LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ sorg2r()

 subroutine sorg2r ( integer m, integer n, integer k, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer info )

SORG2R generates all or part of the orthogonal matrix Q from a QR factorization determined by sgeqrf (unblocked algorithm).

Purpose:
``` SORG2R generates an m by n real matrix Q with orthonormal columns,
which is defined as the first n columns of a product of k elementary
reflectors of order m

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

as returned by SGEQRF.```
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 REAL array, dimension (LDA,N) On entry, the i-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by SGEQRF in the first 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 REAL array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SGEQRF.``` [out] WORK ` WORK is REAL 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 sorg2r.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 REAL A( LDA, * ), TAU( * ), WORK( * )
124* ..
125*
126* =====================================================================
127*
128* .. Parameters ..
129 REAL ONE, ZERO
130 parameter( one = 1.0e+0, zero = 0.0e+0 )
131* ..
132* .. Local Scalars ..
133 INTEGER I, J, L
134* ..
135* .. External Subroutines ..
136 EXTERNAL slarf, sscal, 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( 'SORG2R', -info )
157 RETURN
158 END IF
159*
160* Quick return if possible
161*
162 IF( n.LE.0 )
163 \$ RETURN
164*
165* Initialise columns k+1:n to columns of the unit matrix
166*
167 DO 20 j = k + 1, n
168 DO 10 l = 1, m
169 a( l, j ) = zero
170 10 CONTINUE
171 a( j, j ) = one
172 20 CONTINUE
173*
174 DO 40 i = k, 1, -1
175*
176* Apply H(i) to A(i:m,i:n) from the left
177*
178 IF( i.LT.n ) THEN
179 a( i, i ) = one
180 CALL slarf( 'Left', m-i+1, n-i, a( i, i ), 1, tau( i ),
181 \$ a( i, i+1 ), lda, work )
182 END IF
183 IF( i.LT.m )
184 \$ CALL sscal( m-i, -tau( i ), a( i+1, i ), 1 )
185 a( i, i ) = one - tau( i )
186*
187* Set A(1:i-1,i) to zero
188*
189 DO 30 l = 1, i - 1
190 a( l, i ) = zero
191 30 CONTINUE
192 40 CONTINUE
193 RETURN
194*
195* End of SORG2R
196*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine slarf(side, m, n, v, incv, tau, c, ldc, work)
SLARF applies an elementary reflector to a general rectangular matrix.
Definition slarf.f:124
subroutine sscal(n, sa, sx, incx)
SSCAL
Definition sscal.f:79
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