LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ slarge()

subroutine slarge ( integer  N,
real, dimension( lda, * )  A,
integer  LDA,
integer, dimension( 4 )  ISEED,
real, dimension( * )  WORK,
integer  INFO 
)

SLARGE

Purpose:
 SLARGE pre- and post-multiplies a real general n by n matrix A
 with a random orthogonal matrix: A = U*D*U'.
Parameters
[in]N
          N is INTEGER
          The order of the matrix A.  N >= 0.
[in,out]A
          A is REAL 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.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= N.
[in,out]ISEED
          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.
[out]WORK
          WORK is REAL array, dimension (2*N)
[out]INFO
          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -i, the i-th argument had an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
December 2016

Definition at line 89 of file slarge.f.

89 *
90 * -- LAPACK auxiliary routine (version 3.7.0) --
91 * -- LAPACK is a software package provided by Univ. of Tennessee, --
92 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
93 * December 2016
94 *
95 * .. Scalar Arguments ..
96  INTEGER info, lda, n
97 * ..
98 * .. Array Arguments ..
99  INTEGER iseed( 4 )
100  REAL a( lda, * ), work( * )
101 * ..
102 *
103 * =====================================================================
104 *
105 * .. Parameters ..
106  REAL zero, one
107  parameter( zero = 0.0e+0, one = 1.0e+0 )
108 * ..
109 * .. Local Scalars ..
110  INTEGER i
111  REAL tau, wa, wb, wn
112 * ..
113 * .. External Subroutines ..
114  EXTERNAL sgemv, sger, slarnv, sscal, xerbla
115 * ..
116 * .. Intrinsic Functions ..
117  INTRINSIC max, sign
118 * ..
119 * .. External Functions ..
120  REAL snrm2
121  EXTERNAL snrm2
122 * ..
123 * .. Executable Statements ..
124 *
125 * Test the input arguments
126 *
127  info = 0
128  IF( n.LT.0 ) THEN
129  info = -1
130  ELSE IF( lda.LT.max( 1, n ) ) THEN
131  info = -3
132  END IF
133  IF( info.LT.0 ) THEN
134  CALL xerbla( 'SLARGE', -info )
135  RETURN
136  END IF
137 *
138 * pre- and post-multiply A by random orthogonal matrix
139 *
140  DO 10 i = n, 1, -1
141 *
142 * generate random reflection
143 *
144  CALL slarnv( 3, iseed, n-i+1, work )
145  wn = snrm2( n-i+1, work, 1 )
146  wa = sign( wn, work( 1 ) )
147  IF( wn.EQ.zero ) THEN
148  tau = zero
149  ELSE
150  wb = work( 1 ) + wa
151  CALL sscal( n-i, one / wb, work( 2 ), 1 )
152  work( 1 ) = one
153  tau = wb / wa
154  END IF
155 *
156 * multiply A(i:n,1:n) by random reflection from the left
157 *
158  CALL sgemv( 'Transpose', n-i+1, n, one, a( i, 1 ), lda, work,
159  $ 1, zero, work( n+1 ), 1 )
160  CALL sger( n-i+1, n, -tau, work, 1, work( n+1 ), 1, a( i, 1 ),
161  $ lda )
162 *
163 * multiply A(1:n,i:n) by random reflection from the right
164 *
165  CALL sgemv( 'No transpose', n, n-i+1, one, a( 1, i ), lda,
166  $ work, 1, zero, work( n+1 ), 1 )
167  CALL sger( n, n-i+1, -tau, work( n+1 ), 1, work, 1, a( 1, i ),
168  $ lda )
169  10 CONTINUE
170  RETURN
171 *
172 * End of SLARGE
173 *
subroutine sger(M, N, ALPHA, X, INCX, Y, INCY, A, LDA)
SGER
Definition: sger.f:132
subroutine sgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
SGEMV
Definition: sgemv.f:158
real function snrm2(N, X, INCX)
SNRM2
Definition: snrm2.f:76
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine slarnv(IDIST, ISEED, N, X)
SLARNV returns a vector of random numbers from a uniform or normal distribution.
Definition: slarnv.f:99
subroutine sscal(N, SA, SX, INCX)
SSCAL
Definition: sscal.f:81
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