 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ sorbdb5()

 subroutine sorbdb5 ( integer M1, integer M2, integer N, real, dimension(*) X1, integer INCX1, real, dimension(*) X2, integer INCX2, real, dimension(ldq1,*) Q1, integer LDQ1, real, dimension(ldq2,*) Q2, integer LDQ2, real, dimension(*) WORK, integer LWORK, integer INFO )

SORBDB5

Purpose:
``` SORBDB5 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 REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 sorbdb5.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  REAL Q1(LDQ1,*), Q2(LDQ2,*), WORK(*), X1(*), X2(*)
167 * ..
168 *
169 * =====================================================================
170 *
171 * .. Parameters ..
172  REAL ONE, ZERO
173  parameter( one = 1.0e0, zero = 0.0e0 )
174 * ..
175 * .. Local Scalars ..
176  INTEGER CHILDINFO, I, J
177 * ..
178 * .. External Subroutines ..
179  EXTERNAL sorbdb6, xerbla
180 * ..
181 * .. External Functions ..
182  REAL SNRM2
183  EXTERNAL snrm2
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( 'SORBDB5', -info )
213  RETURN
214  END IF
215 *
216 * Project X onto the orthogonal complement of Q
217 *
218  CALL sorbdb6( 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( snrm2(m1,x1,incx1) .NE. zero
224  \$ .OR. snrm2(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 sorbdb6( m1, m2, n, x1, incx1, x2, incx2, q1, ldq1, q2,
240  \$ ldq2, work, lwork, childinfo )
241  IF( snrm2(m1,x1,incx1) .NE. zero
242  \$ .OR. snrm2(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 sorbdb6( m1, m2, n, x1, incx1, x2, incx2, q1, ldq1, q2,
259  \$ ldq2, work, lwork, childinfo )
260  IF( snrm2(m1,x1,incx1) .NE. zero
261  \$ .OR. snrm2(m2,x2,incx2) .NE. zero ) THEN
262  RETURN
263  END IF
264  END DO
265 *
266  RETURN
267 *
268 * End of SORBDB5
269 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine sorbdb6(M1, M2, N, X1, INCX1, X2, INCX2, Q1, LDQ1, Q2, LDQ2, WORK, LWORK, INFO)
SORBDB6
Definition: sorbdb6.f:154
real(wp) function snrm2(n, x, incx)
SNRM2
Definition: snrm2.f90:89
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