 LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ dorg2l()

 subroutine dorg2l ( integer M, integer N, integer K, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( * ) TAU, double precision, dimension( * ) WORK, integer INFO )

DORG2L generates all or part of the orthogonal matrix Q from a QL factorization determined by sgeqlf (unblocked algorithm).

Purpose:
``` DORG2L generates an m by n real matrix Q with orthonormal columns,
which is defined as the last n columns of a product of k elementary
reflectors of order m

Q  =  H(k) . . . H(2) H(1)

as returned by DGEQLF.```
Parameters
 [in] M ``` M is INTEGER The number of rows of the matrix Q. M >= 0.``` [in] N ``` N is INTEGER The number of columns of the matrix Q. M >= N >= 0.``` [in] K ``` K is INTEGER The number of elementary reflectors whose product defines the matrix Q. N >= K >= 0.``` [in,out] A ``` A is DOUBLE PRECISION array, dimension (LDA,N) On entry, the (n-k+i)-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by DGEQLF in the last k columns of its array argument A. On exit, the m by n matrix Q.``` [in] LDA ``` LDA is INTEGER The first dimension of the array A. LDA >= max(1,M).``` [in] TAU ``` TAU is DOUBLE PRECISION array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DGEQLF.``` [out] WORK ` WORK is DOUBLE PRECISION array, dimension (N)` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument has an illegal value```
Date
December 2016

Definition at line 116 of file dorg2l.f.

116 *
117 * -- LAPACK computational routine (version 3.7.0) --
118 * -- LAPACK is a software package provided by Univ. of Tennessee, --
119 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
120 * December 2016
121 *
122 * .. Scalar Arguments ..
123  INTEGER info, k, lda, m, n
124 * ..
125 * .. Array Arguments ..
126  DOUBLE PRECISION a( lda, * ), tau( * ), work( * )
127 * ..
128 *
129 * =====================================================================
130 *
131 * .. Parameters ..
132  DOUBLE PRECISION one, zero
133  parameter( one = 1.0d+0, zero = 0.0d+0 )
134 * ..
135 * .. Local Scalars ..
136  INTEGER i, ii, j, l
137 * ..
138 * .. External Subroutines ..
139  EXTERNAL dlarf, dscal, xerbla
140 * ..
141 * .. Intrinsic Functions ..
142  INTRINSIC max
143 * ..
144 * .. Executable Statements ..
145 *
146 * Test the input arguments
147 *
148  info = 0
149  IF( m.LT.0 ) THEN
150  info = -1
151  ELSE IF( n.LT.0 .OR. n.GT.m ) THEN
152  info = -2
153  ELSE IF( k.LT.0 .OR. k.GT.n ) THEN
154  info = -3
155  ELSE IF( lda.LT.max( 1, m ) ) THEN
156  info = -5
157  END IF
158  IF( info.NE.0 ) THEN
159  CALL xerbla( 'DORG2L', -info )
160  RETURN
161  END IF
162 *
163 * Quick return if possible
164 *
165  IF( n.LE.0 )
166  \$ RETURN
167 *
168 * Initialise columns 1:n-k to columns of the unit matrix
169 *
170  DO 20 j = 1, n - k
171  DO 10 l = 1, m
172  a( l, j ) = zero
173  10 CONTINUE
174  a( m-n+j, j ) = one
175  20 CONTINUE
176 *
177  DO 40 i = 1, k
178  ii = n - k + i
179 *
180 * Apply H(i) to A(1:m-k+i,1:n-k+i) from the left
181 *
182  a( m-n+ii, ii ) = one
183  CALL dlarf( 'Left', m-n+ii, ii-1, a( 1, ii ), 1, tau( i ), a,
184  \$ lda, work )
185  CALL dscal( m-n+ii-1, -tau( i ), a( 1, ii ), 1 )
186  a( m-n+ii, ii ) = one - tau( i )
187 *
188 * Set A(m-k+i+1:m,n-k+i) to zero
189 *
190  DO 30 l = m - n + ii + 1, m
191  a( l, ii ) = zero
192  30 CONTINUE
193  40 CONTINUE
194  RETURN
195 *
196 * End of DORG2L
197 *
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 dscal(N, DA, DX, INCX)
DSCAL
Definition: dscal.f:81
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