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).

Download SORGR2 + dependencies [TGZ] [ZIP] [TXT]

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
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
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 sscal(N, SA, SX, INCX)
SSCAL
Definition: sscal.f:81
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
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