 LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ sorgr2()

 subroutine sorgr2 ( integer M, integer N, integer K, real, dimension( lda, * ) A, integer LDA, real, dimension( * ) TAU, real, dimension( * ) WORK, integer INFO )

SORGR2 generates all or part of the orthogonal matrix Q from an RQ factorization determined by sgerqf (unblocked algorithm).

Purpose:
``` SORGR2 generates an m by n real matrix Q with orthonormal rows,
which is defined as the last m rows of a product of k elementary
reflectors of order n

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

as returned by SGERQF.```
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 (m-k+i)-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by SGERQF in the last 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 SGERQF.``` [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```
Date
December 2016

Definition at line 116 of file sorgr2.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  REAL a( lda, * ), tau( * ), work( * )
127 * ..
128 *
129 * =====================================================================
130 *
131 * .. Parameters ..
132  REAL one, zero
133  parameter( one = 1.0e+0, zero = 0.0e+0 )
134 * ..
135 * .. Local Scalars ..
136  INTEGER i, ii, j, l
137 * ..
138 * .. External Subroutines ..
139  EXTERNAL slarf, sscal, 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.m ) THEN
152  info = -2
153  ELSE IF( k.LT.0 .OR. k.GT.m ) 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( 'SORGR2', -info )
160  RETURN
161  END IF
162 *
163 * Quick return if possible
164 *
165  IF( m.LE.0 )
166  \$ RETURN
167 *
168  IF( k.LT.m ) THEN
169 *
170 * Initialise rows 1:m-k to rows of the unit matrix
171 *
172  DO 20 j = 1, n
173  DO 10 l = 1, m - k
174  a( l, j ) = zero
175  10 CONTINUE
176  IF( j.GT.n-m .AND. j.LE.n-k )
177  \$ a( m-n+j, j ) = one
178  20 CONTINUE
179  END IF
180 *
181  DO 40 i = 1, k
182  ii = m - k + i
183 *
184 * Apply H(i) to A(1:m-k+i,1:n-k+i) from the right
185 *
186  a( ii, n-m+ii ) = one
187  CALL slarf( 'Right', ii-1, n-m+ii, a( ii, 1 ), lda, tau( i ),
188  \$ a, lda, work )
189  CALL sscal( n-m+ii-1, -tau( i ), a( ii, 1 ), lda )
190  a( ii, n-m+ii ) = one - tau( i )
191 *
192 * Set A(m-k+i,n-k+i+1:n) to zero
193 *
194  DO 30 l = n - m + ii + 1, n
195  a( ii, l ) = zero
196  30 CONTINUE
197  40 CONTINUE
198  RETURN
199 *
200 * End of SORGR2
201 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine slarf(SIDE, M, N, V, INCV, TAU, C, LDC, WORK)
SLARF applies an elementary reflector to a general rectangular matrix.
Definition: slarf.f:126
subroutine sscal(N, SA, SX, INCX)
SSCAL
Definition: sscal.f:81
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