LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ 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.

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```
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 cgeql2.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 A( LDA, * ), TAU( * ), WORK( * )
133* ..
134*
135* =====================================================================
136*
137* .. Parameters ..
138 COMPLEX ONE
139 parameter( one = ( 1.0e+0, 0.0e+0 ) )
140* ..
141* .. Local Scalars ..
142 INTEGER I, K
143 COMPLEX ALPHA
144* ..
145* .. External Subroutines ..
146 EXTERNAL clarf, clarfg, xerbla
147* ..
148* .. Intrinsic Functions ..
149 INTRINSIC conjg, 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( 'CGEQL2', -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 clarfg( 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 clarf( 'Left', m-k+i, n-k+i-1, a( 1, n-k+i ), 1,
182 \$ conjg( tau( i ) ), a, lda, work )
183 a( m-k+i, n-k+i ) = alpha
184 10 CONTINUE
185 RETURN
186*
187* End of CGEQL2
188*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine clarf(side, m, n, v, incv, tau, c, ldc, work)
CLARF applies an elementary reflector to a general rectangular matrix.
Definition clarf.f:128
subroutine clarfg(n, alpha, x, incx, tau)
CLARFG generates an elementary reflector (Householder matrix).
Definition clarfg.f:106
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