 LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ 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).

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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```
Date
December 2016

Definition at line 116 of file zungr2.f.

116 *
117 * -- LAPACK computational routine (version 3.7.0) --
118 * -- LAPACK is a software package provided by Univ. of Tennessee, --
119 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
120 * December 2016
121 *
122 * .. Scalar Arguments ..
123  INTEGER info, k, lda, m, n
124 * ..
125 * .. Array Arguments ..
126  COMPLEX*16 a( lda, * ), tau( * ), work( * )
127 * ..
128 *
129 * =====================================================================
130 *
131 * .. Parameters ..
132  COMPLEX*16 one, zero
133  parameter( one = ( 1.0d+0, 0.0d+0 ),
134  \$ zero = ( 0.0d+0, 0.0d+0 ) )
135 * ..
136 * .. Local Scalars ..
137  INTEGER i, ii, j, l
138 * ..
139 * .. External Subroutines ..
140  EXTERNAL xerbla, zlacgv, zlarf, zscal
141 * ..
142 * .. Intrinsic Functions ..
143  INTRINSIC dconjg, max
144 * ..
145 * .. Executable Statements ..
146 *
147 * Test the input arguments
148 *
149  info = 0
150  IF( m.LT.0 ) THEN
151  info = -1
152  ELSE IF( n.LT.m ) THEN
153  info = -2
154  ELSE IF( k.LT.0 .OR. k.GT.m ) THEN
155  info = -3
156  ELSE IF( lda.LT.max( 1, m ) ) THEN
157  info = -5
158  END IF
159  IF( info.NE.0 ) THEN
160  CALL xerbla( 'ZUNGR2', -info )
161  RETURN
162  END IF
163 *
164 * Quick return if possible
165 *
166  IF( m.LE.0 )
167  \$ RETURN
168 *
169  IF( k.LT.m ) THEN
170 *
171 * Initialise rows 1:m-k to rows of the unit matrix
172 *
173  DO 20 j = 1, n
174  DO 10 l = 1, m - k
175  a( l, j ) = zero
176  10 CONTINUE
177  IF( j.GT.n-m .AND. j.LE.n-k )
178  \$ a( m-n+j, j ) = one
179  20 CONTINUE
180  END IF
181 *
182  DO 40 i = 1, k
183  ii = m - k + i
184 *
185 * Apply H(i)**H to A(1:m-k+i,1:n-k+i) from the right
186 *
187  CALL zlacgv( n-m+ii-1, a( ii, 1 ), lda )
188  a( ii, n-m+ii ) = one
189  CALL zlarf( 'Right', ii-1, n-m+ii, a( ii, 1 ), lda,
190  \$ dconjg( tau( i ) ), a, lda, work )
191  CALL zscal( n-m+ii-1, -tau( i ), a( ii, 1 ), lda )
192  CALL zlacgv( n-m+ii-1, a( ii, 1 ), lda )
193  a( ii, n-m+ii ) = one - dconjg( tau( i ) )
194 *
195 * Set A(m-k+i,n-k+i+1:n) to zero
196 *
197  DO 30 l = n - m + ii + 1, n
198  a( ii, l ) = zero
199  30 CONTINUE
200  40 CONTINUE
201  RETURN
202 *
203 * End of ZUNGR2
204 *
subroutine zlacgv(N, X, INCX)
ZLACGV conjugates a complex vector.
Definition: zlacgv.f:76
subroutine zscal(N, ZA, ZX, INCX)
ZSCAL
Definition: zscal.f:80
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine zlarf(SIDE, M, N, V, INCV, TAU, C, LDC, WORK)
ZLARF applies an elementary reflector to a general rectangular matrix.
Definition: zlarf.f:130
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