 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ dorbdb5()

 subroutine dorbdb5 ( integer M1, integer M2, integer N, double precision, dimension(*) X1, integer INCX1, double precision, dimension(*) X2, integer INCX2, double precision, dimension(ldq1,*) Q1, integer LDQ1, double precision, dimension(ldq2,*) Q2, integer LDQ2, double precision, dimension(*) WORK, integer LWORK, integer INFO )

DORBDB5

Purpose:
``` DORBDB5 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 dorbdb5.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  DOUBLE PRECISION Q1(LDQ1,*), Q2(LDQ2,*), WORK(*), X1(*), X2(*)
167 * ..
168 *
169 * =====================================================================
170 *
171 * .. Parameters ..
172  DOUBLE PRECISION ONE, ZERO
173  parameter( one = 1.0d0, zero = 0.0d0 )
174 * ..
175 * .. Local Scalars ..
176  INTEGER CHILDINFO, I, J
177 * ..
178 * .. External Subroutines ..
179  EXTERNAL dorbdb6, xerbla
180 * ..
181 * .. External Functions ..
182  DOUBLE PRECISION DNRM2
183  EXTERNAL dnrm2
184 * ..
185 * .. Intrinsic Function ..
186  INTRINSIC max
187 * ..
188 * .. Executable Statements ..
189 *
190 * Test input arguments
191 *
192  info = 0
193  IF( m1 .LT. 0 ) THEN
194  info = -1
195  ELSE IF( m2 .LT. 0 ) THEN
196  info = -2
197  ELSE IF( n .LT. 0 ) THEN
198  info = -3
199  ELSE IF( incx1 .LT. 1 ) THEN
200  info = -5
201  ELSE IF( incx2 .LT. 1 ) THEN
202  info = -7
203  ELSE IF( ldq1 .LT. max( 1, m1 ) ) THEN
204  info = -9
205  ELSE IF( ldq2 .LT. max( 1, m2 ) ) THEN
206  info = -11
207  ELSE IF( lwork .LT. n ) THEN
208  info = -13
209  END IF
210 *
211  IF( info .NE. 0 ) THEN
212  CALL xerbla( 'DORBDB5', -info )
213  RETURN
214  END IF
215 *
216 * Project X onto the orthogonal complement of Q
217 *
218  CALL dorbdb6( m1, m2, n, x1, incx1, x2, incx2, q1, ldq1, q2, ldq2,
219  \$ work, lwork, childinfo )
220 *
221 * If the projection is nonzero, then return
222 *
223  IF( dnrm2(m1,x1,incx1) .NE. zero
224  \$ .OR. dnrm2(m2,x2,incx2) .NE. zero ) THEN
225  RETURN
226  END IF
227 *
228 * Project each standard basis vector e_1,...,e_M1 in turn, stopping
229 * when a nonzero projection is found
230 *
231  DO i = 1, m1
232  DO j = 1, m1
233  x1(j) = zero
234  END DO
235  x1(i) = one
236  DO j = 1, m2
237  x2(j) = zero
238  END DO
239  CALL dorbdb6( m1, m2, n, x1, incx1, x2, incx2, q1, ldq1, q2,
240  \$ ldq2, work, lwork, childinfo )
241  IF( dnrm2(m1,x1,incx1) .NE. zero
242  \$ .OR. dnrm2(m2,x2,incx2) .NE. zero ) THEN
243  RETURN
244  END IF
245  END DO
246 *
247 * Project each standard basis vector e_(M1+1),...,e_(M1+M2) in turn,
248 * stopping when a nonzero projection is found
249 *
250  DO i = 1, m2
251  DO j = 1, m1
252  x1(j) = zero
253  END DO
254  DO j = 1, m2
255  x2(j) = zero
256  END DO
257  x2(i) = one
258  CALL dorbdb6( m1, m2, n, x1, incx1, x2, incx2, q1, ldq1, q2,
259  \$ ldq2, work, lwork, childinfo )
260  IF( dnrm2(m1,x1,incx1) .NE. zero
261  \$ .OR. dnrm2(m2,x2,incx2) .NE. zero ) THEN
262  RETURN
263  END IF
264  END DO
265 *
266  RETURN
267 *
268 * End of DORBDB5
269 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine dorbdb6(M1, M2, N, X1, INCX1, X2, INCX2, Q1, LDQ1, Q2, LDQ2, WORK, LWORK, INFO)
DORBDB6
Definition: dorbdb6.f:154
real(wp) function dnrm2(n, x, incx)
DNRM2
Definition: dnrm2.f90:89
Here is the call graph for this function:
Here is the caller graph for this function: