 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ clatsp()

 subroutine clatsp ( character UPLO, integer N, complex, dimension( * ) X, integer, dimension( * ) ISEED )

CLATSP

Purpose:
``` CLATSP generates a special test matrix for the complex symmetric
(indefinite) factorization for packed matrices.  The pivot blocks of
the generated matrix will be in the following order:
2x2 pivot block, non diagonalizable
1x1 pivot block
2x2 pivot block, diagonalizable
(cycle repeats)
A row interchange is required for each non-diagonalizable 2x2 block.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER Specifies whether the generated matrix is to be upper or lower triangular. = 'U': Upper triangular = 'L': Lower triangular``` [in] N ``` N is INTEGER The dimension of the matrix to be generated.``` [out] X ``` X is COMPLEX array, dimension (N*(N+1)/2) The generated matrix in packed storage format. The matrix consists of 3x3 and 2x2 diagonal blocks which result in the pivot sequence given above. The matrix outside these diagonal blocks is zero.``` [in,out] ISEED ``` ISEED is INTEGER array, dimension (4) On entry, the seed for the random number generator. The last of the four integers must be odd. (modified on exit)```

Definition at line 83 of file clatsp.f.

84 *
85 * -- LAPACK test routine --
86 * -- LAPACK is a software package provided by Univ. of Tennessee, --
87 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
88 *
89 * .. Scalar Arguments ..
90  CHARACTER UPLO
91  INTEGER N
92 * ..
93 * .. Array Arguments ..
94  INTEGER ISEED( * )
95  COMPLEX X( * )
96 * ..
97 *
98 * =====================================================================
99 *
100 * .. Parameters ..
101  COMPLEX EYE
102  parameter( eye = ( 0.0, 1.0 ) )
103 * ..
104 * .. Local Scalars ..
105  INTEGER J, JJ, N5
106  REAL ALPHA, ALPHA3, BETA
107  COMPLEX A, B, C, R
108 * ..
109 * .. External Functions ..
110  COMPLEX CLARND
111  EXTERNAL clarnd
112 * ..
113 * .. Intrinsic Functions ..
114  INTRINSIC abs, sqrt
115 * ..
116 * .. Executable Statements ..
117 *
118 * Initialize constants
119 *
120  alpha = ( 1.+sqrt( 17. ) ) / 8.
121  beta = alpha - 1. / 1000.
122  alpha3 = alpha*alpha*alpha
123 *
124 * Fill the matrix with zeros.
125 *
126  DO 10 j = 1, n*( n+1 ) / 2
127  x( j ) = 0.0
128  10 CONTINUE
129 *
130 * UPLO = 'U': Upper triangular storage
131 *
132  IF( uplo.EQ.'U' ) THEN
133  n5 = n / 5
134  n5 = n - 5*n5 + 1
135 *
136  jj = n*( n+1 ) / 2
137  DO 20 j = n, n5, -5
138  a = alpha3*clarnd( 5, iseed )
139  b = clarnd( 5, iseed ) / alpha
140  c = a - 2.*b*eye
141  r = c / beta
142  x( jj ) = a
143  x( jj-2 ) = b
144  jj = jj - j
145  x( jj ) = clarnd( 2, iseed )
146  x( jj-1 ) = r
147  jj = jj - ( j-1 )
148  x( jj ) = c
149  jj = jj - ( j-2 )
150  x( jj ) = clarnd( 2, iseed )
151  jj = jj - ( j-3 )
152  x( jj ) = clarnd( 2, iseed )
153  IF( abs( x( jj+( j-3 ) ) ).GT.abs( x( jj ) ) ) THEN
154  x( jj+( j-4 ) ) = 2.0*x( jj+( j-3 ) )
155  ELSE
156  x( jj+( j-4 ) ) = 2.0*x( jj )
157  END IF
158  jj = jj - ( j-4 )
159  20 CONTINUE
160 *
161 * Clean-up for N not a multiple of 5.
162 *
163  j = n5 - 1
164  IF( j.GT.2 ) THEN
165  a = alpha3*clarnd( 5, iseed )
166  b = clarnd( 5, iseed ) / alpha
167  c = a - 2.*b*eye
168  r = c / beta
169  x( jj ) = a
170  x( jj-2 ) = b
171  jj = jj - j
172  x( jj ) = clarnd( 2, iseed )
173  x( jj-1 ) = r
174  jj = jj - ( j-1 )
175  x( jj ) = c
176  jj = jj - ( j-2 )
177  j = j - 3
178  END IF
179  IF( j.GT.1 ) THEN
180  x( jj ) = clarnd( 2, iseed )
181  x( jj-j ) = clarnd( 2, iseed )
182  IF( abs( x( jj ) ).GT.abs( x( jj-j ) ) ) THEN
183  x( jj-1 ) = 2.0*x( jj )
184  ELSE
185  x( jj-1 ) = 2.0*x( jj-j )
186  END IF
187  jj = jj - j - ( j-1 )
188  j = j - 2
189  ELSE IF( j.EQ.1 ) THEN
190  x( jj ) = clarnd( 2, iseed )
191  j = j - 1
192  END IF
193 *
194 * UPLO = 'L': Lower triangular storage
195 *
196  ELSE
197  n5 = n / 5
198  n5 = n5*5
199 *
200  jj = 1
201  DO 30 j = 1, n5, 5
202  a = alpha3*clarnd( 5, iseed )
203  b = clarnd( 5, iseed ) / alpha
204  c = a - 2.*b*eye
205  r = c / beta
206  x( jj ) = a
207  x( jj+2 ) = b
208  jj = jj + ( n-j+1 )
209  x( jj ) = clarnd( 2, iseed )
210  x( jj+1 ) = r
211  jj = jj + ( n-j )
212  x( jj ) = c
213  jj = jj + ( n-j-1 )
214  x( jj ) = clarnd( 2, iseed )
215  jj = jj + ( n-j-2 )
216  x( jj ) = clarnd( 2, iseed )
217  IF( abs( x( jj-( n-j-2 ) ) ).GT.abs( x( jj ) ) ) THEN
218  x( jj-( n-j-2 )+1 ) = 2.0*x( jj-( n-j-2 ) )
219  ELSE
220  x( jj-( n-j-2 )+1 ) = 2.0*x( jj )
221  END IF
222  jj = jj + ( n-j-3 )
223  30 CONTINUE
224 *
225 * Clean-up for N not a multiple of 5.
226 *
227  j = n5 + 1
228  IF( j.LT.n-1 ) THEN
229  a = alpha3*clarnd( 5, iseed )
230  b = clarnd( 5, iseed ) / alpha
231  c = a - 2.*b*eye
232  r = c / beta
233  x( jj ) = a
234  x( jj+2 ) = b
235  jj = jj + ( n-j+1 )
236  x( jj ) = clarnd( 2, iseed )
237  x( jj+1 ) = r
238  jj = jj + ( n-j )
239  x( jj ) = c
240  jj = jj + ( n-j-1 )
241  j = j + 3
242  END IF
243  IF( j.LT.n ) THEN
244  x( jj ) = clarnd( 2, iseed )
245  x( jj+( n-j+1 ) ) = clarnd( 2, iseed )
246  IF( abs( x( jj ) ).GT.abs( x( jj+( n-j+1 ) ) ) ) THEN
247  x( jj+1 ) = 2.0*x( jj )
248  ELSE
249  x( jj+1 ) = 2.0*x( jj+( n-j+1 ) )
250  END IF
251  jj = jj + ( n-j+1 ) + ( n-j )
252  j = j + 2
253  ELSE IF( j.EQ.n ) THEN
254  x( jj ) = clarnd( 2, iseed )
255  jj = jj + ( n-j+1 )
256  j = j + 1
257  END IF
258  END IF
259 *
260  RETURN
261 *
262 * End of CLATSP
263 *
complex function clarnd(IDIST, ISEED)
CLARND
Definition: clarnd.f:75
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