LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ 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
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
December 2016

Definition at line 116 of file zung2l.f.

116 *
117 * -- LAPACK computational routine (version 3.7.0) --
118 * -- LAPACK is a software package provided by Univ. of Tennessee, --
119 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
120 * December 2016
121 *
122 * .. Scalar Arguments ..
123  INTEGER info, k, lda, m, n
124 * ..
125 * .. Array Arguments ..
126  COMPLEX*16 a( lda, * ), tau( * ), work( * )
127 * ..
128 *
129 * =====================================================================
130 *
131 * .. Parameters ..
132  COMPLEX*16 one, zero
133  parameter( one = ( 1.0d+0, 0.0d+0 ),
134  $ zero = ( 0.0d+0, 0.0d+0 ) )
135 * ..
136 * .. Local Scalars ..
137  INTEGER i, ii, j, l
138 * ..
139 * .. External Subroutines ..
140  EXTERNAL xerbla, zlarf, zscal
141 * ..
142 * .. Intrinsic Functions ..
143  INTRINSIC max
144 * ..
145 * .. Executable Statements ..
146 *
147 * Test the input arguments
148 *
149  info = 0
150  IF( m.LT.0 ) THEN
151  info = -1
152  ELSE IF( n.LT.0 .OR. n.GT.m ) THEN
153  info = -2
154  ELSE IF( k.LT.0 .OR. k.GT.n ) THEN
155  info = -3
156  ELSE IF( lda.LT.max( 1, m ) ) THEN
157  info = -5
158  END IF
159  IF( info.NE.0 ) THEN
160  CALL xerbla( 'ZUNG2L', -info )
161  RETURN
162  END IF
163 *
164 * Quick return if possible
165 *
166  IF( n.LE.0 )
167  $ RETURN
168 *
169 * Initialise columns 1:n-k to columns of the unit matrix
170 *
171  DO 20 j = 1, n - k
172  DO 10 l = 1, m
173  a( l, j ) = zero
174  10 CONTINUE
175  a( m-n+j, j ) = one
176  20 CONTINUE
177 *
178  DO 40 i = 1, k
179  ii = n - k + i
180 *
181 * Apply H(i) to A(1:m-k+i,1:n-k+i) from the left
182 *
183  a( m-n+ii, ii ) = one
184  CALL zlarf( 'Left', m-n+ii, ii-1, a( 1, ii ), 1, tau( i ), a,
185  $ lda, work )
186  CALL zscal( m-n+ii-1, -tau( i ), a( 1, ii ), 1 )
187  a( m-n+ii, ii ) = one - tau( i )
188 *
189 * Set A(m-k+i+1:m,n-k+i) to zero
190 *
191  DO 30 l = m - n + ii + 1, m
192  a( l, ii ) = zero
193  30 CONTINUE
194  40 CONTINUE
195  RETURN
196 *
197 * End of ZUNG2L
198 *
subroutine zlarf(SIDE, M, N, V, INCV, TAU, C, LDC, WORK)
ZLARF applies an elementary reflector to a general rectangular matrix.
Definition: zlarf.f:130
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine zscal(N, ZA, ZX, INCX)
ZSCAL
Definition: zscal.f:80
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