LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ zlatm1()

subroutine zlatm1 ( integer  mode,
double precision  cond,
integer  irsign,
integer  idist,
integer, dimension( 4 )  iseed,
complex*16, dimension( * )  d,
integer  n,
integer  info 
)

ZLATM1

Purpose:
    ZLATM1 computes the entries of D(1..N) as specified by
    MODE, COND and IRSIGN. IDIST and ISEED determine the generation
    of random numbers. ZLATM1 is called by ZLATMR to generate
    random test matrices for LAPACK programs.
Parameters
[in]MODE
          MODE is INTEGER
           On entry describes how D is to be computed:
           MODE = 0 means do not change D.
           MODE = 1 sets D(1)=1 and D(2:N)=1.0/COND
           MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND
           MODE = 3 sets D(I)=COND**(-(I-1)/(N-1))
           MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND)
           MODE = 5 sets D to random numbers in the range
                    ( 1/COND , 1 ) such that their logarithms
                    are uniformly distributed.
           MODE = 6 set D to random numbers from same distribution
                    as the rest of the matrix.
           MODE < 0 has the same meaning as ABS(MODE), except that
              the order of the elements of D is reversed.
           Thus if MODE is positive, D has entries ranging from
              1 to 1/COND, if negative, from 1/COND to 1,
           Not modified.
[in]COND
          COND is DOUBLE PRECISION
           On entry, used as described under MODE above.
           If used, it must be >= 1. Not modified.
[in]IRSIGN
          IRSIGN is INTEGER
           On entry, if MODE neither -6, 0 nor 6, determines sign of
           entries of D
           0 => leave entries of D unchanged
           1 => multiply each entry of D by random complex number
                uniformly distributed with absolute value 1
[in]IDIST
          IDIST is INTEGER
           On entry, IDIST specifies the type of distribution to be
           used to generate a random matrix .
           1 => real and imaginary parts each UNIFORM( 0, 1 )
           2 => real and imaginary parts each UNIFORM( -1, 1 )
           3 => real and imaginary parts each NORMAL( 0, 1 )
           4 => complex number uniform in DISK( 0, 1 )
           Not modified.
[in,out]ISEED
          ISEED is INTEGER array, dimension ( 4 )
           On entry ISEED specifies the seed of the random number
           generator. The random number generator uses a
           linear congruential sequence limited to small
           integers, and so should produce machine independent
           random numbers. The values of ISEED are changed on
           exit, and can be used in the next call to ZLATM1
           to continue the same random number sequence.
           Changed on exit.
[in,out]D
          D is COMPLEX*16 array, dimension ( N )
           Array to be computed according to MODE, COND and IRSIGN.
           May be changed on exit if MODE is nonzero.
[in]N
          N is INTEGER
           Number of entries of D. Not modified.
[out]INFO
          INFO is INTEGER
            0  => normal termination
           -1  => if MODE not in range -6 to 6
           -2  => if MODE neither -6, 0 nor 6, and
                  IRSIGN neither 0 nor 1
           -3  => if MODE neither -6, 0 nor 6 and COND less than 1
           -4  => if MODE equals 6 or -6 and IDIST not in range 1 to 4
           -7  => if N negative
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 136 of file zlatm1.f.

137*
138* -- LAPACK auxiliary routine --
139* -- LAPACK is a software package provided by Univ. of Tennessee, --
140* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
141*
142* .. Scalar Arguments ..
143 INTEGER IDIST, INFO, IRSIGN, MODE, N
144 DOUBLE PRECISION COND
145* ..
146* .. Array Arguments ..
147 INTEGER ISEED( 4 )
148 COMPLEX*16 D( * )
149* ..
150*
151* =====================================================================
152*
153* .. Parameters ..
154 DOUBLE PRECISION ONE
155 parameter( one = 1.0d0 )
156* ..
157* .. Local Scalars ..
158 INTEGER I
159 DOUBLE PRECISION ALPHA, TEMP
160 COMPLEX*16 CTEMP
161* ..
162* .. External Functions ..
163 DOUBLE PRECISION DLARAN
164 COMPLEX*16 ZLARND
165 EXTERNAL dlaran, zlarnd
166* ..
167* .. External Subroutines ..
168 EXTERNAL xerbla, zlarnv
169* ..
170* .. Intrinsic Functions ..
171 INTRINSIC abs, dble, exp, log
172* ..
173* .. Executable Statements ..
174*
175* Decode and Test the input parameters. Initialize flags & seed.
176*
177 info = 0
178*
179* Quick return if possible
180*
181 IF( n.EQ.0 )
182 $ RETURN
183*
184* Set INFO if an error
185*
186 IF( mode.LT.-6 .OR. mode.GT.6 ) THEN
187 info = -1
188 ELSE IF( ( mode.NE.-6 .AND. mode.NE.0 .AND. mode.NE.6 ) .AND.
189 $ ( irsign.NE.0 .AND. irsign.NE.1 ) ) THEN
190 info = -2
191 ELSE IF( ( mode.NE.-6 .AND. mode.NE.0 .AND. mode.NE.6 ) .AND.
192 $ cond.LT.one ) THEN
193 info = -3
194 ELSE IF( ( mode.EQ.6 .OR. mode.EQ.-6 ) .AND.
195 $ ( idist.LT.1 .OR. idist.GT.4 ) ) THEN
196 info = -4
197 ELSE IF( n.LT.0 ) THEN
198 info = -7
199 END IF
200*
201 IF( info.NE.0 ) THEN
202 CALL xerbla( 'ZLATM1', -info )
203 RETURN
204 END IF
205*
206* Compute D according to COND and MODE
207*
208 IF( mode.NE.0 ) THEN
209 GO TO ( 10, 30, 50, 70, 90, 110 )abs( mode )
210*
211* One large D value:
212*
213 10 CONTINUE
214 DO 20 i = 1, n
215 d( i ) = one / cond
216 20 CONTINUE
217 d( 1 ) = one
218 GO TO 120
219*
220* One small D value:
221*
222 30 CONTINUE
223 DO 40 i = 1, n
224 d( i ) = one
225 40 CONTINUE
226 d( n ) = one / cond
227 GO TO 120
228*
229* Exponentially distributed D values:
230*
231 50 CONTINUE
232 d( 1 ) = one
233 IF( n.GT.1 ) THEN
234 alpha = cond**( -one / dble( n-1 ) )
235 DO 60 i = 2, n
236 d( i ) = alpha**( i-1 )
237 60 CONTINUE
238 END IF
239 GO TO 120
240*
241* Arithmetically distributed D values:
242*
243 70 CONTINUE
244 d( 1 ) = one
245 IF( n.GT.1 ) THEN
246 temp = one / cond
247 alpha = ( one-temp ) / dble( n-1 )
248 DO 80 i = 2, n
249 d( i ) = dble( n-i )*alpha + temp
250 80 CONTINUE
251 END IF
252 GO TO 120
253*
254* Randomly distributed D values on ( 1/COND , 1):
255*
256 90 CONTINUE
257 alpha = log( one / cond )
258 DO 100 i = 1, n
259 d( i ) = exp( alpha*dlaran( iseed ) )
260 100 CONTINUE
261 GO TO 120
262*
263* Randomly distributed D values from IDIST
264*
265 110 CONTINUE
266 CALL zlarnv( idist, iseed, n, d )
267*
268 120 CONTINUE
269*
270* If MODE neither -6 nor 0 nor 6, and IRSIGN = 1, assign
271* random signs to D
272*
273 IF( ( mode.NE.-6 .AND. mode.NE.0 .AND. mode.NE.6 ) .AND.
274 $ irsign.EQ.1 ) THEN
275 DO 130 i = 1, n
276 ctemp = zlarnd( 3, iseed )
277 d( i ) = d( i )*( ctemp / abs( ctemp ) )
278 130 CONTINUE
279 END IF
280*
281* Reverse if MODE < 0
282*
283 IF( mode.LT.0 ) THEN
284 DO 140 i = 1, n / 2
285 ctemp = d( i )
286 d( i ) = d( n+1-i )
287 d( n+1-i ) = ctemp
288 140 CONTINUE
289 END IF
290*
291 END IF
292*
293 RETURN
294*
295* End of ZLATM1
296*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
dlaran
double precision function dlaran(iseed)
DLARAN
Definition dlaran.f:67
zlarnv
subroutine zlarnv(idist, iseed, n, x)
ZLARNV returns a vector of random numbers from a uniform or normal distribution.
Definition zlarnv.f:99
zlarnd
complex *16 function zlarnd(idist, iseed)
ZLARND
Definition zlarnd.f:75
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