 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ sorgl2()

 subroutine sorgl2 ( integer M, integer N, integer K, real, dimension( lda, * ) A, integer LDA, real, dimension( * ) TAU, real, dimension( * ) WORK, integer INFO )

SORGL2

Purpose:
``` SORGL2 generates an m by n real matrix Q with orthonormal rows,
which is defined as the first m rows of a product of k elementary
reflectors of order n

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

as returned by SGELQF.```
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. N >= M.``` [in] K ``` K is INTEGER The number of elementary reflectors whose product defines the matrix Q. M >= K >= 0.``` [in,out] A ``` A is REAL array, dimension (LDA,N) On entry, the i-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by SGELQF in the first k rows 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 SGELQF.``` [out] WORK ` WORK is REAL array, dimension (M)` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument has an illegal value```

Definition at line 112 of file sorgl2.f.

113*
114* -- LAPACK computational routine --
115* -- LAPACK is a software package provided by Univ. of Tennessee, --
116* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
117*
118* .. Scalar Arguments ..
119 INTEGER INFO, K, LDA, M, N
120* ..
121* .. Array Arguments ..
122 REAL A( LDA, * ), TAU( * ), WORK( * )
123* ..
124*
125* =====================================================================
126*
127* .. Parameters ..
128 REAL ONE, ZERO
129 parameter( one = 1.0e+0, zero = 0.0e+0 )
130* ..
131* .. Local Scalars ..
132 INTEGER I, J, L
133* ..
134* .. External Subroutines ..
135 EXTERNAL slarf, sscal, xerbla
136* ..
137* .. Intrinsic Functions ..
138 INTRINSIC max
139* ..
140* .. Executable Statements ..
141*
142* Test the input arguments
143*
144 info = 0
145 IF( m.LT.0 ) THEN
146 info = -1
147 ELSE IF( n.LT.m ) THEN
148 info = -2
149 ELSE IF( k.LT.0 .OR. k.GT.m ) THEN
150 info = -3
151 ELSE IF( lda.LT.max( 1, m ) ) THEN
152 info = -5
153 END IF
154 IF( info.NE.0 ) THEN
155 CALL xerbla( 'SORGL2', -info )
156 RETURN
157 END IF
158*
159* Quick return if possible
160*
161 IF( m.LE.0 )
162 \$ RETURN
163*
164 IF( k.LT.m ) THEN
165*
166* Initialise rows k+1:m to rows of the unit matrix
167*
168 DO 20 j = 1, n
169 DO 10 l = k + 1, m
170 a( l, j ) = zero
171 10 CONTINUE
172 IF( j.GT.k .AND. j.LE.m )
173 \$ a( j, j ) = one
174 20 CONTINUE
175 END IF
176*
177 DO 40 i = k, 1, -1
178*
179* Apply H(i) to A(i:m,i:n) from the right
180*
181 IF( i.LT.n ) THEN
182 IF( i.LT.m ) THEN
183 a( i, i ) = one
184 CALL slarf( 'Right', m-i, n-i+1, a( i, i ), lda,
185 \$ tau( i ), a( i+1, i ), lda, work )
186 END IF
187 CALL sscal( n-i, -tau( i ), a( i, i+1 ), lda )
188 END IF
189 a( i, i ) = one - tau( i )
190*
191* Set A(i,1:i-1) to zero
192*
193 DO 30 l = 1, i - 1
194 a( i, l ) = zero
195 30 CONTINUE
196 40 CONTINUE
197 RETURN
198*
199* End of SORGL2
200*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
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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