LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ zgerq2()

subroutine zgerq2 ( integer  m,
integer  n,
complex*16, dimension( lda, * )  a,
integer  lda,
complex*16, dimension( * )  tau,
complex*16, dimension( * )  work,
integer  info 
)

ZGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.

Download ZGERQ2 + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 ZGERQ2 computes an RQ factorization of a complex m by n matrix A:
 A = R * Q.
Parameters
[in]M
          M is INTEGER
          The number of rows of the matrix A.  M >= 0.
[in]N
          N is INTEGER
          The number of columns of the matrix A.  N >= 0.
[in,out]A
          A is COMPLEX*16 array, dimension (LDA,N)
          On entry, the m by n matrix A.
          On exit, if m <= n, the upper triangle of the subarray
          A(1:m,n-m+1:n) contains the m by m upper triangular matrix R;
          if m >= n, the elements on and above the (m-n)-th subdiagonal
          contain the m by n upper trapezoidal matrix R; the remaining
          elements, with the array TAU, represent the unitary matrix
          Q as a product of elementary reflectors (see Further
          Details).
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,M).
[out]TAU
          TAU is COMPLEX*16 array, dimension (min(M,N))
          The scalar factors of the elementary reflectors (see Further
          Details).
[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 had an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
  The matrix Q is represented as a product of elementary reflectors

     Q = H(1)**H H(2)**H . . . H(k)**H, where k = min(m,n).

  Each H(i) has the form

     H(i) = I - tau * v * v**H

  where tau is a complex scalar, and v is a complex vector with
  v(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on
  exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i).

Definition at line 122 of file zgerq2.f.

123*
124* -- LAPACK computational routine --
125* -- LAPACK is a software package provided by Univ. of Tennessee, --
126* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
127*
128* .. Scalar Arguments ..
129 INTEGER INFO, LDA, M, N
130* ..
131* .. Array Arguments ..
132 COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * )
133* ..
134*
135* =====================================================================
136*
137* .. Parameters ..
138 COMPLEX*16 ONE
139 parameter( one = ( 1.0d+0, 0.0d+0 ) )
140* ..
141* .. Local Scalars ..
142 INTEGER I, K
143 COMPLEX*16 ALPHA
144* ..
145* .. External Subroutines ..
146 EXTERNAL xerbla, zlacgv, zlarf, zlarfg
147* ..
148* .. Intrinsic Functions ..
149 INTRINSIC max, min
150* ..
151* .. Executable Statements ..
152*
153* Test the input arguments
154*
155 info = 0
156 IF( m.LT.0 ) THEN
157 info = -1
158 ELSE IF( n.LT.0 ) THEN
159 info = -2
160 ELSE IF( lda.LT.max( 1, m ) ) THEN
161 info = -4
162 END IF
163 IF( info.NE.0 ) THEN
164 CALL xerbla( 'ZGERQ2', -info )
165 RETURN
166 END IF
167*
168 k = min( m, n )
169*
170 DO 10 i = k, 1, -1
171*
172* Generate elementary reflector H(i) to annihilate
173* A(m-k+i,1:n-k+i-1)
174*
175 CALL zlacgv( n-k+i, a( m-k+i, 1 ), lda )
176 alpha = a( m-k+i, n-k+i )
177 CALL zlarfg( n-k+i, alpha, a( m-k+i, 1 ), lda, tau( i ) )
178*
179* Apply H(i) to A(1:m-k+i-1,1:n-k+i) from the right
180*
181 a( m-k+i, n-k+i ) = one
182 CALL zlarf( 'Right', m-k+i-1, n-k+i, a( m-k+i, 1 ), lda,
183 $ tau( i ), a, lda, work )
184 a( m-k+i, n-k+i ) = alpha
185 CALL zlacgv( n-k+i-1, a( m-k+i, 1 ), lda )
186 10 CONTINUE
187 RETURN
188*
189* End of ZGERQ2
190*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
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
subroutine zlarfg(n, alpha, x, incx, tau)
ZLARFG generates an elementary reflector (Householder matrix).
Definition zlarfg.f:106
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