 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ cungl2()

 subroutine cungl2 ( integer M, integer N, integer K, complex, dimension( lda, * ) A, integer LDA, complex, dimension( * ) TAU, complex, dimension( * ) WORK, integer INFO )

CUNGL2 generates all or part of the unitary matrix Q from an LQ factorization determined by cgelqf (unblocked algorithm).

Purpose:
``` CUNGL2 generates an m-by-n complex matrix Q with orthonormal rows,
which is defined as the first m rows of a product of k elementary
reflectors of order n

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

as returned by CGELQF.```
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 i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by CGELQF in the first 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 CGELQF.``` [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 112 of file cungl2.f.

113 *
114 * -- LAPACK computational routine --
115 * -- LAPACK is a software package provided by Univ. of Tennessee, --
116 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
117 *
118 * .. Scalar Arguments ..
119  INTEGER INFO, K, LDA, M, N
120 * ..
121 * .. Array Arguments ..
122  COMPLEX A( LDA, * ), TAU( * ), WORK( * )
123 * ..
124 *
125 * =====================================================================
126 *
127 * .. Parameters ..
128  COMPLEX ONE, ZERO
129  parameter( one = ( 1.0e+0, 0.0e+0 ),
130  \$ zero = ( 0.0e+0, 0.0e+0 ) )
131 * ..
132 * .. Local Scalars ..
133  INTEGER I, J, L
134 * ..
135 * .. External Subroutines ..
136  EXTERNAL clacgv, clarf, cscal, xerbla
137 * ..
138 * .. Intrinsic Functions ..
139  INTRINSIC conjg, max
140 * ..
141 * .. Executable Statements ..
142 *
143 * Test the input arguments
144 *
145  info = 0
146  IF( m.LT.0 ) THEN
147  info = -1
148  ELSE IF( n.LT.m ) THEN
149  info = -2
150  ELSE IF( k.LT.0 .OR. k.GT.m ) THEN
151  info = -3
152  ELSE IF( lda.LT.max( 1, m ) ) THEN
153  info = -5
154  END IF
155  IF( info.NE.0 ) THEN
156  CALL xerbla( 'CUNGL2', -info )
157  RETURN
158  END IF
159 *
160 * Quick return if possible
161 *
162  IF( m.LE.0 )
163  \$ RETURN
164 *
165  IF( k.LT.m ) THEN
166 *
167 * Initialise rows k+1:m to rows of the unit matrix
168 *
169  DO 20 j = 1, n
170  DO 10 l = k + 1, m
171  a( l, j ) = zero
172  10 CONTINUE
173  IF( j.GT.k .AND. j.LE.m )
174  \$ a( j, j ) = one
175  20 CONTINUE
176  END IF
177 *
178  DO 40 i = k, 1, -1
179 *
180 * Apply H(i)**H to A(i:m,i:n) from the right
181 *
182  IF( i.LT.n ) THEN
183  CALL clacgv( n-i, a( i, i+1 ), lda )
184  IF( i.LT.m ) THEN
185  a( i, i ) = one
186  CALL clarf( 'Right', m-i, n-i+1, a( i, i ), lda,
187  \$ conjg( tau( i ) ), a( i+1, i ), lda, work )
188  END IF
189  CALL cscal( n-i, -tau( i ), a( i, i+1 ), lda )
190  CALL clacgv( n-i, a( i, i+1 ), lda )
191  END IF
192  a( i, i ) = one - conjg( tau( i ) )
193 *
194 * Set A(i,1:i-1,i) to zero
195 *
196  DO 30 l = 1, i - 1
197  a( i, l ) = zero
198  30 CONTINUE
199  40 CONTINUE
200  RETURN
201 *
202 * End of CUNGL2
203 *
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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