LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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◆ clarge()

subroutine clarge ( integer  N,
complex, dimension( lda, * )  A,
integer  LDA,
integer, dimension( 4 )  ISEED,
complex, dimension( * )  WORK,
integer  INFO 
)

CLARGE

Purpose:
 CLARGE pre- and post-multiplies a complex general n by n matrix A
 with a random unitary matrix: A = U*D*U'.
Parameters
[in]N
          N is INTEGER
          The order of the matrix A.  N >= 0.
[in,out]A
          A is COMPLEX 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
          unitary 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 COMPLEX 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.

Definition at line 86 of file clarge.f.

87*
88* -- LAPACK auxiliary routine --
89* -- LAPACK is a software package provided by Univ. of Tennessee, --
90* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
91*
92* .. Scalar Arguments ..
93 INTEGER INFO, LDA, N
94* ..
95* .. Array Arguments ..
96 INTEGER ISEED( 4 )
97 COMPLEX A( LDA, * ), WORK( * )
98* ..
99*
100* =====================================================================
101*
102* .. Parameters ..
103 COMPLEX ZERO, ONE
104 parameter( zero = ( 0.0e+0, 0.0e+0 ),
105 $ one = ( 1.0e+0, 0.0e+0 ) )
106* ..
107* .. Local Scalars ..
108 INTEGER I
109 REAL WN
110 COMPLEX TAU, WA, WB
111* ..
112* .. External Subroutines ..
113 EXTERNAL cgemv, cgerc, clarnv, cscal, xerbla
114* ..
115* .. Intrinsic Functions ..
116 INTRINSIC abs, max, real
117* ..
118* .. External Functions ..
119 REAL SCNRM2
120 EXTERNAL scnrm2
121* ..
122* .. Executable Statements ..
123*
124* Test the input arguments
125*
126 info = 0
127 IF( n.LT.0 ) THEN
128 info = -1
129 ELSE IF( lda.LT.max( 1, n ) ) THEN
130 info = -3
131 END IF
132 IF( info.LT.0 ) THEN
133 CALL xerbla( 'CLARGE', -info )
134 RETURN
135 END IF
136*
137* pre- and post-multiply A by random unitary matrix
138*
139 DO 10 i = n, 1, -1
140*
141* generate random reflection
142*
143 CALL clarnv( 3, iseed, n-i+1, work )
144 wn = scnrm2( n-i+1, work, 1 )
145 wa = ( wn / abs( work( 1 ) ) )*work( 1 )
146 IF( wn.EQ.zero ) THEN
147 tau = zero
148 ELSE
149 wb = work( 1 ) + wa
150 CALL cscal( n-i, one / wb, work( 2 ), 1 )
151 work( 1 ) = one
152 tau = real( wb / wa )
153 END IF
154*
155* multiply A(i:n,1:n) by random reflection from the left
156*
157 CALL cgemv( 'Conjugate transpose', n-i+1, n, one, a( i, 1 ),
158 $ lda, work, 1, zero, work( n+1 ), 1 )
159 CALL cgerc( n-i+1, n, -tau, work, 1, work( n+1 ), 1, a( i, 1 ),
160 $ lda )
161*
162* multiply A(1:n,i:n) by random reflection from the right
163*
164 CALL cgemv( 'No transpose', n, n-i+1, one, a( 1, i ), lda,
165 $ work, 1, zero, work( n+1 ), 1 )
166 CALL cgerc( n, n-i+1, -tau, work( n+1 ), 1, work, 1, a( 1, i ),
167 $ lda )
168 10 CONTINUE
169 RETURN
170*
171* End of CLARGE
172*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine cscal(N, CA, CX, INCX)
CSCAL
Definition: cscal.f:78
subroutine cgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
CGEMV
Definition: cgemv.f:158
subroutine cgerc(M, N, ALPHA, X, INCX, Y, INCY, A, LDA)
CGERC
Definition: cgerc.f:130
subroutine clarnv(IDIST, ISEED, N, X)
CLARNV returns a vector of random numbers from a uniform or normal distribution.
Definition: clarnv.f:99
real(wp) function scnrm2(n, x, incx)
SCNRM2
Definition: scnrm2.f90:90
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