LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ zung2r()

 subroutine zung2r ( integer M, integer N, integer K, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( * ) TAU, complex*16, dimension( * ) WORK, integer INFO )

ZUNG2R

Purpose:
``` ZUNG2R generates an m by n complex matrix Q with orthonormal columns,
which is defined as the first n columns of a product of k elementary
reflectors of order m

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

as returned by ZGEQRF.```
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 i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by ZGEQRF in the first 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 ZGEQRF.``` [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```

Definition at line 113 of file zung2r.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, J, L
135 * ..
136 * .. External Subroutines ..
137  EXTERNAL xerbla, zlarf, zscal
138 * ..
139 * .. Intrinsic Functions ..
140  INTRINSIC 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.0 .OR. n.GT.m ) THEN
150  info = -2
151  ELSE IF( k.LT.0 .OR. k.GT.n ) 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( 'ZUNG2R', -info )
158  RETURN
159  END IF
160 *
161 * Quick return if possible
162 *
163  IF( n.LE.0 )
164  \$ RETURN
165 *
166 * Initialise columns k+1:n to columns of the unit matrix
167 *
168  DO 20 j = k + 1, n
169  DO 10 l = 1, m
170  a( l, j ) = zero
171  10 CONTINUE
172  a( j, j ) = one
173  20 CONTINUE
174 *
175  DO 40 i = k, 1, -1
176 *
177 * Apply H(i) to A(i:m,i:n) from the left
178 *
179  IF( i.LT.n ) THEN
180  a( i, i ) = one
181  CALL zlarf( 'Left', m-i+1, n-i, a( i, i ), 1, tau( i ),
182  \$ a( i, i+1 ), lda, work )
183  END IF
184  IF( i.LT.m )
185  \$ CALL zscal( m-i, -tau( i ), a( i+1, i ), 1 )
186  a( i, i ) = one - tau( i )
187 *
188 * Set A(1:i-1,i) to zero
189 *
190  DO 30 l = 1, i - 1
191  a( l, i ) = zero
192  30 CONTINUE
193  40 CONTINUE
194  RETURN
195 *
196 * End of ZUNG2R
197 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine zscal(N, ZA, ZX, INCX)
ZSCAL
Definition: zscal.f:78
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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