LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine dgelq2 ( integer M, integer N, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( * ) TAU, double precision, dimension( * ) WORK, integer INFO )

DGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.

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Purpose:
``` DGELQ2 computes an LQ factorization of a real m by n matrix A:
A = L * 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 DOUBLE PRECISION array, dimension (LDA,N) On entry, the m by n matrix A. On exit, the elements on and below the diagonal of the array contain the m by min(m,n) lower trapezoidal matrix L (L is lower triangular if m <= n); the elements above the diagonal, with the array TAU, represent the orthogonal 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 DOUBLE PRECISION array, dimension (min(M,N)) The scalar factors of the elementary reflectors (see Further Details).``` [out] WORK ` WORK is DOUBLE PRECISION array, dimension (M)` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value```
Date
September 2012
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**T

where tau is a real scalar, and v is a real vector with
v(1:i-1) = 0 and v(i) = 1; v(i+1:n) is stored on exit in A(i,i+1:n),
and tau in TAU(i).```

Definition at line 123 of file dgelq2.f.

123 *
124 * -- LAPACK computational routine (version 3.4.2) --
125 * -- LAPACK is a software package provided by Univ. of Tennessee, --
126 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
127 * September 2012
128 *
129 * .. Scalar Arguments ..
130  INTEGER info, lda, m, n
131 * ..
132 * .. Array Arguments ..
133  DOUBLE PRECISION a( lda, * ), tau( * ), work( * )
134 * ..
135 *
136 * =====================================================================
137 *
138 * .. Parameters ..
139  DOUBLE PRECISION one
140  parameter ( one = 1.0d+0 )
141 * ..
142 * .. Local Scalars ..
143  INTEGER i, k
144  DOUBLE PRECISION aii
145 * ..
146 * .. External Subroutines ..
147  EXTERNAL dlarf, dlarfg, xerbla
148 * ..
149 * .. Intrinsic Functions ..
150  INTRINSIC max, min
151 * ..
152 * .. Executable Statements ..
153 *
154 * Test the input arguments
155 *
156  info = 0
157  IF( m.LT.0 ) THEN
158  info = -1
159  ELSE IF( n.LT.0 ) THEN
160  info = -2
161  ELSE IF( lda.LT.max( 1, m ) ) THEN
162  info = -4
163  END IF
164  IF( info.NE.0 ) THEN
165  CALL xerbla( 'DGELQ2', -info )
166  RETURN
167  END IF
168 *
169  k = min( m, n )
170 *
171  DO 10 i = 1, k
172 *
173 * Generate elementary reflector H(i) to annihilate A(i,i+1:n)
174 *
175  CALL dlarfg( n-i+1, a( i, i ), a( i, min( i+1, n ) ), lda,
176  \$ tau( i ) )
177  IF( i.LT.m ) THEN
178 *
179 * Apply H(i) to A(i+1:m,i:n) from the right
180 *
181  aii = a( i, i )
182  a( i, i ) = one
183  CALL dlarf( 'Right', m-i, n-i+1, a( i, i ), lda, tau( i ),
184  \$ a( i+1, i ), lda, work )
185  a( i, i ) = aii
186  END IF
187  10 CONTINUE
188  RETURN
189 *
190 * End of DGELQ2
191 *
subroutine dlarf(SIDE, M, N, V, INCV, TAU, C, LDC, WORK)
DLARF applies an elementary reflector to a general rectangular matrix.
Definition: dlarf.f:126
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine dlarfg(N, ALPHA, X, INCX, TAU)
DLARFG generates an elementary reflector (Householder matrix).
Definition: dlarfg.f:108

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