LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ zgeql2()

subroutine zgeql2 ( integer  m,
integer  n,
complex*16, dimension( lda, * )  a,
integer  lda,
complex*16, dimension( * )  tau,
complex*16, dimension( * )  work,
integer  info 
)

ZGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm.

Download ZGEQL2 + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 ZGEQL2 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*16 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*16 array, dimension (min(M,N))
          The scalar factors of the elementary reflectors (see Further
          Details).
[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 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(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 122 of file zgeql2.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, zlarf, zlarfg
147* ..
148* .. Intrinsic Functions ..
149 INTRINSIC dconjg, 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( 'ZGEQL2', -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(1:m-k+i-1,n-k+i)
174*
175 alpha = a( m-k+i, n-k+i )
176 CALL zlarfg( m-k+i, alpha, a( 1, n-k+i ), 1, tau( i ) )
177*
178* Apply H(i)**H to A(1:m-k+i,1:n-k+i-1) from the left
179*
180 a( m-k+i, n-k+i ) = one
181 CALL zlarf( 'Left', m-k+i, n-k+i-1, a( 1, n-k+i ), 1,
182 $ dconjg( tau( i ) ), a, lda, work )
183 a( m-k+i, n-k+i ) = alpha
184 10 CONTINUE
185 RETURN
186*
187* End of ZGEQL2
188*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
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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