LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ zung2l()

 subroutine zung2l ( integer m, integer n, integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer info )

ZUNG2L generates all or part of the unitary matrix Q from a QL factorization determined by cgeqlf (unblocked algorithm).

Download ZUNG2L + dependencies [TGZ] [ZIP] [TXT]

Purpose:
``` ZUNG2L generates an m by n complex matrix Q with orthonormal columns,
which is defined as the last n columns of a product of k elementary
reflectors of order m

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

as returned by ZGEQLF.```
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 (n-k+i)-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by ZGEQLF in the last 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 ZGEQLF.``` [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 zung2l.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, 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( 'ZUNG2L', -info )
158 RETURN
159 END IF
160*
161* Quick return if possible
162*
163 IF( n.LE.0 )
164 \$ RETURN
165*
166* Initialise columns 1:n-k to columns of the unit matrix
167*
168 DO 20 j = 1, n - k
169 DO 10 l = 1, m
170 a( l, j ) = zero
171 10 CONTINUE
172 a( m-n+j, j ) = one
173 20 CONTINUE
174*
175 DO 40 i = 1, k
176 ii = n - k + i
177*
178* Apply H(i) to A(1:m-k+i,1:n-k+i) from the left
179*
180 a( m-n+ii, ii ) = one
181 CALL zlarf( 'Left', m-n+ii, ii-1, a( 1, ii ), 1, tau( i ), a,
182 \$ lda, work )
183 CALL zscal( m-n+ii-1, -tau( i ), a( 1, ii ), 1 )
184 a( m-n+ii, ii ) = one - tau( i )
185*
186* Set A(m-k+i+1:m,n-k+i) to zero
187*
188 DO 30 l = m - n + ii + 1, m
189 a( l, ii ) = zero
190 30 CONTINUE
191 40 CONTINUE
192 RETURN
193*
194* End of ZUNG2L
195*
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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