LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ zungr2()

subroutine zungr2 ( integer  M,
integer  N,
integer  K,
complex*16, dimension( lda, * )  A,
integer  LDA,
complex*16, dimension( * )  TAU,
complex*16, dimension( * )  WORK,
integer  INFO 
)

ZUNGR2 generates all or part of the unitary matrix Q from an RQ factorization determined by cgerqf (unblocked algorithm).

Download ZUNGR2 + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 ZUNGR2 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 ZGERQF.
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*16 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 ZGERQF 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*16 array, dimension (K)
          TAU(i) must contain the scalar factor of the elementary
          reflector H(i), as returned by ZGERQF.
[out]WORK
          WORK is COMPLEX*16 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 113 of file zungr2.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, zlacgv, zlarf, zscal
138 * ..
139 * .. Intrinsic Functions ..
140  INTRINSIC dconjg, 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( 'ZUNGR2', -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 zlacgv( n-m+ii-1, a( ii, 1 ), lda )
185  a( ii, n-m+ii ) = one
186  CALL zlarf( 'Right', ii-1, n-m+ii, a( ii, 1 ), lda,
187  $ dconjg( tau( i ) ), a, lda, work )
188  CALL zscal( n-m+ii-1, -tau( i ), a( ii, 1 ), lda )
189  CALL zlacgv( n-m+ii-1, a( ii, 1 ), lda )
190  a( ii, n-m+ii ) = one - dconjg( 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 ZUNGR2
201 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine zscal(N, ZA, ZX, INCX)
ZSCAL
Definition: zscal.f:78
subroutine zlacgv(N, X, INCX)
ZLACGV conjugates a complex vector.
Definition: zlacgv.f:74
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
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