268 INTEGER ihiz, iloz, kacc22, kbot, ktop, ldh, ldu, ldv,
269 $ ldwh, ldwv, ldz, n, nh, nshfts, nv
273 DOUBLE PRECISION h( ldh, * ), si( * ), sr( * ), u( ldu, * ),
274 $ v( ldv, * ), wh( ldwh, * ), wv( ldwv, * ),
280 DOUBLE PRECISION zero, one
281 parameter ( zero = 0.0d0, one = 1.0d0 )
284 DOUBLE PRECISION alpha, beta, h11, h12, h21, h22, refsum,
285 $ safmax, safmin, scl, smlnum, swap, tst1, tst2,
287 INTEGER i, i2, i4, incol, j, j2, j4, jbot, jcol, jlen,
288 $ jrow, jtop, k, k1, kdu, kms, knz, krcol, kzs,
289 $ m, m22, mbot, mend, mstart, mtop, nbmps, ndcol,
291 LOGICAL accum, blk22, bmp22
299 INTRINSIC abs, dble, max, min, mod
302 DOUBLE PRECISION vt( 3 )
326 DO 10 i = 1, nshfts - 2, 2
327 IF( si( i ).NE.-si( i+1 ) )
THEN
331 sr( i+1 ) = sr( i+2 )
336 si( i+1 ) = si( i+2 )
346 ns = nshfts - mod( nshfts, 2 )
350 safmin =
dlamch(
'SAFE MINIMUM' )
351 safmax = one / safmin
352 CALL dlabad( safmin, safmax )
353 ulp =
dlamch(
'PRECISION' )
354 smlnum = safmin*( dble( n ) / ulp )
359 accum = ( kacc22.EQ.1 ) .OR. ( kacc22.EQ.2 )
363 blk22 = ( ns.GT.2 ) .AND. ( kacc22.EQ.2 )
368 $ h( ktop+2, ktop ) = zero
380 DO 220 incol = 3*( 1-nbmps ) + ktop - 1, kbot - 2, 3*nbmps - 2
383 $
CALL dlaset(
'ALL', kdu, kdu, zero, one, u, ldu )
397 DO 150 krcol = incol, min( incol+3*nbmps-3, kbot-2 )
406 mtop = max( 1, ( ( ktop-1 )-krcol+2 ) / 3+1 )
407 mbot = min( nbmps, ( kbot-krcol ) / 3 )
409 bmp22 = ( mbot.LT.nbmps ) .AND. ( krcol+3*( m22-1 ) ).EQ.
416 k = krcol + 3*( m-1 )
417 IF( k.EQ.ktop-1 )
THEN
418 CALL dlaqr1( 3, h( ktop, ktop ), ldh, sr( 2*m-1 ),
419 $ si( 2*m-1 ), sr( 2*m ), si( 2*m ),
422 CALL dlarfg( 3, alpha, v( 2, m ), 1, v( 1, m ) )
425 v( 2, m ) = h( k+2, k )
426 v( 3, m ) = h( k+3, k )
427 CALL dlarfg( 3, beta, v( 2, m ), 1, v( 1, m ) )
434 IF( h( k+3, k ).NE.zero .OR. h( k+3, k+1 ).NE.
435 $ zero .OR. h( k+3, k+2 ).EQ.zero )
THEN
450 CALL dlaqr1( 3, h( k+1, k+1 ), ldh, sr( 2*m-1 ),
451 $ si( 2*m-1 ), sr( 2*m ), si( 2*m ),
454 CALL dlarfg( 3, alpha, vt( 2 ), 1, vt( 1 ) )
455 refsum = vt( 1 )*( h( k+1, k )+vt( 2 )*
458 IF( abs( h( k+2, k )-refsum*vt( 2 ) )+
459 $ abs( refsum*vt( 3 ) ).GT.ulp*
460 $ ( abs( h( k, k ) )+abs( h( k+1,
461 $ k+1 ) )+abs( h( k+2, k+2 ) ) ) )
THEN
477 h( k+1, k ) = h( k+1, k ) - refsum
490 k = krcol + 3*( m22-1 )
492 IF( k.EQ.ktop-1 )
THEN
493 CALL dlaqr1( 2, h( k+1, k+1 ), ldh, sr( 2*m22-1 ),
494 $ si( 2*m22-1 ), sr( 2*m22 ), si( 2*m22 ),
497 CALL dlarfg( 2, beta, v( 2, m22 ), 1, v( 1, m22 ) )
500 v( 2, m22 ) = h( k+2, k )
501 CALL dlarfg( 2, beta, v( 2, m22 ), 1, v( 1, m22 ) )
510 jbot = min( ndcol, kbot )
511 ELSE IF( wantt )
THEN
516 DO 40 j = max( ktop, krcol ), jbot
517 mend = min( mbot, ( j-krcol+2 ) / 3 )
519 k = krcol + 3*( m-1 )
520 refsum = v( 1, m )*( h( k+1, j )+v( 2, m )*
521 $ h( k+2, j )+v( 3, m )*h( k+3, j ) )
522 h( k+1, j ) = h( k+1, j ) - refsum
523 h( k+2, j ) = h( k+2, j ) - refsum*v( 2, m )
524 h( k+3, j ) = h( k+3, j ) - refsum*v( 3, m )
528 k = krcol + 3*( m22-1 )
529 DO 50 j = max( k+1, ktop ), jbot
530 refsum = v( 1, m22 )*( h( k+1, j )+v( 2, m22 )*
532 h( k+1, j ) = h( k+1, j ) - refsum
533 h( k+2, j ) = h( k+2, j ) - refsum*v( 2, m22 )
542 jtop = max( ktop, incol )
543 ELSE IF( wantt )
THEN
549 IF( v( 1, m ).NE.zero )
THEN
550 k = krcol + 3*( m-1 )
551 DO 60 j = jtop, min( kbot, k+3 )
552 refsum = v( 1, m )*( h( j, k+1 )+v( 2, m )*
553 $ h( j, k+2 )+v( 3, m )*h( j, k+3 ) )
554 h( j, k+1 ) = h( j, k+1 ) - refsum
555 h( j, k+2 ) = h( j, k+2 ) - refsum*v( 2, m )
556 h( j, k+3 ) = h( j, k+3 ) - refsum*v( 3, m )
566 DO 70 j = max( 1, ktop-incol ), kdu
567 refsum = v( 1, m )*( u( j, kms+1 )+v( 2, m )*
568 $ u( j, kms+2 )+v( 3, m )*u( j, kms+3 ) )
569 u( j, kms+1 ) = u( j, kms+1 ) - refsum
570 u( j, kms+2 ) = u( j, kms+2 ) - refsum*v( 2, m )
571 u( j, kms+3 ) = u( j, kms+3 ) - refsum*v( 3, m )
573 ELSE IF( wantz )
THEN
580 refsum = v( 1, m )*( z( j, k+1 )+v( 2, m )*
581 $ z( j, k+2 )+v( 3, m )*z( j, k+3 ) )
582 z( j, k+1 ) = z( j, k+1 ) - refsum
583 z( j, k+2 ) = z( j, k+2 ) - refsum*v( 2, m )
584 z( j, k+3 ) = z( j, k+3 ) - refsum*v( 3, m )
592 k = krcol + 3*( m22-1 )
594 IF ( v( 1, m22 ).NE.zero )
THEN
595 DO 100 j = jtop, min( kbot, k+3 )
596 refsum = v( 1, m22 )*( h( j, k+1 )+v( 2, m22 )*
598 h( j, k+1 ) = h( j, k+1 ) - refsum
599 h( j, k+2 ) = h( j, k+2 ) - refsum*v( 2, m22 )
604 DO 110 j = max( 1, ktop-incol ), kdu
605 refsum = v( 1, m22 )*( u( j, kms+1 )+
606 $ v( 2, m22 )*u( j, kms+2 ) )
607 u( j, kms+1 ) = u( j, kms+1 ) - refsum
608 u( j, kms+2 ) = u( j, kms+2 ) -
611 ELSE IF( wantz )
THEN
612 DO 120 j = iloz, ihiz
613 refsum = v( 1, m22 )*( z( j, k+1 )+v( 2, m22 )*
615 z( j, k+1 ) = z( j, k+1 ) - refsum
616 z( j, k+2 ) = z( j, k+2 ) - refsum*v( 2, m22 )
625 IF( krcol+3*( mstart-1 ).LT.ktop )
626 $ mstart = mstart + 1
630 IF( krcol.EQ.kbot-2 )
632 DO 130 m = mstart, mend
633 k = min( kbot-1, krcol+3*( m-1 ) )
644 IF( h( k+1, k ).NE.zero )
THEN
645 tst1 = abs( h( k, k ) ) + abs( h( k+1, k+1 ) )
646 IF( tst1.EQ.zero )
THEN
648 $ tst1 = tst1 + abs( h( k, k-1 ) )
650 $ tst1 = tst1 + abs( h( k, k-2 ) )
652 $ tst1 = tst1 + abs( h( k, k-3 ) )
654 $ tst1 = tst1 + abs( h( k+2, k+1 ) )
656 $ tst1 = tst1 + abs( h( k+3, k+1 ) )
658 $ tst1 = tst1 + abs( h( k+4, k+1 ) )
660 IF( abs( h( k+1, k ) ).LE.max( smlnum, ulp*tst1 ) )
662 h12 = max( abs( h( k+1, k ) ), abs( h( k, k+1 ) ) )
663 h21 = min( abs( h( k+1, k ) ), abs( h( k, k+1 ) ) )
664 h11 = max( abs( h( k+1, k+1 ) ),
665 $ abs( h( k, k )-h( k+1, k+1 ) ) )
666 h22 = min( abs( h( k+1, k+1 ) ),
667 $ abs( h( k, k )-h( k+1, k+1 ) ) )
669 tst2 = h22*( h11 / scl )
671 IF( tst2.EQ.zero .OR. h21*( h12 / scl ).LE.
672 $ max( smlnum, ulp*tst2 ) )h( k+1, k ) = zero
679 mend = min( nbmps, ( kbot-krcol-1 ) / 3 )
680 DO 140 m = mtop, mend
681 k = krcol + 3*( m-1 )
682 refsum = v( 1, m )*v( 3, m )*h( k+4, k+3 )
683 h( k+4, k+1 ) = -refsum
684 h( k+4, k+2 ) = -refsum*v( 2, m )
685 h( k+4, k+3 ) = h( k+4, k+3 ) - refsum*v( 3, m )
704 IF( ( .NOT.blk22 ) .OR. ( incol.LT.ktop ) .OR.
705 $ ( ndcol.GT.kbot ) .OR. ( ns.LE.2 ) )
THEN
716 k1 = max( 1, ktop-incol )
717 nu = ( kdu-max( 0, ndcol-kbot ) ) - k1 + 1
721 DO 160 jcol = min( ndcol, kbot ) + 1, jbot, nh
722 jlen = min( nh, jbot-jcol+1 )
723 CALL dgemm(
'C',
'N', nu, jlen, nu, one, u( k1, k1 ),
724 $ ldu, h( incol+k1, jcol ), ldh, zero, wh,
726 CALL dlacpy(
'ALL', nu, jlen, wh, ldwh,
727 $ h( incol+k1, jcol ), ldh )
732 DO 170 jrow = jtop, max( ktop, incol ) - 1, nv
733 jlen = min( nv, max( ktop, incol )-jrow )
734 CALL dgemm(
'N',
'N', jlen, nu, nu, one,
735 $ h( jrow, incol+k1 ), ldh, u( k1, k1 ),
736 $ ldu, zero, wv, ldwv )
737 CALL dlacpy(
'ALL', jlen, nu, wv, ldwv,
738 $ h( jrow, incol+k1 ), ldh )
744 DO 180 jrow = iloz, ihiz, nv
745 jlen = min( nv, ihiz-jrow+1 )
746 CALL dgemm(
'N',
'N', jlen, nu, nu, one,
747 $ z( jrow, incol+k1 ), ldz, u( k1, k1 ),
748 $ ldu, zero, wv, ldwv )
749 CALL dlacpy(
'ALL', jlen, nu, wv, ldwv,
750 $ z( jrow, incol+k1 ), ldz )
768 kzs = ( j4-j2 ) - ( ns+1 )
773 DO 190 jcol = min( ndcol, kbot ) + 1, jbot, nh
774 jlen = min( nh, jbot-jcol+1 )
779 CALL dlacpy(
'ALL', knz, jlen, h( incol+1+j2, jcol ),
780 $ ldh, wh( kzs+1, 1 ), ldwh )
784 CALL dlaset(
'ALL', kzs, jlen, zero, zero, wh, ldwh )
785 CALL dtrmm(
'L',
'U',
'C',
'N', knz, jlen, one,
786 $ u( j2+1, 1+kzs ), ldu, wh( kzs+1, 1 ),
791 CALL dgemm(
'C',
'N', i2, jlen, j2, one, u, ldu,
792 $ h( incol+1, jcol ), ldh, one, wh, ldwh )
796 CALL dlacpy(
'ALL', j2, jlen, h( incol+1, jcol ), ldh,
797 $ wh( i2+1, 1 ), ldwh )
801 CALL dtrmm(
'L',
'L',
'C',
'N', j2, jlen, one,
802 $ u( 1, i2+1 ), ldu, wh( i2+1, 1 ), ldwh )
806 CALL dgemm(
'C',
'N', i4-i2, jlen, j4-j2, one,
807 $ u( j2+1, i2+1 ), ldu,
808 $ h( incol+1+j2, jcol ), ldh, one,
809 $ wh( i2+1, 1 ), ldwh )
813 CALL dlacpy(
'ALL', kdu, jlen, wh, ldwh,
814 $ h( incol+1, jcol ), ldh )
819 DO 200 jrow = jtop, max( incol, ktop ) - 1, nv
820 jlen = min( nv, max( incol, ktop )-jrow )
825 CALL dlacpy(
'ALL', jlen, knz, h( jrow, incol+1+j2 ),
826 $ ldh, wv( 1, 1+kzs ), ldwv )
830 CALL dlaset(
'ALL', jlen, kzs, zero, zero, wv, ldwv )
831 CALL dtrmm(
'R',
'U',
'N',
'N', jlen, knz, one,
832 $ u( j2+1, 1+kzs ), ldu, wv( 1, 1+kzs ),
837 CALL dgemm(
'N',
'N', jlen, i2, j2, one,
838 $ h( jrow, incol+1 ), ldh, u, ldu, one, wv,
843 CALL dlacpy(
'ALL', jlen, j2, h( jrow, incol+1 ), ldh,
844 $ wv( 1, 1+i2 ), ldwv )
848 CALL dtrmm(
'R',
'L',
'N',
'N', jlen, i4-i2, one,
849 $ u( 1, i2+1 ), ldu, wv( 1, 1+i2 ), ldwv )
853 CALL dgemm(
'N',
'N', jlen, i4-i2, j4-j2, one,
854 $ h( jrow, incol+1+j2 ), ldh,
855 $ u( j2+1, i2+1 ), ldu, one, wv( 1, 1+i2 ),
860 CALL dlacpy(
'ALL', jlen, kdu, wv, ldwv,
861 $ h( jrow, incol+1 ), ldh )
867 DO 210 jrow = iloz, ihiz, nv
868 jlen = min( nv, ihiz-jrow+1 )
873 CALL dlacpy(
'ALL', jlen, knz,
874 $ z( jrow, incol+1+j2 ), ldz,
875 $ wv( 1, 1+kzs ), ldwv )
879 CALL dlaset(
'ALL', jlen, kzs, zero, zero, wv,
881 CALL dtrmm(
'R',
'U',
'N',
'N', jlen, knz, one,
882 $ u( j2+1, 1+kzs ), ldu, wv( 1, 1+kzs ),
887 CALL dgemm(
'N',
'N', jlen, i2, j2, one,
888 $ z( jrow, incol+1 ), ldz, u, ldu, one,
893 CALL dlacpy(
'ALL', jlen, j2, z( jrow, incol+1 ),
894 $ ldz, wv( 1, 1+i2 ), ldwv )
898 CALL dtrmm(
'R',
'L',
'N',
'N', jlen, i4-i2, one,
899 $ u( 1, i2+1 ), ldu, wv( 1, 1+i2 ),
904 CALL dgemm(
'N',
'N', jlen, i4-i2, j4-j2, one,
905 $ z( jrow, incol+1+j2 ), ldz,
906 $ u( j2+1, i2+1 ), ldu, one,
907 $ wv( 1, 1+i2 ), ldwv )
911 CALL dlacpy(
'ALL', jlen, kdu, wv, ldwv,
912 $ z( jrow, incol+1 ), ldz )
subroutine dlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
DLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values...
double precision function dlamch(CMACH)
DLAMCH
subroutine dtrmm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
DTRMM
subroutine dlacpy(UPLO, M, N, A, LDA, B, LDB)
DLACPY copies all or part of one two-dimensional array to another.
subroutine dgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DGEMM
subroutine dlabad(SMALL, LARGE)
DLABAD
subroutine dlaqr1(N, H, LDH, SR1, SI1, SR2, SI2, V)
DLAQR1 sets a scalar multiple of the first column of the product of 2-by-2 or 3-by-3 matrix H and spe...
subroutine dlarfg(N, ALPHA, X, INCX, TAU)
DLARFG generates an elementary reflector (Householder matrix).