numeric-linalg

001
002
003
004
005
006
007
008
009
010
011
012
013
014
015
016
017
018
019
020
021
022
023
024
025
026
027
028
029
030
031
032
033
034
035
036
037
038
039
040
041
042
043
044
045
046
047
048
049
050
051
052
053
054
055
056
057
058
059
060
061
062
063
064
065
066
067
068
069
070
071
072
073
074
075
076
077
078
079
080
081
082
083
084
085
086
087
088
089
090
091
092
093
094
095
096
097
098
099
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171

*> \brief \b DLARGE
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE DLARGE( N, A, LDA, ISEED, WORK, INFO )
*
*       .. Scalar Arguments ..
*       INTEGER            INFO, LDA, N
*       ..
*       .. Array Arguments ..
*       INTEGER            ISEED( 4 )
*       DOUBLE PRECISION   A( LDA, * ), WORK( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DLARGE pre- and post-multiplies a real general n by n matrix A
*> with a random orthogonal matrix: A = U*D*U'.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the matrix A.  N >= 0.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*>          A is DOUBLE PRECISION array, dimension (LDA,N)
*>          On entry, the original n by n matrix A.
*>          On exit, A is overwritten by U*A*U' for some random
*>          orthogonal matrix U.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A.  LDA >= N.
*> \endverbatim
*>
*> \param[in,out] ISEED
*> \verbatim
*>          ISEED is INTEGER array, dimension (4)
*>          On entry, the seed of the random number generator; the array
*>          elements must be between 0 and 4095, and ISEED(4) must be
*>          odd.
*>          On exit, the seed is updated.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is DOUBLE PRECISION array, dimension (2*N)
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*>          INFO is INTEGER
*>          = 0: successful exit
*>          < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup double_matgen
*
*  =====================================================================
      SUBROUTINE DLARGE( N, A, LDA, ISEED, WORK, INFO )
*
*  -- LAPACK auxiliary routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      INTEGER            INFO, LDA, N
*     ..
*     .. Array Arguments ..
      INTEGER            ISEED( 4 )
      DOUBLE PRECISION   A( LDA, * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE
      PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            I
      DOUBLE PRECISION   TAU, WA, WB, WN
*     ..
*     .. External Subroutines ..
      EXTERNAL           DGEMV, DGER, DLARNV, DSCAL, XERBLA
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          MAX, SIGN
*     ..
*     .. External Functions ..
      DOUBLE PRECISION   DNRM2
      EXTERNAL           DNRM2
*     ..
*     .. Executable Statements ..
*
*     Test the input arguments
*
      INFO = 0
      IF( N.LT.0 ) THEN
         INFO = -1
      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
         INFO = -3
      END IF
      IF( INFO.LT.0 ) THEN
         CALL XERBLA( 'DLARGE', -INFO )
         RETURN
      END IF
*
*     pre- and post-multiply A by random orthogonal matrix
*
      DO 10 I = N, 1, -1
*
*        generate random reflection
*
         CALL DLARNV( 3, ISEED, N-I+1, WORK )
         WN = DNRM2( N-I+1, WORK, 1 )
         WA = SIGN( WN, WORK( 1 ) )
         IF( WN.EQ.ZERO ) THEN
            TAU = ZERO
         ELSE
            WB = WORK( 1 ) + WA
            CALL DSCAL( N-I, ONE / WB, WORK( 2 ), 1 )
            WORK( 1 ) = ONE
            TAU = WB / WA
         END IF
*
*        multiply A(i:n,1:n) by random reflection from the left
*
         CALL DGEMV( 'Transpose', N-I+1, N, ONE, A( I, 1 ), LDA, WORK,
     $               1, ZERO, WORK( N+1 ), 1 )
         CALL DGER( N-I+1, N, -TAU, WORK, 1, WORK( N+1 ), 1, A( I, 1 ),
     $              LDA )
*
*        multiply A(1:n,i:n) by random reflection from the right
*
         CALL DGEMV( 'No transpose', N, N-I+1, ONE, A( 1, I ), LDA,
     $               WORK, 1, ZERO, WORK( N+1 ), 1 )
         CALL DGER( N, N-I+1, -TAU, WORK( N+1 ), 1, WORK, 1, A( 1, I ),
     $              LDA )
   10 CONTINUE
      RETURN
*
*     End of DLARGE
*
      END