LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ cunbdb()

subroutine cunbdb ( character  TRANS,
character  SIGNS,
integer  M,
integer  P,
integer  Q,
complex, dimension( ldx11, * )  X11,
integer  LDX11,
complex, dimension( ldx12, * )  X12,
integer  LDX12,
complex, dimension( ldx21, * )  X21,
integer  LDX21,
complex, dimension( ldx22, * )  X22,
integer  LDX22,
real, dimension( * )  THETA,
real, dimension( * )  PHI,
complex, dimension( * )  TAUP1,
complex, dimension( * )  TAUP2,
complex, dimension( * )  TAUQ1,
complex, dimension( * )  TAUQ2,
complex, dimension( * )  WORK,
integer  LWORK,
integer  INFO 
)

CUNBDB

Download CUNBDB + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 CUNBDB simultaneously bidiagonalizes the blocks of an M-by-M
 partitioned unitary matrix X:

                                 [ B11 | B12 0  0 ]
     [ X11 | X12 ]   [ P1 |    ] [  0  |  0 -I  0 ] [ Q1 |    ]**H
 X = [-----------] = [---------] [----------------] [---------]   .
     [ X21 | X22 ]   [    | P2 ] [ B21 | B22 0  0 ] [    | Q2 ]
                                 [  0  |  0  0  I ]

 X11 is P-by-Q. Q must be no larger than P, M-P, or M-Q. (If this is
 not the case, then X must be transposed and/or permuted. This can be
 done in constant time using the TRANS and SIGNS options. See CUNCSD
 for details.)

 The unitary matrices P1, P2, Q1, and Q2 are P-by-P, (M-P)-by-
 (M-P), Q-by-Q, and (M-Q)-by-(M-Q), respectively. They are
 represented implicitly by Householder vectors.

 B11, B12, B21, and B22 are Q-by-Q bidiagonal matrices represented
 implicitly by angles THETA, PHI.
Parameters
[in]TRANS
          TRANS is CHARACTER
          = 'T':      X, U1, U2, V1T, and V2T are stored in row-major
                      order;
          otherwise:  X, U1, U2, V1T, and V2T are stored in column-
                      major order.
[in]SIGNS
          SIGNS is CHARACTER
          = 'O':      The lower-left block is made nonpositive (the
                      "other" convention);
          otherwise:  The upper-right block is made nonpositive (the
                      "default" convention).
[in]M
          M is INTEGER
          The number of rows and columns in X.
[in]P
          P is INTEGER
          The number of rows in X11 and X12. 0 <= P <= M.
[in]Q
          Q is INTEGER
          The number of columns in X11 and X21. 0 <= Q <=
          MIN(P,M-P,M-Q).
[in,out]X11
          X11 is COMPLEX array, dimension (LDX11,Q)
          On entry, the top-left block of the unitary matrix to be
          reduced. On exit, the form depends on TRANS:
          If TRANS = 'N', then
             the columns of tril(X11) specify reflectors for P1,
             the rows of triu(X11,1) specify reflectors for Q1;
          else TRANS = 'T', and
             the rows of triu(X11) specify reflectors for P1,
             the columns of tril(X11,-1) specify reflectors for Q1.
[in]LDX11
          LDX11 is INTEGER
          The leading dimension of X11. If TRANS = 'N', then LDX11 >=
          P; else LDX11 >= Q.
[in,out]X12
          X12 is COMPLEX array, dimension (LDX12,M-Q)
          On entry, the top-right block of the unitary matrix to
          be reduced. On exit, the form depends on TRANS:
          If TRANS = 'N', then
             the rows of triu(X12) specify the first P reflectors for
             Q2;
          else TRANS = 'T', and
             the columns of tril(X12) specify the first P reflectors
             for Q2.
[in]LDX12
          LDX12 is INTEGER
          The leading dimension of X12. If TRANS = 'N', then LDX12 >=
          P; else LDX11 >= M-Q.
[in,out]X21
          X21 is COMPLEX array, dimension (LDX21,Q)
          On entry, the bottom-left block of the unitary matrix to
          be reduced. On exit, the form depends on TRANS:
          If TRANS = 'N', then
             the columns of tril(X21) specify reflectors for P2;
          else TRANS = 'T', and
             the rows of triu(X21) specify reflectors for P2.
[in]LDX21
          LDX21 is INTEGER
          The leading dimension of X21. If TRANS = 'N', then LDX21 >=
          M-P; else LDX21 >= Q.
[in,out]X22
          X22 is COMPLEX array, dimension (LDX22,M-Q)
          On entry, the bottom-right block of the unitary matrix to
          be reduced. On exit, the form depends on TRANS:
          If TRANS = 'N', then
             the rows of triu(X22(Q+1:M-P,P+1:M-Q)) specify the last
             M-P-Q reflectors for Q2,
          else TRANS = 'T', and
             the columns of tril(X22(P+1:M-Q,Q+1:M-P)) specify the last
             M-P-Q reflectors for P2.
[in]LDX22
          LDX22 is INTEGER
          The leading dimension of X22. If TRANS = 'N', then LDX22 >=
          M-P; else LDX22 >= M-Q.
[out]THETA
          THETA is REAL array, dimension (Q)
          The entries of the bidiagonal blocks B11, B12, B21, B22 can
          be computed from the angles THETA and PHI. See Further
          Details.
[out]PHI
          PHI is REAL array, dimension (Q-1)
          The entries of the bidiagonal blocks B11, B12, B21, B22 can
          be computed from the angles THETA and PHI. See Further
          Details.
[out]TAUP1
          TAUP1 is COMPLEX array, dimension (P)
          The scalar factors of the elementary reflectors that define
          P1.
[out]TAUP2
          TAUP2 is COMPLEX array, dimension (M-P)
          The scalar factors of the elementary reflectors that define
          P2.
[out]TAUQ1
          TAUQ1 is COMPLEX array, dimension (Q)
          The scalar factors of the elementary reflectors that define
          Q1.
[out]TAUQ2
          TAUQ2 is COMPLEX array, dimension (M-Q)
          The scalar factors of the elementary reflectors that define
          Q2.
[out]WORK
          WORK is COMPLEX array, dimension (LWORK)
[in]LWORK
          LWORK is INTEGER
          The dimension of the array WORK. LWORK >= M-Q.

          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK is issued by XERBLA.
[out]INFO
          INFO is INTEGER
          = 0:  successful exit.
          < 0:  if INFO = -i, the i-th argument had an illegal value.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
  The bidiagonal blocks B11, B12, B21, and B22 are represented
  implicitly by angles THETA(1), ..., THETA(Q) and PHI(1), ...,
  PHI(Q-1). B11 and B21 are upper bidiagonal, while B21 and B22 are
  lower bidiagonal. Every entry in each bidiagonal band is a product
  of a sine or cosine of a THETA with a sine or cosine of a PHI. See
  [1] or CUNCSD for details.

  P1, P2, Q1, and Q2 are represented as products of elementary
  reflectors. See CUNCSD for details on generating P1, P2, Q1, and Q2
  using CUNGQR and CUNGLQ.
References:
[1] Brian D. Sutton. Computing the complete CS decomposition. Numer. Algorithms, 50(1):33-65, 2009.

Definition at line 284 of file cunbdb.f.

287 *
288 * -- LAPACK computational routine --
289 * -- LAPACK is a software package provided by Univ. of Tennessee, --
290 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
291 *
292 * .. Scalar Arguments ..
293  CHARACTER SIGNS, TRANS
294  INTEGER INFO, LDX11, LDX12, LDX21, LDX22, LWORK, M, P,
295  $ Q
296 * ..
297 * .. Array Arguments ..
298  REAL PHI( * ), THETA( * )
299  COMPLEX TAUP1( * ), TAUP2( * ), TAUQ1( * ), TAUQ2( * ),
300  $ WORK( * ), X11( LDX11, * ), X12( LDX12, * ),
301  $ X21( LDX21, * ), X22( LDX22, * )
302 * ..
303 *
304 * ====================================================================
305 *
306 * .. Parameters ..
307  REAL REALONE
308  parameter( realone = 1.0e0 )
309  COMPLEX ONE
310  parameter( one = (1.0e0,0.0e0) )
311 * ..
312 * .. Local Scalars ..
313  LOGICAL COLMAJOR, LQUERY
314  INTEGER I, LWORKMIN, LWORKOPT
315  REAL Z1, Z2, Z3, Z4
316 * ..
317 * .. External Subroutines ..
318  EXTERNAL caxpy, clarf, clarfgp, cscal, xerbla
319  EXTERNAL clacgv
320 *
321 * ..
322 * .. External Functions ..
323  REAL SCNRM2
324  LOGICAL LSAME
325  EXTERNAL scnrm2, lsame
326 * ..
327 * .. Intrinsic Functions
328  INTRINSIC atan2, cos, max, min, sin
329  INTRINSIC cmplx, conjg
330 * ..
331 * .. Executable Statements ..
332 *
333 * Test input arguments
334 *
335  info = 0
336  colmajor = .NOT. lsame( trans, 'T' )
337  IF( .NOT. lsame( signs, 'O' ) ) THEN
338  z1 = realone
339  z2 = realone
340  z3 = realone
341  z4 = realone
342  ELSE
343  z1 = realone
344  z2 = -realone
345  z3 = realone
346  z4 = -realone
347  END IF
348  lquery = lwork .EQ. -1
349 *
350  IF( m .LT. 0 ) THEN
351  info = -3
352  ELSE IF( p .LT. 0 .OR. p .GT. m ) THEN
353  info = -4
354  ELSE IF( q .LT. 0 .OR. q .GT. p .OR. q .GT. m-p .OR.
355  $ q .GT. m-q ) THEN
356  info = -5
357  ELSE IF( colmajor .AND. ldx11 .LT. max( 1, p ) ) THEN
358  info = -7
359  ELSE IF( .NOT.colmajor .AND. ldx11 .LT. max( 1, q ) ) THEN
360  info = -7
361  ELSE IF( colmajor .AND. ldx12 .LT. max( 1, p ) ) THEN
362  info = -9
363  ELSE IF( .NOT.colmajor .AND. ldx12 .LT. max( 1, m-q ) ) THEN
364  info = -9
365  ELSE IF( colmajor .AND. ldx21 .LT. max( 1, m-p ) ) THEN
366  info = -11
367  ELSE IF( .NOT.colmajor .AND. ldx21 .LT. max( 1, q ) ) THEN
368  info = -11
369  ELSE IF( colmajor .AND. ldx22 .LT. max( 1, m-p ) ) THEN
370  info = -13
371  ELSE IF( .NOT.colmajor .AND. ldx22 .LT. max( 1, m-q ) ) THEN
372  info = -13
373  END IF
374 *
375 * Compute workspace
376 *
377  IF( info .EQ. 0 ) THEN
378  lworkopt = m - q
379  lworkmin = m - q
380  work(1) = lworkopt
381  IF( lwork .LT. lworkmin .AND. .NOT. lquery ) THEN
382  info = -21
383  END IF
384  END IF
385  IF( info .NE. 0 ) THEN
386  CALL xerbla( 'xORBDB', -info )
387  RETURN
388  ELSE IF( lquery ) THEN
389  RETURN
390  END IF
391 *
392 * Handle column-major and row-major separately
393 *
394  IF( colmajor ) THEN
395 *
396 * Reduce columns 1, ..., Q of X11, X12, X21, and X22
397 *
398  DO i = 1, q
399 *
400  IF( i .EQ. 1 ) THEN
401  CALL cscal( p-i+1, cmplx( z1, 0.0e0 ), x11(i,i), 1 )
402  ELSE
403  CALL cscal( p-i+1, cmplx( z1*cos(phi(i-1)), 0.0e0 ),
404  $ x11(i,i), 1 )
405  CALL caxpy( p-i+1, cmplx( -z1*z3*z4*sin(phi(i-1)),
406  $ 0.0e0 ), x12(i,i-1), 1, x11(i,i), 1 )
407  END IF
408  IF( i .EQ. 1 ) THEN
409  CALL cscal( m-p-i+1, cmplx( z2, 0.0e0 ), x21(i,i), 1 )
410  ELSE
411  CALL cscal( m-p-i+1, cmplx( z2*cos(phi(i-1)), 0.0e0 ),
412  $ x21(i,i), 1 )
413  CALL caxpy( m-p-i+1, cmplx( -z2*z3*z4*sin(phi(i-1)),
414  $ 0.0e0 ), x22(i,i-1), 1, x21(i,i), 1 )
415  END IF
416 *
417  theta(i) = atan2( scnrm2( m-p-i+1, x21(i,i), 1 ),
418  $ scnrm2( p-i+1, x11(i,i), 1 ) )
419 *
420  IF( p .GT. i ) THEN
421  CALL clarfgp( p-i+1, x11(i,i), x11(i+1,i), 1, taup1(i) )
422  ELSE IF ( p .EQ. i ) THEN
423  CALL clarfgp( p-i+1, x11(i,i), x11(i,i), 1, taup1(i) )
424  END IF
425  x11(i,i) = one
426  IF ( m-p .GT. i ) THEN
427  CALL clarfgp( m-p-i+1, x21(i,i), x21(i+1,i), 1,
428  $ taup2(i) )
429  ELSE IF ( m-p .EQ. i ) THEN
430  CALL clarfgp( m-p-i+1, x21(i,i), x21(i,i), 1,
431  $ taup2(i) )
432  END IF
433  x21(i,i) = one
434 *
435  IF ( q .GT. i ) THEN
436  CALL clarf( 'L', p-i+1, q-i, x11(i,i), 1,
437  $ conjg(taup1(i)), x11(i,i+1), ldx11, work )
438  CALL clarf( 'L', m-p-i+1, q-i, x21(i,i), 1,
439  $ conjg(taup2(i)), x21(i,i+1), ldx21, work )
440  END IF
441  IF ( m-q+1 .GT. i ) THEN
442  CALL clarf( 'L', p-i+1, m-q-i+1, x11(i,i), 1,
443  $ conjg(taup1(i)), x12(i,i), ldx12, work )
444  CALL clarf( 'L', m-p-i+1, m-q-i+1, x21(i,i), 1,
445  $ conjg(taup2(i)), x22(i,i), ldx22, work )
446  END IF
447 *
448  IF( i .LT. q ) THEN
449  CALL cscal( q-i, cmplx( -z1*z3*sin(theta(i)), 0.0e0 ),
450  $ x11(i,i+1), ldx11 )
451  CALL caxpy( q-i, cmplx( z2*z3*cos(theta(i)), 0.0e0 ),
452  $ x21(i,i+1), ldx21, x11(i,i+1), ldx11 )
453  END IF
454  CALL cscal( m-q-i+1, cmplx( -z1*z4*sin(theta(i)), 0.0e0 ),
455  $ x12(i,i), ldx12 )
456  CALL caxpy( m-q-i+1, cmplx( z2*z4*cos(theta(i)), 0.0e0 ),
457  $ x22(i,i), ldx22, x12(i,i), ldx12 )
458 *
459  IF( i .LT. q )
460  $ phi(i) = atan2( scnrm2( q-i, x11(i,i+1), ldx11 ),
461  $ scnrm2( m-q-i+1, x12(i,i), ldx12 ) )
462 *
463  IF( i .LT. q ) THEN
464  CALL clacgv( q-i, x11(i,i+1), ldx11 )
465  IF ( i .EQ. q-1 ) THEN
466  CALL clarfgp( q-i, x11(i,i+1), x11(i,i+1), ldx11,
467  $ tauq1(i) )
468  ELSE
469  CALL clarfgp( q-i, x11(i,i+1), x11(i,i+2), ldx11,
470  $ tauq1(i) )
471  END IF
472  x11(i,i+1) = one
473  END IF
474  IF ( m-q+1 .GT. i ) THEN
475  CALL clacgv( m-q-i+1, x12(i,i), ldx12 )
476  IF ( m-q .EQ. i ) THEN
477  CALL clarfgp( m-q-i+1, x12(i,i), x12(i,i), ldx12,
478  $ tauq2(i) )
479  ELSE
480  CALL clarfgp( m-q-i+1, x12(i,i), x12(i,i+1), ldx12,
481  $ tauq2(i) )
482  END IF
483  END IF
484  x12(i,i) = one
485 *
486  IF( i .LT. q ) THEN
487  CALL clarf( 'R', p-i, q-i, x11(i,i+1), ldx11, tauq1(i),
488  $ x11(i+1,i+1), ldx11, work )
489  CALL clarf( 'R', m-p-i, q-i, x11(i,i+1), ldx11, tauq1(i),
490  $ x21(i+1,i+1), ldx21, work )
491  END IF
492  IF ( p .GT. i ) THEN
493  CALL clarf( 'R', p-i, m-q-i+1, x12(i,i), ldx12, tauq2(i),
494  $ x12(i+1,i), ldx12, work )
495  END IF
496  IF ( m-p .GT. i ) THEN
497  CALL clarf( 'R', m-p-i, m-q-i+1, x12(i,i), ldx12,
498  $ tauq2(i), x22(i+1,i), ldx22, work )
499  END IF
500 *
501  IF( i .LT. q )
502  $ CALL clacgv( q-i, x11(i,i+1), ldx11 )
503  CALL clacgv( m-q-i+1, x12(i,i), ldx12 )
504 *
505  END DO
506 *
507 * Reduce columns Q + 1, ..., P of X12, X22
508 *
509  DO i = q + 1, p
510 *
511  CALL cscal( m-q-i+1, cmplx( -z1*z4, 0.0e0 ), x12(i,i),
512  $ ldx12 )
513  CALL clacgv( m-q-i+1, x12(i,i), ldx12 )
514  IF ( i .GE. m-q ) THEN
515  CALL clarfgp( m-q-i+1, x12(i,i), x12(i,i), ldx12,
516  $ tauq2(i) )
517  ELSE
518  CALL clarfgp( m-q-i+1, x12(i,i), x12(i,i+1), ldx12,
519  $ tauq2(i) )
520  END IF
521  x12(i,i) = one
522 *
523  IF ( p .GT. i ) THEN
524  CALL clarf( 'R', p-i, m-q-i+1, x12(i,i), ldx12, tauq2(i),
525  $ x12(i+1,i), ldx12, work )
526  END IF
527  IF( m-p-q .GE. 1 )
528  $ CALL clarf( 'R', m-p-q, m-q-i+1, x12(i,i), ldx12,
529  $ tauq2(i), x22(q+1,i), ldx22, work )
530 *
531  CALL clacgv( m-q-i+1, x12(i,i), ldx12 )
532 *
533  END DO
534 *
535 * Reduce columns P + 1, ..., M - Q of X12, X22
536 *
537  DO i = 1, m - p - q
538 *
539  CALL cscal( m-p-q-i+1, cmplx( z2*z4, 0.0e0 ),
540  $ x22(q+i,p+i), ldx22 )
541  CALL clacgv( m-p-q-i+1, x22(q+i,p+i), ldx22 )
542  CALL clarfgp( m-p-q-i+1, x22(q+i,p+i), x22(q+i,p+i+1),
543  $ ldx22, tauq2(p+i) )
544  x22(q+i,p+i) = one
545  CALL clarf( 'R', m-p-q-i, m-p-q-i+1, x22(q+i,p+i), ldx22,
546  $ tauq2(p+i), x22(q+i+1,p+i), ldx22, work )
547 *
548  CALL clacgv( m-p-q-i+1, x22(q+i,p+i), ldx22 )
549 *
550  END DO
551 *
552  ELSE
553 *
554 * Reduce columns 1, ..., Q of X11, X12, X21, X22
555 *
556  DO i = 1, q
557 *
558  IF( i .EQ. 1 ) THEN
559  CALL cscal( p-i+1, cmplx( z1, 0.0e0 ), x11(i,i),
560  $ ldx11 )
561  ELSE
562  CALL cscal( p-i+1, cmplx( z1*cos(phi(i-1)), 0.0e0 ),
563  $ x11(i,i), ldx11 )
564  CALL caxpy( p-i+1, cmplx( -z1*z3*z4*sin(phi(i-1)),
565  $ 0.0e0 ), x12(i-1,i), ldx12, x11(i,i), ldx11 )
566  END IF
567  IF( i .EQ. 1 ) THEN
568  CALL cscal( m-p-i+1, cmplx( z2, 0.0e0 ), x21(i,i),
569  $ ldx21 )
570  ELSE
571  CALL cscal( m-p-i+1, cmplx( z2*cos(phi(i-1)), 0.0e0 ),
572  $ x21(i,i), ldx21 )
573  CALL caxpy( m-p-i+1, cmplx( -z2*z3*z4*sin(phi(i-1)),
574  $ 0.0e0 ), x22(i-1,i), ldx22, x21(i,i), ldx21 )
575  END IF
576 *
577  theta(i) = atan2( scnrm2( m-p-i+1, x21(i,i), ldx21 ),
578  $ scnrm2( p-i+1, x11(i,i), ldx11 ) )
579 *
580  CALL clacgv( p-i+1, x11(i,i), ldx11 )
581  CALL clacgv( m-p-i+1, x21(i,i), ldx21 )
582 *
583  CALL clarfgp( p-i+1, x11(i,i), x11(i,i+1), ldx11, taup1(i) )
584  x11(i,i) = one
585  IF ( i .EQ. m-p ) THEN
586  CALL clarfgp( m-p-i+1, x21(i,i), x21(i,i), ldx21,
587  $ taup2(i) )
588  ELSE
589  CALL clarfgp( m-p-i+1, x21(i,i), x21(i,i+1), ldx21,
590  $ taup2(i) )
591  END IF
592  x21(i,i) = one
593 *
594  CALL clarf( 'R', q-i, p-i+1, x11(i,i), ldx11, taup1(i),
595  $ x11(i+1,i), ldx11, work )
596  CALL clarf( 'R', m-q-i+1, p-i+1, x11(i,i), ldx11, taup1(i),
597  $ x12(i,i), ldx12, work )
598  CALL clarf( 'R', q-i, m-p-i+1, x21(i,i), ldx21, taup2(i),
599  $ x21(i+1,i), ldx21, work )
600  CALL clarf( 'R', m-q-i+1, m-p-i+1, x21(i,i), ldx21,
601  $ taup2(i), x22(i,i), ldx22, work )
602 *
603  CALL clacgv( p-i+1, x11(i,i), ldx11 )
604  CALL clacgv( m-p-i+1, x21(i,i), ldx21 )
605 *
606  IF( i .LT. q ) THEN
607  CALL cscal( q-i, cmplx( -z1*z3*sin(theta(i)), 0.0e0 ),
608  $ x11(i+1,i), 1 )
609  CALL caxpy( q-i, cmplx( z2*z3*cos(theta(i)), 0.0e0 ),
610  $ x21(i+1,i), 1, x11(i+1,i), 1 )
611  END IF
612  CALL cscal( m-q-i+1, cmplx( -z1*z4*sin(theta(i)), 0.0e0 ),
613  $ x12(i,i), 1 )
614  CALL caxpy( m-q-i+1, cmplx( z2*z4*cos(theta(i)), 0.0e0 ),
615  $ x22(i,i), 1, x12(i,i), 1 )
616 *
617  IF( i .LT. q )
618  $ phi(i) = atan2( scnrm2( q-i, x11(i+1,i), 1 ),
619  $ scnrm2( m-q-i+1, x12(i,i), 1 ) )
620 *
621  IF( i .LT. q ) THEN
622  CALL clarfgp( q-i, x11(i+1,i), x11(i+2,i), 1, tauq1(i) )
623  x11(i+1,i) = one
624  END IF
625  CALL clarfgp( m-q-i+1, x12(i,i), x12(i+1,i), 1, tauq2(i) )
626  x12(i,i) = one
627 *
628  IF( i .LT. q ) THEN
629  CALL clarf( 'L', q-i, p-i, x11(i+1,i), 1,
630  $ conjg(tauq1(i)), x11(i+1,i+1), ldx11, work )
631  CALL clarf( 'L', q-i, m-p-i, x11(i+1,i), 1,
632  $ conjg(tauq1(i)), x21(i+1,i+1), ldx21, work )
633  END IF
634  CALL clarf( 'L', m-q-i+1, p-i, x12(i,i), 1, conjg(tauq2(i)),
635  $ x12(i,i+1), ldx12, work )
636 
637  IF ( m-p .GT. i ) THEN
638  CALL clarf( 'L', m-q-i+1, m-p-i, x12(i,i), 1,
639  $ conjg(tauq2(i)), x22(i,i+1), ldx22, work )
640  END IF
641  END DO
642 *
643 * Reduce columns Q + 1, ..., P of X12, X22
644 *
645  DO i = q + 1, p
646 *
647  CALL cscal( m-q-i+1, cmplx( -z1*z4, 0.0e0 ), x12(i,i), 1 )
648  CALL clarfgp( m-q-i+1, x12(i,i), x12(i+1,i), 1, tauq2(i) )
649  x12(i,i) = one
650 *
651  IF ( p .GT. i ) THEN
652  CALL clarf( 'L', m-q-i+1, p-i, x12(i,i), 1,
653  $ conjg(tauq2(i)), x12(i,i+1), ldx12, work )
654  END IF
655  IF( m-p-q .GE. 1 )
656  $ CALL clarf( 'L', m-q-i+1, m-p-q, x12(i,i), 1,
657  $ conjg(tauq2(i)), x22(i,q+1), ldx22, work )
658 *
659  END DO
660 *
661 * Reduce columns P + 1, ..., M - Q of X12, X22
662 *
663  DO i = 1, m - p - q
664 *
665  CALL cscal( m-p-q-i+1, cmplx( z2*z4, 0.0e0 ),
666  $ x22(p+i,q+i), 1 )
667  CALL clarfgp( m-p-q-i+1, x22(p+i,q+i), x22(p+i+1,q+i), 1,
668  $ tauq2(p+i) )
669  x22(p+i,q+i) = one
670  IF ( m-p-q .NE. i ) THEN
671  CALL clarf( 'L', m-p-q-i+1, m-p-q-i, x22(p+i,q+i), 1,
672  $ conjg(tauq2(p+i)), x22(p+i,q+i+1), ldx22,
673  $ work )
674  END IF
675  END DO
676 *
677  END IF
678 *
679  RETURN
680 *
681 * End of CUNBDB
682 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine caxpy(N, CA, CX, INCX, CY, INCY)
CAXPY
Definition: caxpy.f:88
subroutine cscal(N, CA, CX, INCX)
CSCAL
Definition: cscal.f:78
subroutine clarfgp(N, ALPHA, X, INCX, TAU)
CLARFGP generates an elementary reflector (Householder matrix) with non-negative beta.
Definition: clarfgp.f:104
subroutine clacgv(N, X, INCX)
CLACGV conjugates a complex vector.
Definition: clacgv.f:74
subroutine clarf(SIDE, M, N, V, INCV, TAU, C, LDC, WORK)
CLARF applies an elementary reflector to a general rectangular matrix.
Definition: clarf.f:128
real(wp) function scnrm2(n, x, incx)
SCNRM2
Definition: scnrm2.f90:90
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