LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ zunbdb5()

 subroutine zunbdb5 ( integer m1, integer m2, integer n, complex*16, dimension(*) x1, integer incx1, complex*16, dimension(*) x2, integer incx2, complex*16, dimension(ldq1,*) q1, integer ldq1, complex*16, dimension(ldq2,*) q2, integer ldq2, complex*16, dimension(*) work, integer lwork, integer info )

ZUNBDB5

Purpose:
``` ZUNBDB5 orthogonalizes the column vector
X = [ X1 ]
[ X2 ]
with respect to the columns of
Q = [ Q1 ] .
[ Q2 ]
The columns of Q must be orthonormal.

If the projection is zero according to Kahan's "twice is enough"
criterion, then some other vector from the orthogonal complement
is returned. This vector is chosen in an arbitrary but deterministic
way.```
Parameters
 [in] M1 ``` M1 is INTEGER The dimension of X1 and the number of rows in Q1. 0 <= M1.``` [in] M2 ``` M2 is INTEGER The dimension of X2 and the number of rows in Q2. 0 <= M2.``` [in] N ``` N is INTEGER The number of columns in Q1 and Q2. 0 <= N.``` [in,out] X1 ``` X1 is COMPLEX*16 array, dimension (M1) On entry, the top part of the vector to be orthogonalized. On exit, the top part of the projected vector.``` [in] INCX1 ``` INCX1 is INTEGER Increment for entries of X1.``` [in,out] X2 ``` X2 is COMPLEX*16 array, dimension (M2) On entry, the bottom part of the vector to be orthogonalized. On exit, the bottom part of the projected vector.``` [in] INCX2 ``` INCX2 is INTEGER Increment for entries of X2.``` [in] Q1 ``` Q1 is COMPLEX*16 array, dimension (LDQ1, N) The top part of the orthonormal basis matrix.``` [in] LDQ1 ``` LDQ1 is INTEGER The leading dimension of Q1. LDQ1 >= M1.``` [in] Q2 ``` Q2 is COMPLEX*16 array, dimension (LDQ2, N) The bottom part of the orthonormal basis matrix.``` [in] LDQ2 ``` LDQ2 is INTEGER The leading dimension of Q2. LDQ2 >= M2.``` [out] WORK ` WORK is COMPLEX*16 array, dimension (LWORK)` [in] LWORK ``` LWORK is INTEGER The dimension of the array WORK. LWORK >= N.``` [out] INFO ``` INFO is INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value.```

Definition at line 154 of file zunbdb5.f.

156*
157* -- LAPACK computational routine --
158* -- LAPACK is a software package provided by Univ. of Tennessee, --
159* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
160*
161* .. Scalar Arguments ..
162 INTEGER INCX1, INCX2, INFO, LDQ1, LDQ2, LWORK, M1, M2,
163 \$ N
164* ..
165* .. Array Arguments ..
166 COMPLEX*16 Q1(LDQ1,*), Q2(LDQ2,*), WORK(*), X1(*), X2(*)
167* ..
168*
169* =====================================================================
170*
171* .. Parameters ..
172 DOUBLE PRECISION REALZERO
173 parameter( realzero = 0.0d0 )
174 COMPLEX*16 ONE, ZERO
175 parameter( one = (1.0d0,0.0d0), zero = (0.0d0,0.0d0) )
176* ..
177* .. Local Scalars ..
178 INTEGER CHILDINFO, I, J
179 DOUBLE PRECISION EPS, NORM, SCL, SSQ
180* ..
181* .. External Subroutines ..
182 EXTERNAL zlassq, zunbdb6, zscal, xerbla
183* ..
184* .. External Functions ..
185 DOUBLE PRECISION DLAMCH, DZNRM2
186 EXTERNAL dlamch, dznrm2
187* ..
188* .. Intrinsic Function ..
189 INTRINSIC max
190* ..
191* .. Executable Statements ..
192*
193* Test input arguments
194*
195 info = 0
196 IF( m1 .LT. 0 ) THEN
197 info = -1
198 ELSE IF( m2 .LT. 0 ) THEN
199 info = -2
200 ELSE IF( n .LT. 0 ) THEN
201 info = -3
202 ELSE IF( incx1 .LT. 1 ) THEN
203 info = -5
204 ELSE IF( incx2 .LT. 1 ) THEN
205 info = -7
206 ELSE IF( ldq1 .LT. max( 1, m1 ) ) THEN
207 info = -9
208 ELSE IF( ldq2 .LT. max( 1, m2 ) ) THEN
209 info = -11
210 ELSE IF( lwork .LT. n ) THEN
211 info = -13
212 END IF
213*
214 IF( info .NE. 0 ) THEN
215 CALL xerbla( 'ZUNBDB5', -info )
216 RETURN
217 END IF
218*
219 eps = dlamch( 'Precision' )
220*
221* Project X onto the orthogonal complement of Q if X is nonzero
222*
223 scl = realzero
224 ssq = realzero
225 CALL zlassq( m1, x1, incx1, scl, ssq )
226 CALL zlassq( m2, x2, incx2, scl, ssq )
227 norm = scl * sqrt( ssq )
228*
229 IF( norm .GT. n * eps ) THEN
230* Scale vector to unit norm to avoid problems in the caller code.
231* Computing the reciprocal is undesirable but
232* * xLASCL cannot be used because of the vector increments and
233* * the round-off error has a negligible impact on
234* orthogonalization.
235 CALL zscal( m1, one / norm, x1, incx1 )
236 CALL zscal( m2, one / norm, x2, incx2 )
237 CALL zunbdb6( m1, m2, n, x1, incx1, x2, incx2, q1, ldq1, q2,
238 \$ ldq2, work, lwork, childinfo )
239*
240* If the projection is nonzero, then return
241*
242 IF( dznrm2(m1,x1,incx1) .NE. realzero
243 \$ .OR. dznrm2(m2,x2,incx2) .NE. realzero ) THEN
244 RETURN
245 END IF
246 END IF
247*
248* Project each standard basis vector e_1,...,e_M1 in turn, stopping
249* when a nonzero projection is found
250*
251 DO i = 1, m1
252 DO j = 1, m1
253 x1(j) = zero
254 END DO
255 x1(i) = one
256 DO j = 1, m2
257 x2(j) = zero
258 END DO
259 CALL zunbdb6( m1, m2, n, x1, incx1, x2, incx2, q1, ldq1, q2,
260 \$ ldq2, work, lwork, childinfo )
261 IF( dznrm2(m1,x1,incx1) .NE. realzero
262 \$ .OR. dznrm2(m2,x2,incx2) .NE. realzero ) THEN
263 RETURN
264 END IF
265 END DO
266*
267* Project each standard basis vector e_(M1+1),...,e_(M1+M2) in turn,
268* stopping when a nonzero projection is found
269*
270 DO i = 1, m2
271 DO j = 1, m1
272 x1(j) = zero
273 END DO
274 DO j = 1, m2
275 x2(j) = zero
276 END DO
277 x2(i) = one
278 CALL zunbdb6( m1, m2, n, x1, incx1, x2, incx2, q1, ldq1, q2,
279 \$ ldq2, work, lwork, childinfo )
280 IF( dznrm2(m1,x1,incx1) .NE. realzero
281 \$ .OR. dznrm2(m2,x2,incx2) .NE. realzero ) THEN
282 RETURN
283 END IF
284 END DO
285*
286 RETURN
287*
288* End of ZUNBDB5
289*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
subroutine zlassq(n, x, incx, scale, sumsq)
ZLASSQ updates a sum of squares represented in scaled form.
Definition zlassq.f90:124
real(wp) function dznrm2(n, x, incx)
DZNRM2
Definition dznrm2.f90:90
subroutine zscal(n, za, zx, incx)
ZSCAL
Definition zscal.f:78
subroutine zunbdb6(m1, m2, n, x1, incx1, x2, incx2, q1, ldq1, q2, ldq2, work, lwork, info)
ZUNBDB6
Definition zunbdb6.f:159
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