LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ zunbdb()

 subroutine zunbdb ( character TRANS, character SIGNS, integer M, integer P, integer Q, complex*16, dimension( ldx11, * ) X11, integer LDX11, complex*16, dimension( ldx12, * ) X12, integer LDX12, complex*16, dimension( ldx21, * ) X21, integer LDX21, complex*16, dimension( ldx22, * ) X22, integer LDX22, double precision, dimension( * ) THETA, double precision, dimension( * ) PHI, complex*16, dimension( * ) TAUP1, complex*16, dimension( * ) TAUP2, complex*16, dimension( * ) TAUQ1, complex*16, dimension( * ) TAUQ2, complex*16, dimension( * ) WORK, integer LWORK, integer INFO )

ZUNBDB

Purpose:
``` ZUNBDB 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 ZUNCSD
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*16 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*16 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*16 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*16 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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*16 array, dimension (P) The scalar factors of the elementary reflectors that define P1.``` [out] TAUP2 ``` TAUP2 is COMPLEX*16 array, dimension (M-P) The scalar factors of the elementary reflectors that define P2.``` [out] TAUQ1 ``` TAUQ1 is COMPLEX*16 array, dimension (Q) The scalar factors of the elementary reflectors that define Q1.``` [out] TAUQ2 ``` TAUQ2 is COMPLEX*16 array, dimension (M-Q) The scalar factors of the elementary reflectors that define Q2.``` [out] WORK ` WORK is COMPLEX*16 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.```
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 ZUNCSD for details.

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

Definition at line 284 of file zunbdb.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  DOUBLE PRECISION PHI( * ), THETA( * )
299  COMPLEX*16 TAUP1( * ), TAUP2( * ), TAUQ1( * ), TAUQ2( * ),
300  \$ WORK( * ), X11( LDX11, * ), X12( LDX12, * ),
301  \$ X21( LDX21, * ), X22( LDX22, * )
302 * ..
303 *
304 * ====================================================================
305 *
306 * .. Parameters ..
307  DOUBLE PRECISION REALONE
308  parameter( realone = 1.0d0 )
309  COMPLEX*16 ONE
310  parameter( one = (1.0d0,0.0d0) )
311 * ..
312 * .. Local Scalars ..
313  LOGICAL COLMAJOR, LQUERY
314  INTEGER I, LWORKMIN, LWORKOPT
315  DOUBLE PRECISION Z1, Z2, Z3, Z4
316 * ..
317 * .. External Subroutines ..
318  EXTERNAL zaxpy, zlarf, zlarfgp, zscal, xerbla
319  EXTERNAL zlacgv
320 *
321 * ..
322 * .. External Functions ..
323  DOUBLE PRECISION DZNRM2
324  LOGICAL LSAME
325  EXTERNAL dznrm2, lsame
326 * ..
327 * .. Intrinsic Functions
328  INTRINSIC atan2, cos, max, min, sin
329  INTRINSIC dcmplx, dconjg
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 zscal( p-i+1, dcmplx( z1, 0.0d0 ), x11(i,i), 1 )
402  ELSE
403  CALL zscal( p-i+1, dcmplx( z1*cos(phi(i-1)), 0.0d0 ),
404  \$ x11(i,i), 1 )
405  CALL zaxpy( p-i+1, dcmplx( -z1*z3*z4*sin(phi(i-1)),
406  \$ 0.0d0 ), x12(i,i-1), 1, x11(i,i), 1 )
407  END IF
408  IF( i .EQ. 1 ) THEN
409  CALL zscal( m-p-i+1, dcmplx( z2, 0.0d0 ), x21(i,i), 1 )
410  ELSE
411  CALL zscal( m-p-i+1, dcmplx( z2*cos(phi(i-1)), 0.0d0 ),
412  \$ x21(i,i), 1 )
413  CALL zaxpy( m-p-i+1, dcmplx( -z2*z3*z4*sin(phi(i-1)),
414  \$ 0.0d0 ), x22(i,i-1), 1, x21(i,i), 1 )
415  END IF
416 *
417  theta(i) = atan2( dznrm2( m-p-i+1, x21(i,i), 1 ),
418  \$ dznrm2( p-i+1, x11(i,i), 1 ) )
419 *
420  IF( p .GT. i ) THEN
421  CALL zlarfgp( p-i+1, x11(i,i), x11(i+1,i), 1, taup1(i) )
422  ELSE IF ( p .EQ. i ) THEN
423  CALL zlarfgp( 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 zlarfgp( 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 zlarfgp( 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 zlarf( 'L', p-i+1, q-i, x11(i,i), 1,
437  \$ dconjg(taup1(i)), x11(i,i+1), ldx11, work )
438  CALL zlarf( 'L', m-p-i+1, q-i, x21(i,i), 1,
439  \$ dconjg(taup2(i)), x21(i,i+1), ldx21, work )
440  END IF
441  IF ( m-q+1 .GT. i ) THEN
442  CALL zlarf( 'L', p-i+1, m-q-i+1, x11(i,i), 1,
443  \$ dconjg(taup1(i)), x12(i,i), ldx12, work )
444  CALL zlarf( 'L', m-p-i+1, m-q-i+1, x21(i,i), 1,
445  \$ dconjg(taup2(i)), x22(i,i), ldx22, work )
446  END IF
447 *
448  IF( i .LT. q ) THEN
449  CALL zscal( q-i, dcmplx( -z1*z3*sin(theta(i)), 0.0d0 ),
450  \$ x11(i,i+1), ldx11 )
451  CALL zaxpy( q-i, dcmplx( z2*z3*cos(theta(i)), 0.0d0 ),
452  \$ x21(i,i+1), ldx21, x11(i,i+1), ldx11 )
453  END IF
454  CALL zscal( m-q-i+1, dcmplx( -z1*z4*sin(theta(i)), 0.0d0 ),
455  \$ x12(i,i), ldx12 )
456  CALL zaxpy( m-q-i+1, dcmplx( z2*z4*cos(theta(i)), 0.0d0 ),
457  \$ x22(i,i), ldx22, x12(i,i), ldx12 )
458 *
459  IF( i .LT. q )
460  \$ phi(i) = atan2( dznrm2( q-i, x11(i,i+1), ldx11 ),
461  \$ dznrm2( m-q-i+1, x12(i,i), ldx12 ) )
462 *
463  IF( i .LT. q ) THEN
464  CALL zlacgv( q-i, x11(i,i+1), ldx11 )
465  IF ( i .EQ. q-1 ) THEN
466  CALL zlarfgp( q-i, x11(i,i+1), x11(i,i+1), ldx11,
467  \$ tauq1(i) )
468  ELSE
469  CALL zlarfgp( 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 zlacgv( m-q-i+1, x12(i,i), ldx12 )
476  IF ( m-q .EQ. i ) THEN
477  CALL zlarfgp( m-q-i+1, x12(i,i), x12(i,i), ldx12,
478  \$ tauq2(i) )
479  ELSE
480  CALL zlarfgp( 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 zlarf( 'R', p-i, q-i, x11(i,i+1), ldx11, tauq1(i),
488  \$ x11(i+1,i+1), ldx11, work )
489  CALL zlarf( '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 zlarf( '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 zlarf( '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 zlacgv( q-i, x11(i,i+1), ldx11 )
503  CALL zlacgv( 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 zscal( m-q-i+1, dcmplx( -z1*z4, 0.0d0 ), x12(i,i),
512  \$ ldx12 )
513  CALL zlacgv( m-q-i+1, x12(i,i), ldx12 )
514  IF ( i .GE. m-q ) THEN
515  CALL zlarfgp( m-q-i+1, x12(i,i), x12(i,i), ldx12,
516  \$ tauq2(i) )
517  ELSE
518  CALL zlarfgp( 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 zlarf( '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 zlarf( 'R', m-p-q, m-q-i+1, x12(i,i), ldx12,
529  \$ tauq2(i), x22(q+1,i), ldx22, work )
530 *
531  CALL zlacgv( 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 zscal( m-p-q-i+1, dcmplx( z2*z4, 0.0d0 ),
540  \$ x22(q+i,p+i), ldx22 )
541  CALL zlacgv( m-p-q-i+1, x22(q+i,p+i), ldx22 )
542  CALL zlarfgp( 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 zlarf( '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 zlacgv( 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 zscal( p-i+1, dcmplx( z1, 0.0d0 ), x11(i,i),
560  \$ ldx11 )
561  ELSE
562  CALL zscal( p-i+1, dcmplx( z1*cos(phi(i-1)), 0.0d0 ),
563  \$ x11(i,i), ldx11 )
564  CALL zaxpy( p-i+1, dcmplx( -z1*z3*z4*sin(phi(i-1)),
565  \$ 0.0d0 ), x12(i-1,i), ldx12, x11(i,i), ldx11 )
566  END IF
567  IF( i .EQ. 1 ) THEN
568  CALL zscal( m-p-i+1, dcmplx( z2, 0.0d0 ), x21(i,i),
569  \$ ldx21 )
570  ELSE
571  CALL zscal( m-p-i+1, dcmplx( z2*cos(phi(i-1)), 0.0d0 ),
572  \$ x21(i,i), ldx21 )
573  CALL zaxpy( m-p-i+1, dcmplx( -z2*z3*z4*sin(phi(i-1)),
574  \$ 0.0d0 ), x22(i-1,i), ldx22, x21(i,i), ldx21 )
575  END IF
576 *
577  theta(i) = atan2( dznrm2( m-p-i+1, x21(i,i), ldx21 ),
578  \$ dznrm2( p-i+1, x11(i,i), ldx11 ) )
579 *
580  CALL zlacgv( p-i+1, x11(i,i), ldx11 )
581  CALL zlacgv( m-p-i+1, x21(i,i), ldx21 )
582 *
583  CALL zlarfgp( 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 zlarfgp( m-p-i+1, x21(i,i), x21(i,i), ldx21,
587  \$ taup2(i) )
588  ELSE
589  CALL zlarfgp( 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 zlarf( 'R', q-i, p-i+1, x11(i,i), ldx11, taup1(i),
595  \$ x11(i+1,i), ldx11, work )
596  CALL zlarf( 'R', m-q-i+1, p-i+1, x11(i,i), ldx11, taup1(i),
597  \$ x12(i,i), ldx12, work )
598  CALL zlarf( 'R', q-i, m-p-i+1, x21(i,i), ldx21, taup2(i),
599  \$ x21(i+1,i), ldx21, work )
600  CALL zlarf( 'R', m-q-i+1, m-p-i+1, x21(i,i), ldx21,
601  \$ taup2(i), x22(i,i), ldx22, work )
602 *
603  CALL zlacgv( p-i+1, x11(i,i), ldx11 )
604  CALL zlacgv( m-p-i+1, x21(i,i), ldx21 )
605 *
606  IF( i .LT. q ) THEN
607  CALL zscal( q-i, dcmplx( -z1*z3*sin(theta(i)), 0.0d0 ),
608  \$ x11(i+1,i), 1 )
609  CALL zaxpy( q-i, dcmplx( z2*z3*cos(theta(i)), 0.0d0 ),
610  \$ x21(i+1,i), 1, x11(i+1,i), 1 )
611  END IF
612  CALL zscal( m-q-i+1, dcmplx( -z1*z4*sin(theta(i)), 0.0d0 ),
613  \$ x12(i,i), 1 )
614  CALL zaxpy( m-q-i+1, dcmplx( z2*z4*cos(theta(i)), 0.0d0 ),
615  \$ x22(i,i), 1, x12(i,i), 1 )
616 *
617  IF( i .LT. q )
618  \$ phi(i) = atan2( dznrm2( q-i, x11(i+1,i), 1 ),
619  \$ dznrm2( m-q-i+1, x12(i,i), 1 ) )
620 *
621  IF( i .LT. q ) THEN
622  CALL zlarfgp( q-i, x11(i+1,i), x11(i+2,i), 1, tauq1(i) )
623  x11(i+1,i) = one
624  END IF
625  CALL zlarfgp( 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 zlarf( 'L', q-i, p-i, x11(i+1,i), 1,
630  \$ dconjg(tauq1(i)), x11(i+1,i+1), ldx11, work )
631  CALL zlarf( 'L', q-i, m-p-i, x11(i+1,i), 1,
632  \$ dconjg(tauq1(i)), x21(i+1,i+1), ldx21, work )
633  END IF
634  CALL zlarf( 'L', m-q-i+1, p-i, x12(i,i), 1,
635  \$ dconjg(tauq2(i)), x12(i,i+1), ldx12, work )
636  IF ( m-p .GT. i ) THEN
637  CALL zlarf( 'L', m-q-i+1, m-p-i, x12(i,i), 1,
638  \$ dconjg(tauq2(i)), x22(i,i+1), ldx22, work )
639  END IF
640 *
641  END DO
642 *
643 * Reduce columns Q + 1, ..., P of X12, X22
644 *
645  DO i = q + 1, p
646 *
647  CALL zscal( m-q-i+1, dcmplx( -z1*z4, 0.0d0 ), x12(i,i), 1 )
648  CALL zlarfgp( 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 zlarf( 'L', m-q-i+1, p-i, x12(i,i), 1,
653  \$ dconjg(tauq2(i)), x12(i,i+1), ldx12, work )
654  END IF
655  IF( m-p-q .GE. 1 )
656  \$ CALL zlarf( 'L', m-q-i+1, m-p-q, x12(i,i), 1,
657  \$ dconjg(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 zscal( m-p-q-i+1, dcmplx( z2*z4, 0.0d0 ),
666  \$ x22(p+i,q+i), 1 )
667  CALL zlarfgp( 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 *
671  IF ( m-p-q .NE. i ) THEN
672  CALL zlarf( 'L', m-p-q-i+1, m-p-q-i, x22(p+i,q+i), 1,
673  \$ dconjg(tauq2(p+i)), x22(p+i,q+i+1), ldx22,
674  \$ work )
675  END IF
676 *
677  END DO
678 *
679  END IF
680 *
681  RETURN
682 *
683 * End of ZUNBDB
684 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine zaxpy(N, ZA, ZX, INCX, ZY, INCY)
ZAXPY
Definition: zaxpy.f:88
subroutine zscal(N, ZA, ZX, INCX)
ZSCAL
Definition: zscal.f:78
subroutine zlarfgp(N, ALPHA, X, INCX, TAU)
ZLARFGP generates an elementary reflector (Householder matrix) with non-negative beta.
Definition: zlarfgp.f:104
subroutine zlacgv(N, X, INCX)
ZLACGV conjugates a complex vector.
Definition: zlacgv.f:74
subroutine zlarf(SIDE, M, N, V, INCV, TAU, C, LDC, WORK)
ZLARF applies an elementary reflector to a general rectangular matrix.
Definition: zlarf.f:128
real(wp) function dznrm2(n, x, incx)
DZNRM2
Definition: dznrm2.f90:90
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