LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ zungr2()

 subroutine zungr2 ( integer m, integer n, integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer info )

ZUNGR2 generates all or part of the unitary matrix Q from an RQ factorization determined by cgerqf (unblocked algorithm).

Purpose:
``` ZUNGR2 generates an m by n complex matrix Q with orthonormal rows,
which is defined as the last m rows of a product of k elementary
reflectors of order n

Q  =  H(1)**H H(2)**H . . . H(k)**H

as returned by ZGERQF.```
Parameters
 [in] M ``` M is INTEGER The number of rows of the matrix Q. M >= 0.``` [in] N ``` N is INTEGER The number of columns of the matrix Q. N >= M.``` [in] K ``` K is INTEGER The number of elementary reflectors whose product defines the matrix Q. M >= K >= 0.``` [in,out] A ``` A is COMPLEX*16 array, dimension (LDA,N) On entry, the (m-k+i)-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by ZGERQF in the last k rows of its array argument A. On exit, the m-by-n matrix Q.``` [in] LDA ``` LDA is INTEGER The first dimension of the array A. LDA >= max(1,M).``` [in] TAU ``` TAU is COMPLEX*16 array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by ZGERQF.``` [out] WORK ` WORK is COMPLEX*16 array, dimension (M)` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument has an illegal value```

Definition at line 113 of file zungr2.f.

114*
115* -- LAPACK computational routine --
116* -- LAPACK is a software package provided by Univ. of Tennessee, --
117* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
118*
119* .. Scalar Arguments ..
120 INTEGER INFO, K, LDA, M, N
121* ..
122* .. Array Arguments ..
123 COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
124* ..
125*
126* =====================================================================
127*
128* .. Parameters ..
129 COMPLEX*16 ONE, ZERO
130 parameter( one = ( 1.0d+0, 0.0d+0 ),
131 \$ zero = ( 0.0d+0, 0.0d+0 ) )
132* ..
133* .. Local Scalars ..
134 INTEGER I, II, J, L
135* ..
136* .. External Subroutines ..
137 EXTERNAL xerbla, zlacgv, zlarf, zscal
138* ..
139* .. Intrinsic Functions ..
140 INTRINSIC dconjg, max
141* ..
142* .. Executable Statements ..
143*
144* Test the input arguments
145*
146 info = 0
147 IF( m.LT.0 ) THEN
148 info = -1
149 ELSE IF( n.LT.m ) THEN
150 info = -2
151 ELSE IF( k.LT.0 .OR. k.GT.m ) THEN
152 info = -3
153 ELSE IF( lda.LT.max( 1, m ) ) THEN
154 info = -5
155 END IF
156 IF( info.NE.0 ) THEN
157 CALL xerbla( 'ZUNGR2', -info )
158 RETURN
159 END IF
160*
161* Quick return if possible
162*
163 IF( m.LE.0 )
164 \$ RETURN
165*
166 IF( k.LT.m ) THEN
167*
168* Initialise rows 1:m-k to rows of the unit matrix
169*
170 DO 20 j = 1, n
171 DO 10 l = 1, m - k
172 a( l, j ) = zero
173 10 CONTINUE
174 IF( j.GT.n-m .AND. j.LE.n-k )
175 \$ a( m-n+j, j ) = one
176 20 CONTINUE
177 END IF
178*
179 DO 40 i = 1, k
180 ii = m - k + i
181*
182* Apply H(i)**H to A(1:m-k+i,1:n-k+i) from the right
183*
184 CALL zlacgv( n-m+ii-1, a( ii, 1 ), lda )
185 a( ii, n-m+ii ) = one
186 CALL zlarf( 'Right', ii-1, n-m+ii, a( ii, 1 ), lda,
187 \$ dconjg( tau( i ) ), a, lda, work )
188 CALL zscal( n-m+ii-1, -tau( i ), a( ii, 1 ), lda )
189 CALL zlacgv( n-m+ii-1, a( ii, 1 ), lda )
190 a( ii, n-m+ii ) = one - dconjg( tau( i ) )
191*
192* Set A(m-k+i,n-k+i+1:n) to zero
193*
194 DO 30 l = n - m + ii + 1, n
195 a( ii, l ) = zero
196 30 CONTINUE
197 40 CONTINUE
198 RETURN
199*
200* End of ZUNGR2
201*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
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
subroutine zscal(n, za, zx, incx)
ZSCAL
Definition zscal.f:78
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