 LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

## ◆ slatm7()

 subroutine slatm7 ( integer MODE, real COND, integer IRSIGN, integer IDIST, integer, dimension( 4 ) ISEED, real, dimension( * ) D, integer N, integer RANK, integer INFO )

SLATM7

Purpose:
```    SLATM7 computes the entries of D as specified by MODE
COND and IRSIGN. IDIST and ISEED determine the generation
of random numbers. SLATM7 is called by SLATMT to generate
random test matrices.```
```  MODE   - 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:RANK)=1.0/COND
MODE = 2 sets D(1:RANK-1)=1 and D(RANK)=1.0/COND
MODE = 3 sets D(I)=COND**(-(I-1)/(RANK-1)) I=1:RANK

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.

COND   - REAL
On entry, used as described under MODE above.
If used, it must be >= 1. Not modified.

IRSIGN - 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 1 or -1 with probability .5

IDIST  - CHARACTER*1
On entry, IDIST specifies the type of distribution to be
used to generate a random matrix .
1 => UNIFORM( 0, 1 )
2 => UNIFORM( -1, 1 )
3 => NORMAL( 0, 1 )
Not modified.

ISEED  - 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 SLATM7
to continue the same random number sequence.
Changed on exit.

D      - REAL array, dimension ( MIN( M , N ) )
Array to be computed according to MODE, COND and IRSIGN.
May be changed on exit if MODE is nonzero.

N      - INTEGER
Number of entries of D. Not modified.

RANK   - INTEGER
The rank of matrix to be generated for modes 1,2,3 only.
D( RANK+1:N ) = 0.
Not modified.

INFO   - 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 3
-7  => if N negative```

Definition at line 120 of file slatm7.f.

122 *
123 * -- LAPACK computational routine --
124 * -- LAPACK is a software package provided by Univ. of Tennessee, --
125 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
126 *
127 * .. Scalar Arguments ..
128  REAL COND
129  INTEGER IDIST, INFO, IRSIGN, MODE, N, RANK
130 * ..
131 * .. Array Arguments ..
132  REAL D( * )
133  INTEGER ISEED( 4 )
134 * ..
135 *
136 * =====================================================================
137 *
138 * .. Parameters ..
139  REAL ONE
140  parameter( one = 1.0e0 )
141  REAL ZERO
142  parameter( zero = 0.0e0 )
143  REAL HALF
144  parameter( half = 0.5e0 )
145 * ..
146 * .. Local Scalars ..
147  REAL ALPHA, TEMP
148  INTEGER I
149 * ..
150 * .. External Functions ..
151  REAL SLARAN
152  EXTERNAL slaran
153 * ..
154 * .. External Subroutines ..
155  EXTERNAL slarnv, xerbla
156 * ..
157 * .. Intrinsic Functions ..
158  INTRINSIC abs, exp, log, real
159 * ..
160 * .. Executable Statements ..
161 *
162 * Decode and Test the input parameters. Initialize flags & seed.
163 *
164  info = 0
165 *
166 * Quick return if possible
167 *
168  IF( n.EQ.0 )
169  \$ RETURN
170 *
171 * Set INFO if an error
172 *
173  IF( mode.LT.-6 .OR. mode.GT.6 ) THEN
174  info = -1
175  ELSE IF( ( mode.NE.-6 .AND. mode.NE.0 .AND. mode.NE.6 ) .AND.
176  \$ ( irsign.NE.0 .AND. irsign.NE.1 ) ) THEN
177  info = -2
178  ELSE IF( ( mode.NE.-6 .AND. mode.NE.0 .AND. mode.NE.6 ) .AND.
179  \$ cond.LT.one ) THEN
180  info = -3
181  ELSE IF( ( mode.EQ.6 .OR. mode.EQ.-6 ) .AND.
182  \$ ( idist.LT.1 .OR. idist.GT.3 ) ) THEN
183  info = -4
184  ELSE IF( n.LT.0 ) THEN
185  info = -7
186  END IF
187 *
188  IF( info.NE.0 ) THEN
189  CALL xerbla( 'SLATM7', -info )
190  RETURN
191  END IF
192 *
193 * Compute D according to COND and MODE
194 *
195  IF( mode.NE.0 ) THEN
196  GO TO ( 100, 130, 160, 190, 210, 230 )abs( mode )
197 *
198 * One large D value:
199 *
200  100 CONTINUE
201  DO 110 i = 2, rank
202  d( i ) = one / cond
203  110 CONTINUE
204  DO 120 i = rank + 1, n
205  d( i ) = zero
206  120 CONTINUE
207  d( 1 ) = one
208  GO TO 240
209 *
210 * One small D value:
211 *
212  130 CONTINUE
213  DO 140 i = 1, rank - 1
214  d( i ) = one
215  140 CONTINUE
216  DO 150 i = rank + 1, n
217  d( i ) = zero
218  150 CONTINUE
219  d( rank ) = one / cond
220  GO TO 240
221 *
222 * Exponentially distributed D values:
223 *
224  160 CONTINUE
225  d( 1 ) = one
226  IF( n.GT.1 .AND. rank.GT.1 ) THEN
227  alpha = cond**( -one / real( rank-1 ) )
228  DO 170 i = 2, rank
229  d( i ) = alpha**( i-1 )
230  170 CONTINUE
231  DO 180 i = rank + 1, n
232  d( i ) = zero
233  180 CONTINUE
234  END IF
235  GO TO 240
236 *
237 * Arithmetically distributed D values:
238 *
239  190 CONTINUE
240  d( 1 ) = one
241  IF( n.GT.1 ) THEN
242  temp = one / cond
243  alpha = ( one-temp ) / real( n-1 )
244  DO 200 i = 2, n
245  d( i ) = real( n-i )*alpha + temp
246  200 CONTINUE
247  END IF
248  GO TO 240
249 *
250 * Randomly distributed D values on ( 1/COND , 1):
251 *
252  210 CONTINUE
253  alpha = log( one / cond )
254  DO 220 i = 1, n
255  d( i ) = exp( alpha*slaran( iseed ) )
256  220 CONTINUE
257  GO TO 240
258 *
259 * Randomly distributed D values from IDIST
260 *
261  230 CONTINUE
262  CALL slarnv( idist, iseed, n, d )
263 *
264  240 CONTINUE
265 *
266 * If MODE neither -6 nor 0 nor 6, and IRSIGN = 1, assign
267 * random signs to D
268 *
269  IF( ( mode.NE.-6 .AND. mode.NE.0 .AND. mode.NE.6 ) .AND.
270  \$ irsign.EQ.1 ) THEN
271  DO 250 i = 1, n
272  temp = slaran( iseed )
273  IF( temp.GT.half )
274  \$ d( i ) = -d( i )
275  250 CONTINUE
276  END IF
277 *
278 * Reverse if MODE < 0
279 *
280  IF( mode.LT.0 ) THEN
281  DO 260 i = 1, n / 2
282  temp = d( i )
283  d( i ) = d( n+1-i )
284  d( n+1-i ) = temp
285  260 CONTINUE
286  END IF
287 *
288  END IF
289 *
290  RETURN
291 *
292 * End of SLATM7
293 *
subroutine slarnv(IDIST, ISEED, N, X)
SLARNV returns a vector of random numbers from a uniform or normal distribution.
Definition: slarnv.f:97
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
real function slaran(ISEED)
SLARAN
Definition: slaran.f:67
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