LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ zung2r()

 subroutine zung2r ( integer m, integer n, integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer info )

ZUNG2R

Purpose:
``` ZUNG2R generates an m by n complex matrix Q with orthonormal columns,
which is defined as the first n columns of a product of k elementary
reflectors of order m

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

as returned by ZGEQRF.```
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. M >= N >= 0.``` [in] K ``` K is INTEGER The number of elementary reflectors whose product defines the matrix Q. N >= K >= 0.``` [in,out] A ``` A is COMPLEX*16 array, dimension (LDA,N) On entry, the i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by ZGEQRF in the first k columns 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 ZGEQRF.``` [out] WORK ` WORK is COMPLEX*16 array, dimension (N)` [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 zung2r.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, J, L
135* ..
136* .. External Subroutines ..
137 EXTERNAL xerbla, zlarf, zscal
138* ..
139* .. Intrinsic Functions ..
140 INTRINSIC 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.0 .OR. n.GT.m ) THEN
150 info = -2
151 ELSE IF( k.LT.0 .OR. k.GT.n ) 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( 'ZUNG2R', -info )
158 RETURN
159 END IF
160*
161* Quick return if possible
162*
163 IF( n.LE.0 )
164 \$ RETURN
165*
166* Initialise columns k+1:n to columns of the unit matrix
167*
168 DO 20 j = k + 1, n
169 DO 10 l = 1, m
170 a( l, j ) = zero
171 10 CONTINUE
172 a( j, j ) = one
173 20 CONTINUE
174*
175 DO 40 i = k, 1, -1
176*
177* Apply H(i) to A(i:m,i:n) from the left
178*
179 IF( i.LT.n ) THEN
180 a( i, i ) = one
181 CALL zlarf( 'Left', m-i+1, n-i, a( i, i ), 1, tau( i ),
182 \$ a( i, i+1 ), lda, work )
183 END IF
184 IF( i.LT.m )
185 \$ CALL zscal( m-i, -tau( i ), a( i+1, i ), 1 )
186 a( i, i ) = one - tau( i )
187*
188* Set A(1:i-1,i) to zero
189*
190 DO 30 l = 1, i - 1
191 a( l, i ) = zero
192 30 CONTINUE
193 40 CONTINUE
194 RETURN
195*
196* End of ZUNG2R
197*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
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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