 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ dorgr2()

 subroutine dorgr2 ( integer M, integer N, integer K, double precision, dimension( lda, * ) A, integer LDA, double precision, dimension( * ) TAU, double precision, dimension( * ) WORK, integer INFO )

DORGR2 generates all or part of the orthogonal matrix Q from an RQ factorization determined by sgerqf (unblocked algorithm).

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Purpose:
``` DORGR2 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 DGERQF.```
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 DOUBLE PRECISION 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 DGERQF 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 DOUBLE PRECISION array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DGERQF.``` [out] WORK ` WORK is DOUBLE PRECISION 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 113 of file dorgr2.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.m ) THEN
149  info = -2
150  ELSE IF( k.LT.0 .OR. k.GT.m ) 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( 'DORGR2', -info )
157  RETURN
158  END IF
159 *
160 * Quick return if possible
161 *
162  IF( m.LE.0 )
163  \$ RETURN
164 *
165  IF( k.LT.m ) THEN
166 *
167 * Initialise rows 1:m-k to rows of the unit matrix
168 *
169  DO 20 j = 1, n
170  DO 10 l = 1, m - k
171  a( l, j ) = zero
172  10 CONTINUE
173  IF( j.GT.n-m .AND. j.LE.n-k )
174  \$ a( m-n+j, j ) = one
175  20 CONTINUE
176  END IF
177 *
178  DO 40 i = 1, k
179  ii = m - k + i
180 *
181 * Apply H(i) to A(1:m-k+i,1:n-k+i) from the right
182 *
183  a( ii, n-m+ii ) = one
184  CALL dlarf( 'Right', ii-1, n-m+ii, a( ii, 1 ), lda, tau( i ),
185  \$ a, lda, work )
186  CALL dscal( n-m+ii-1, -tau( i ), a( ii, 1 ), lda )
187  a( ii, n-m+ii ) = one - tau( i )
188 *
189 * Set A(m-k+i,n-k+i+1:n) to zero
190 *
191  DO 30 l = n - m + ii + 1, n
192  a( ii, l ) = zero
193  30 CONTINUE
194  40 CONTINUE
195  RETURN
196 *
197 * End of DORGR2
198 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine dscal(N, DA, DX, INCX)
DSCAL
Definition: dscal.f:79
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
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