LAPACK  3.10.0 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.

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)
XERBLA
Definition: xerbla.f:60
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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