LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ 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).

Download SORG2R + dependencies [TGZ] [ZIP] [TXT]

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
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

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)
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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