LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ cgeql2()

subroutine cgeql2 ( integer  M,
integer  N,
complex, dimension( lda, * )  A,
integer  LDA,
complex, dimension( * )  TAU,
complex, dimension( * )  WORK,
integer  INFO 
)

CGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm.

Download CGEQL2 + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 CGEQL2 computes a QL factorization of a complex m by n matrix A:
 A = Q * L.
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 lower triangle of the subarray
          A(m-n+1:m,1:n) contains the n by n lower triangular matrix L;
          if m <= n, the elements on and below the (n-m)-th
          superdiagonal contain the m by n lower trapezoidal matrix L;
          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 (N)
[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(k) . . . H(2) H(1), 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(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
  A(1:m-k+i-1,n-k+i), and tau in TAU(i).

Definition at line 125 of file cgeql2.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 clarf, clarfg, xerbla
150 * ..
151 * .. Intrinsic Functions ..
152  INTRINSIC conjg, 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( 'CGEQL2', -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(1:m-k+i-1,n-k+i)
177 *
178  alpha = a( m-k+i, n-k+i )
179  CALL clarfg( m-k+i, alpha, a( 1, n-k+i ), 1, tau( i ) )
180 *
181 * Apply H(i)**H to A(1:m-k+i,1:n-k+i-1) from the left
182 *
183  a( m-k+i, n-k+i ) = one
184  CALL clarf( 'Left', m-k+i, n-k+i-1, a( 1, n-k+i ), 1,
185  $ conjg( tau( i ) ), a, lda, work )
186  a( m-k+i, n-k+i ) = alpha
187  10 CONTINUE
188  RETURN
189 *
190 * End of CGEQL2
191 *
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 clarf(SIDE, M, N, V, INCV, TAU, C, LDC, WORK)
CLARF applies an elementary reflector to a general rectangular matrix.
Definition: clarf.f:130
Here is the call graph for this function:
Here is the caller graph for this function: