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).

Download CUNGL2 + dependencies [TGZ] [ZIP] [TXT]

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
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

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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