LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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◆ claghe()

subroutine claghe ( integer  N,
integer  K,
real, dimension( * )  D,
complex, dimension( lda, * )  A,
integer  LDA,
integer, dimension( 4 )  ISEED,
complex, dimension( * )  WORK,
integer  INFO 
)

CLAGHE

Purpose:
 CLAGHE generates a complex hermitian matrix A, by pre- and post-
 multiplying a real diagonal matrix D with a random unitary matrix:
 A = U*D*U'. The semi-bandwidth may then be reduced to k by additional
 unitary transformations.
Parameters
[in]N
          N is INTEGER
          The order of the matrix A.  N >= 0.
[in]K
          K is INTEGER
          The number of nonzero subdiagonals within the band of A.
          0 <= K <= N-1.
[in]D
          D is REAL array, dimension (N)
          The diagonal elements of the diagonal matrix D.
[out]A
          A is COMPLEX array, dimension (LDA,N)
          The generated n by n hermitian matrix A (the full matrix is
          stored).
[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 101 of file claghe.f.

102*
103* -- LAPACK auxiliary routine --
104* -- LAPACK is a software package provided by Univ. of Tennessee, --
105* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
106*
107* .. Scalar Arguments ..
108 INTEGER INFO, K, LDA, N
109* ..
110* .. Array Arguments ..
111 INTEGER ISEED( 4 )
112 REAL D( * )
113 COMPLEX A( LDA, * ), WORK( * )
114* ..
115*
116* =====================================================================
117*
118* .. Parameters ..
119 COMPLEX ZERO, ONE, HALF
120 parameter( zero = ( 0.0e+0, 0.0e+0 ),
121 $ one = ( 1.0e+0, 0.0e+0 ),
122 $ half = ( 0.5e+0, 0.0e+0 ) )
123* ..
124* .. Local Scalars ..
125 INTEGER I, J
126 REAL WN
127 COMPLEX ALPHA, TAU, WA, WB
128* ..
129* .. External Subroutines ..
130 EXTERNAL caxpy, cgemv, cgerc, chemv, cher2, clarnv,
131 $ cscal, xerbla
132* ..
133* .. External Functions ..
134 REAL SCNRM2
135 COMPLEX CDOTC
136 EXTERNAL scnrm2, cdotc
137* ..
138* .. Intrinsic Functions ..
139 INTRINSIC abs, conjg, max, real
140* ..
141* .. Executable Statements ..
142*
143* Test the input arguments
144*
145 info = 0
146 IF( n.LT.0 ) THEN
147 info = -1
148 ELSE IF( k.LT.0 .OR. k.GT.n-1 ) THEN
149 info = -2
150 ELSE IF( lda.LT.max( 1, n ) ) THEN
151 info = -5
152 END IF
153 IF( info.LT.0 ) THEN
154 CALL xerbla( 'CLAGHE', -info )
155 RETURN
156 END IF
157*
158* initialize lower triangle of A to diagonal matrix
159*
160 DO 20 j = 1, n
161 DO 10 i = j + 1, n
162 a( i, j ) = zero
163 10 CONTINUE
164 20 CONTINUE
165 DO 30 i = 1, n
166 a( i, i ) = d( i )
167 30 CONTINUE
168*
169* Generate lower triangle of hermitian matrix
170*
171 DO 40 i = n - 1, 1, -1
172*
173* generate random reflection
174*
175 CALL clarnv( 3, iseed, n-i+1, work )
176 wn = scnrm2( n-i+1, work, 1 )
177 wa = ( wn / abs( work( 1 ) ) )*work( 1 )
178 IF( wn.EQ.zero ) THEN
179 tau = zero
180 ELSE
181 wb = work( 1 ) + wa
182 CALL cscal( n-i, one / wb, work( 2 ), 1 )
183 work( 1 ) = one
184 tau = real( wb / wa )
185 END IF
186*
187* apply random reflection to A(i:n,i:n) from the left
188* and the right
189*
190* compute y := tau * A * u
191*
192 CALL chemv( 'Lower', n-i+1, tau, a( i, i ), lda, work, 1, zero,
193 $ work( n+1 ), 1 )
194*
195* compute v := y - 1/2 * tau * ( y, u ) * u
196*
197 alpha = -half*tau*cdotc( n-i+1, work( n+1 ), 1, work, 1 )
198 CALL caxpy( n-i+1, alpha, work, 1, work( n+1 ), 1 )
199*
200* apply the transformation as a rank-2 update to A(i:n,i:n)
201*
202 CALL cher2( 'Lower', n-i+1, -one, work, 1, work( n+1 ), 1,
203 $ a( i, i ), lda )
204 40 CONTINUE
205*
206* Reduce number of subdiagonals to K
207*
208 DO 60 i = 1, n - 1 - k
209*
210* generate reflection to annihilate A(k+i+1:n,i)
211*
212 wn = scnrm2( n-k-i+1, a( k+i, i ), 1 )
213 wa = ( wn / abs( a( k+i, i ) ) )*a( k+i, i )
214 IF( wn.EQ.zero ) THEN
215 tau = zero
216 ELSE
217 wb = a( k+i, i ) + wa
218 CALL cscal( n-k-i, one / wb, a( k+i+1, i ), 1 )
219 a( k+i, i ) = one
220 tau = real( wb / wa )
221 END IF
222*
223* apply reflection to A(k+i:n,i+1:k+i-1) from the left
224*
225 CALL cgemv( 'Conjugate transpose', n-k-i+1, k-1, one,
226 $ a( k+i, i+1 ), lda, a( k+i, i ), 1, zero, work, 1 )
227 CALL cgerc( n-k-i+1, k-1, -tau, a( k+i, i ), 1, work, 1,
228 $ a( k+i, i+1 ), lda )
229*
230* apply reflection to A(k+i:n,k+i:n) from the left and the right
231*
232* compute y := tau * A * u
233*
234 CALL chemv( 'Lower', n-k-i+1, tau, a( k+i, k+i ), lda,
235 $ a( k+i, i ), 1, zero, work, 1 )
236*
237* compute v := y - 1/2 * tau * ( y, u ) * u
238*
239 alpha = -half*tau*cdotc( n-k-i+1, work, 1, a( k+i, i ), 1 )
240 CALL caxpy( n-k-i+1, alpha, a( k+i, i ), 1, work, 1 )
241*
242* apply hermitian rank-2 update to A(k+i:n,k+i:n)
243*
244 CALL cher2( 'Lower', n-k-i+1, -one, a( k+i, i ), 1, work, 1,
245 $ a( k+i, k+i ), lda )
246*
247 a( k+i, i ) = -wa
248 DO 50 j = k + i + 1, n
249 a( j, i ) = zero
250 50 CONTINUE
251 60 CONTINUE
252*
253* Store full hermitian matrix
254*
255 DO 80 j = 1, n
256 DO 70 i = j + 1, n
257 a( j, i ) = conjg( a( i, j ) )
258 70 CONTINUE
259 80 CONTINUE
260 RETURN
261*
262* End of CLAGHE
263*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
complex function cdotc(N, CX, INCX, CY, INCY)
CDOTC
Definition: cdotc.f:83
subroutine caxpy(N, CA, CX, INCX, CY, INCY)
CAXPY
Definition: caxpy.f:88
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 cher2(UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA)
CHER2
Definition: cher2.f:150
subroutine chemv(UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
CHEMV
Definition: chemv.f:154
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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