 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ cungr2()

 subroutine cungr2 ( integer M, integer N, integer K, complex, dimension( lda, * ) A, integer LDA, complex, dimension( * ) TAU, complex, dimension( * ) WORK, integer INFO )

CUNGR2 generates all or part of the unitary matrix Q from an RQ factorization determined by cgerqf (unblocked algorithm).

Purpose:
``` CUNGR2 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 CGERQF.```
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 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 CGERQF 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 array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by CGERQF.``` [out] WORK ` WORK is COMPLEX 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 cungr2.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 A( LDA, * ), TAU( * ), WORK( * )
124 * ..
125 *
126 * =====================================================================
127 *
128 * .. Parameters ..
129  COMPLEX ONE, ZERO
130  parameter( one = ( 1.0e+0, 0.0e+0 ),
131  \$ zero = ( 0.0e+0, 0.0e+0 ) )
132 * ..
133 * .. Local Scalars ..
134  INTEGER I, II, J, L
135 * ..
136 * .. External Subroutines ..
137  EXTERNAL clacgv, clarf, cscal, xerbla
138 * ..
139 * .. Intrinsic Functions ..
140  INTRINSIC conjg, 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( 'CUNGR2', -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 clacgv( n-m+ii-1, a( ii, 1 ), lda )
185  a( ii, n-m+ii ) = one
186  CALL clarf( 'Right', ii-1, n-m+ii, a( ii, 1 ), lda,
187  \$ conjg( tau( i ) ), a, lda, work )
188  CALL cscal( n-m+ii-1, -tau( i ), a( ii, 1 ), lda )
189  CALL clacgv( n-m+ii-1, a( ii, 1 ), lda )
190  a( ii, n-m+ii ) = one - conjg( 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 CUNGR2
201 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine cscal(N, CA, CX, INCX)
CSCAL
Definition: cscal.f:78
subroutine clacgv(N, X, INCX)
CLACGV conjugates a complex vector.
Definition: clacgv.f:74
subroutine clarf(SIDE, M, N, V, INCV, TAU, C, LDC, WORK)
CLARF applies an elementary reflector to a general rectangular matrix.
Definition: clarf.f:128
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