LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ 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```

Definition at line 113 of file dorg2l.f.

114*
115* -- LAPACK computational routine --
116* -- LAPACK is a software package provided by Univ. of Tennessee, --
117* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
118*
119* .. Scalar Arguments ..
120 INTEGER INFO, K, LDA, M, N
121* ..
122* .. Array Arguments ..
123 DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
124* ..
125*
126* =====================================================================
127*
128* .. Parameters ..
129 DOUBLE PRECISION ONE, ZERO
130 parameter( one = 1.0d+0, zero = 0.0d+0 )
131* ..
132* .. Local Scalars ..
133 INTEGER I, II, J, L
134* ..
135* .. External Subroutines ..
136 EXTERNAL dlarf, dscal, xerbla
137* ..
138* .. Intrinsic Functions ..
139 INTRINSIC max
140* ..
141* .. Executable Statements ..
142*
143* Test the input arguments
144*
145 info = 0
146 IF( m.LT.0 ) THEN
147 info = -1
148 ELSE IF( n.LT.0 .OR. n.GT.m ) THEN
149 info = -2
150 ELSE IF( k.LT.0 .OR. k.GT.n ) THEN
151 info = -3
152 ELSE IF( lda.LT.max( 1, m ) ) THEN
153 info = -5
154 END IF
155 IF( info.NE.0 ) THEN
156 CALL xerbla( 'DORG2L', -info )
157 RETURN
158 END IF
159*
160* Quick return if possible
161*
162 IF( n.LE.0 )
163 \$ RETURN
164*
165* Initialise columns 1:n-k to columns of the unit matrix
166*
167 DO 20 j = 1, n - k
168 DO 10 l = 1, m
169 a( l, j ) = zero
170 10 CONTINUE
171 a( m-n+j, j ) = one
172 20 CONTINUE
173*
174 DO 40 i = 1, k
175 ii = n - k + i
176*
177* Apply H(i) to A(1:m-k+i,1:n-k+i) from the left
178*
179 a( m-n+ii, ii ) = one
180 CALL dlarf( 'Left', m-n+ii, ii-1, a( 1, ii ), 1, tau( i ), a,
181 \$ lda, work )
182 CALL dscal( m-n+ii-1, -tau( i ), a( 1, ii ), 1 )
183 a( m-n+ii, ii ) = one - tau( i )
184*
185* Set A(m-k+i+1:m,n-k+i) to zero
186*
187 DO 30 l = m - n + ii + 1, m
188 a( l, ii ) = zero
189 30 CONTINUE
190 40 CONTINUE
191 RETURN
192*
193* End of DORG2L
194*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine dlarf(side, m, n, v, incv, tau, c, ldc, work)
DLARF applies an elementary reflector to a general rectangular matrix.
Definition dlarf.f:124
subroutine dscal(n, da, dx, incx)
DSCAL
Definition dscal.f:79
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