1 ) |
$ 1, A( 1, q ), 1 ) |
CALL DLASCL( 'G', 0, 0, ONE, AAQQ, |
CALL DLASCL( 'G', 0, 0, ONE, AAQQ, |
+ M, 1, A( 1, q ), LDA, |
$ M, 1, A( 1, q ), LDA, |
+ IERR ) |
$ IERR ) |
SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO, |
SVA( q ) = AAQQ*DSQRT( DMAX1( ZERO, |
+ ONE-AAPQ*AAPQ ) ) |
$ ONE-AAPQ*AAPQ ) ) |
MXSINJ = DMAX1( MXSINJ, SFMIN ) |
MXSINJ = DMAX1( MXSINJ, SFMIN ) |
ELSE |
ELSE |
CALL DCOPY( M, A( 1, q ), 1, |
CALL DCOPY( M, A( 1, q ), 1, |
+ WORK( N+1 ), 1 ) |
$ WORK( N+1 ), 1 ) |
CALL DLASCL( 'G', 0, 0, AAQQ, ONE, |
CALL DLASCL( 'G', 0, 0, AAQQ, ONE, |
+ M, 1, WORK( N+1 ), LDA, |
$ M, 1, WORK( N+1 ), LDA, |
+ IERR ) |
$ IERR ) |
CALL DLASCL( 'G', 0, 0, AAPP, ONE, |
CALL DLASCL( 'G', 0, 0, AAPP, ONE, |
+ M, 1, A( 1, p ), LDA, |
$ M, 1, A( 1, p ), LDA, |
+ IERR ) |
$ IERR ) |
TEMP1 = -AAPQ*WORK( q ) / WORK( p ) |
TEMP1 = -AAPQ*WORK( q ) / WORK( p ) |
CALL DAXPY( M, TEMP1, WORK( N+1 ), |
CALL DAXPY( M, TEMP1, WORK( N+1 ), |
+ 1, A( 1, p ), 1 ) |
$ 1, A( 1, p ), 1 ) |
CALL DLASCL( 'G', 0, 0, ONE, AAPP, |
CALL DLASCL( 'G', 0, 0, ONE, AAPP, |
+ M, 1, A( 1, p ), LDA, |
$ M, 1, A( 1, p ), LDA, |
+ IERR ) |
$ IERR ) |
SVA( p ) = AAPP*DSQRT( DMAX1( ZERO, |
SVA( p ) = AAPP*DSQRT( DMAX1( ZERO, |
+ ONE-AAPQ*AAPQ ) ) |
$ ONE-AAPQ*AAPQ ) ) |
MXSINJ = DMAX1( MXSINJ, SFMIN ) |
MXSINJ = DMAX1( MXSINJ, SFMIN ) |
END IF |
END IF |
END IF |
END IF |
Line 1309
|
Line 1307
|
* In the case of cancellation in updating SVA(q) |
* In the case of cancellation in updating SVA(q) |
* .. recompute SVA(q) |
* .. recompute SVA(q) |
IF( ( SVA( q ) / AAQQ )**2.LE.ROOTEPS ) |
IF( ( SVA( q ) / AAQQ )**2.LE.ROOTEPS ) |
+ THEN |
$ THEN |
IF( ( AAQQ.LT.ROOTBIG ) .AND. |
IF( ( AAQQ.LT.ROOTBIG ) .AND. |
+ ( AAQQ.GT.ROOTSFMIN ) ) THEN |
$ ( AAQQ.GT.ROOTSFMIN ) ) THEN |
SVA( q ) = DNRM2( M, A( 1, q ), 1 )* |
SVA( q ) = DNRM2( M, A( 1, q ), 1 )* |
+ WORK( q ) |
$ WORK( q ) |
ELSE |
ELSE |
T = ZERO |
T = ZERO |
AAQQ = ZERO |
AAQQ = ONE |
CALL DLASSQ( M, A( 1, q ), 1, T, |
CALL DLASSQ( M, A( 1, q ), 1, T, |
+ AAQQ ) |
$ AAQQ ) |
SVA( q ) = T*DSQRT( AAQQ )*WORK( q ) |
SVA( q ) = T*DSQRT( AAQQ )*WORK( q ) |
END IF |
END IF |
END IF |
END IF |
IF( ( AAPP / AAPP0 )**2.LE.ROOTEPS ) THEN |
IF( ( AAPP / AAPP0 )**2.LE.ROOTEPS ) THEN |
IF( ( AAPP.LT.ROOTBIG ) .AND. |
IF( ( AAPP.LT.ROOTBIG ) .AND. |
+ ( AAPP.GT.ROOTSFMIN ) ) THEN |
$ ( AAPP.GT.ROOTSFMIN ) ) THEN |
AAPP = DNRM2( M, A( 1, p ), 1 )* |
AAPP = DNRM2( M, A( 1, p ), 1 )* |
+ WORK( p ) |
$ WORK( p ) |
ELSE |
ELSE |
T = ZERO |
T = ZERO |
AAPP = ZERO |
AAPP = ONE |
CALL DLASSQ( M, A( 1, p ), 1, T, |
CALL DLASSQ( M, A( 1, p ), 1, T, |
+ AAPP ) |
$ AAPP ) |
AAPP = T*DSQRT( AAPP )*WORK( p ) |
AAPP = T*DSQRT( AAPP )*WORK( p ) |
END IF |
END IF |
SVA( p ) = AAPP |
SVA( p ) = AAPP |
Line 1350
|
Line 1348
|
END IF |
END IF |
* |
* |
IF( ( i.LE.SWBAND ) .AND. ( IJBLSK.GE.BLSKIP ) ) |
IF( ( i.LE.SWBAND ) .AND. ( IJBLSK.GE.BLSKIP ) ) |
+ THEN |
$ THEN |
SVA( p ) = AAPP |
SVA( p ) = AAPP |
NOTROT = 0 |
NOTROT = 0 |
GO TO 2011 |
GO TO 2011 |
END IF |
END IF |
IF( ( i.LE.SWBAND ) .AND. |
IF( ( i.LE.SWBAND ) .AND. |
+ ( PSKIPPED.GT.ROWSKIP ) ) THEN |
$ ( PSKIPPED.GT.ROWSKIP ) ) THEN |
AAPP = -AAPP |
AAPP = -AAPP |
NOTROT = 0 |
NOTROT = 0 |
GO TO 2203 |
GO TO 2203 |
Line 1371
|
Line 1369
|
ELSE |
ELSE |
* |
* |
IF( AAPP.EQ.ZERO )NOTROT = NOTROT + |
IF( AAPP.EQ.ZERO )NOTROT = NOTROT + |
+ MIN0( jgl+KBL-1, N ) - jgl + 1 |
$ MIN0( jgl+KBL-1, N ) - jgl + 1 |
IF( AAPP.LT.ZERO )NOTROT = 0 |
IF( AAPP.LT.ZERO )NOTROT = 0 |
* |
* |
END IF |
END IF |
Line 1391
|
Line 1389
|
* |
* |
* .. update SVA(N) |
* .. update SVA(N) |
IF( ( SVA( N ).LT.ROOTBIG ) .AND. ( SVA( N ).GT.ROOTSFMIN ) ) |
IF( ( SVA( N ).LT.ROOTBIG ) .AND. ( SVA( N ).GT.ROOTSFMIN ) ) |
+ THEN |
$ THEN |
SVA( N ) = DNRM2( M, A( 1, N ), 1 )*WORK( N ) |
SVA( N ) = DNRM2( M, A( 1, N ), 1 )*WORK( N ) |
ELSE |
ELSE |
T = ZERO |
T = ZERO |
AAPP = ZERO |
AAPP = ONE |
CALL DLASSQ( M, A( 1, N ), 1, T, AAPP ) |
CALL DLASSQ( M, A( 1, N ), 1, T, AAPP ) |
SVA( N ) = T*DSQRT( AAPP )*WORK( N ) |
SVA( N ) = T*DSQRT( AAPP )*WORK( N ) |
END IF |
END IF |
Line 1403
|
Line 1401
|
* Additional steering devices |
* Additional steering devices |
* |
* |
IF( ( i.LT.SWBAND ) .AND. ( ( MXAAPQ.LE.ROOTTOL ) .OR. |
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.DSQRT( DBLE( N ) )* |
IF( ( i.GT.SWBAND+1 ) .AND. ( MXAAPQ.LT.DSQRT( DBLE( N ) )* |
+ TOL ) .AND. ( DBLE( N )*MXAAPQ*MXSINJ.LT.TOL ) ) THEN |
$ TOL ) .AND. ( DBLE( N )*MXAAPQ*MXSINJ.LT.TOL ) ) THEN |
GO TO 1994 |
GO TO 1994 |
END IF |
END IF |
* |
* |
Line 1446
|
Line 1444
|
END IF |
END IF |
IF( SVA( p ).NE.ZERO ) THEN |
IF( SVA( p ).NE.ZERO ) THEN |
N4 = N4 + 1 |
N4 = N4 + 1 |
IF( SVA( p )*SCALE.GT.SFMIN )N2 = N2 + 1 |
IF( SVA( p )*SKL.GT.SFMIN )N2 = N2 + 1 |
END IF |
END IF |
5991 CONTINUE |
5991 CONTINUE |
IF( SVA( N ).NE.ZERO ) THEN |
IF( SVA( N ).NE.ZERO ) THEN |
N4 = N4 + 1 |
N4 = N4 + 1 |
IF( SVA( N )*SCALE.GT.SFMIN )N2 = N2 + 1 |
IF( SVA( N )*SKL.GT.SFMIN )N2 = N2 + 1 |
END IF |
END IF |
* |
* |
* Normalize the left singular vectors. |
* Normalize the left singular vectors. |
Line 1478
|
Line 1476
|
END IF |
END IF |
* |
* |
* Undo scaling, if necessary (and possible). |
* Undo scaling, if necessary (and possible). |
IF( ( ( SCALE.GT.ONE ) .AND. ( SVA( 1 ).LT.( BIG / |
IF( ( ( SKL.GT.ONE ) .AND. ( SVA( 1 ).LT.( BIG / |
+ SCALE ) ) ) .OR. ( ( SCALE.LT.ONE ) .AND. ( SVA( N2 ).GT. |
$ SKL) ) ) .OR. ( ( SKL.LT.ONE ) .AND. ( SVA( N2 ).GT. |
+ ( SFMIN / SCALE ) ) ) ) THEN |
$ ( SFMIN / SKL) ) ) ) THEN |
DO 2400 p = 1, N |
DO 2400 p = 1, N |
SVA( p ) = SCALE*SVA( p ) |
SVA( p ) = SKL*SVA( p ) |
2400 CONTINUE |
2400 CONTINUE |
SCALE = ONE |
SKL= ONE |
END IF |
END IF |
* |
* |
WORK( 1 ) = SCALE |
WORK( 1 ) = SKL |
* The singular values of A are SCALE*SVA(1:N). If SCALE.NE.ONE |
* The singular values of A are SKL*SVA(1:N). If SKL.NE.ONE |
* then some of the singular values may overflow or underflow and |
* then some of the singular values may overflow or underflow and |
* the spectrum is given in this factored representation. |
* the spectrum is given in this factored representation. |
* |
* |