LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ cgerq2()

subroutine cgerq2 ( integer  M,
integer  N,
complex, dimension( lda, * )  A,
integer  LDA,
complex, dimension( * )  TAU,
complex, dimension( * )  WORK,
integer  INFO 
)

CGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.

Download CGERQ2 + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 CGERQ2 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 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 array, dimension (min(M,N))
          The scalar factors of the elementary reflectors (see Further
          Details).
[out]WORK
          WORK is COMPLEX 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.
Date
December 2016
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 125 of file cgerq2.f.

125 *
126 * -- LAPACK computational routine (version 3.7.0) --
127 * -- LAPACK is a software package provided by Univ. of Tennessee, --
128 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
129 * December 2016
130 *
131 * .. Scalar Arguments ..
132  INTEGER info, lda, m, n
133 * ..
134 * .. Array Arguments ..
135  COMPLEX a( lda, * ), tau( * ), work( * )
136 * ..
137 *
138 * =====================================================================
139 *
140 * .. Parameters ..
141  COMPLEX one
142  parameter( one = ( 1.0e+0, 0.0e+0 ) )
143 * ..
144 * .. Local Scalars ..
145  INTEGER i, k
146  COMPLEX alpha
147 * ..
148 * .. External Subroutines ..
149  EXTERNAL clacgv, clarf, clarfg, xerbla
150 * ..
151 * .. Intrinsic Functions ..
152  INTRINSIC max, min
153 * ..
154 * .. Executable Statements ..
155 *
156 * Test the input arguments
157 *
158  info = 0
159  IF( m.LT.0 ) THEN
160  info = -1
161  ELSE IF( n.LT.0 ) THEN
162  info = -2
163  ELSE IF( lda.LT.max( 1, m ) ) THEN
164  info = -4
165  END IF
166  IF( info.NE.0 ) THEN
167  CALL xerbla( 'CGERQ2', -info )
168  RETURN
169  END IF
170 *
171  k = min( m, n )
172 *
173  DO 10 i = k, 1, -1
174 *
175 * Generate elementary reflector H(i) to annihilate
176 * A(m-k+i,1:n-k+i-1)
177 *
178  CALL clacgv( n-k+i, a( m-k+i, 1 ), lda )
179  alpha = a( m-k+i, n-k+i )
180  CALL clarfg( n-k+i, alpha, a( m-k+i, 1 ), lda,
181  $ tau( i ) )
182 *
183 * Apply H(i) to A(1:m-k+i-1,1:n-k+i) from the right
184 *
185  a( m-k+i, n-k+i ) = one
186  CALL clarf( 'Right', m-k+i-1, n-k+i, a( m-k+i, 1 ), lda,
187  $ tau( i ), a, lda, work )
188  a( m-k+i, n-k+i ) = alpha
189  CALL clacgv( n-k+i-1, a( m-k+i, 1 ), lda )
190  10 CONTINUE
191  RETURN
192 *
193 * End of CGERQ2
194 *
subroutine clarfg(N, ALPHA, X, INCX, TAU)
CLARFG generates an elementary reflector (Householder matrix).
Definition: clarfg.f:108
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine clacgv(N, X, INCX)
CLACGV conjugates a complex vector.
Definition: clacgv.f:76
subroutine clarf(SIDE, M, N, V, INCV, TAU, C, LDC, WORK)
CLARF applies an elementary reflector to a general rectangular matrix.
Definition: clarf.f:130
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