LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ dqrt15()

subroutine dqrt15 ( integer  scale,
integer  rksel,
integer  m,
integer  n,
integer  nrhs,
double precision, dimension( lda, * )  a,
integer  lda,
double precision, dimension( ldb, * )  b,
integer  ldb,
double precision, dimension( * )  s,
integer  rank,
double precision  norma,
double precision  normb,
integer, dimension( 4 )  iseed,
double precision, dimension( lwork )  work,
integer  lwork 
)

DQRT15

Purpose:
 DQRT15 generates a matrix with full or deficient rank and of various
 norms.
Parameters
[in]SCALE
          SCALE is INTEGER
          SCALE = 1: normally scaled matrix
          SCALE = 2: matrix scaled up
          SCALE = 3: matrix scaled down
[in]RKSEL
          RKSEL is INTEGER
          RKSEL = 1: full rank matrix
          RKSEL = 2: rank-deficient matrix
[in]M
          M is INTEGER
          The number of rows of the matrix A.
[in]N
          N is INTEGER
          The number of columns of A.
[in]NRHS
          NRHS is INTEGER
          The number of columns of B.
[out]A
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The M-by-N matrix A.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.
[out]B
          B is DOUBLE PRECISION array, dimension (LDB, NRHS)
          A matrix that is in the range space of matrix A.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.
[out]S
          S is DOUBLE PRECISION array, dimension MIN(M,N)
          Singular values of A.
[out]RANK
          RANK is INTEGER
          number of nonzero singular values of A.
[out]NORMA
          NORMA is DOUBLE PRECISION
          one-norm of A.
[out]NORMB
          NORMB is DOUBLE PRECISION
          one-norm of B.
[in,out]ISEED
          ISEED is integer array, dimension (4)
          seed for random number generator.
[out]WORK
          WORK is DOUBLE PRECISION array, dimension (LWORK)
[in]LWORK
          LWORK is INTEGER
          length of work space required.
          LWORK >= MAX(M+MIN(M,N),NRHS*MIN(M,N),2*N+M)
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 146 of file dqrt15.f.

148*
149* -- LAPACK test routine --
150* -- LAPACK is a software package provided by Univ. of Tennessee, --
151* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
152*
153* .. Scalar Arguments ..
154 INTEGER LDA, LDB, LWORK, M, N, NRHS, RANK, RKSEL, SCALE
155 DOUBLE PRECISION NORMA, NORMB
156* ..
157* .. Array Arguments ..
158 INTEGER ISEED( 4 )
159 DOUBLE PRECISION A( LDA, * ), B( LDB, * ), S( * ), WORK( LWORK )
160* ..
161*
162* =====================================================================
163*
164* .. Parameters ..
165 DOUBLE PRECISION ZERO, ONE, TWO, SVMIN
166 parameter( zero = 0.0d0, one = 1.0d0, two = 2.0d0,
167 $ svmin = 0.1d0 )
168* ..
169* .. Local Scalars ..
170 INTEGER INFO, J, MN
171 DOUBLE PRECISION BIGNUM, EPS, SMLNUM, TEMP
172* ..
173* .. Local Arrays ..
174 DOUBLE PRECISION DUMMY( 1 )
175* ..
176* .. External Functions ..
177 DOUBLE PRECISION DASUM, DLAMCH, DLANGE, DLARND, DNRM2
178 EXTERNAL dasum, dlamch, dlange, dlarnd, dnrm2
179* ..
180* .. External Subroutines ..
181 EXTERNAL dgemm, dlaord, dlarf, dlarnv, dlaror, dlascl,
182 $ dlaset, dscal, xerbla
183* ..
184* .. Intrinsic Functions ..
185 INTRINSIC abs, max, min
186* ..
187* .. Executable Statements ..
188*
189 mn = min( m, n )
190 IF( lwork.LT.max( m+mn, mn*nrhs, 2*n+m ) ) THEN
191 CALL xerbla( 'DQRT15', 16 )
192 RETURN
193 END IF
194*
195 smlnum = dlamch( 'Safe minimum' )
196 bignum = one / smlnum
197 eps = dlamch( 'Epsilon' )
198 smlnum = ( smlnum / eps ) / eps
199 bignum = one / smlnum
200*
201* Determine rank and (unscaled) singular values
202*
203 IF( rksel.EQ.1 ) THEN
204 rank = mn
205 ELSE IF( rksel.EQ.2 ) THEN
206 rank = ( 3*mn ) / 4
207 DO 10 j = rank + 1, mn
208 s( j ) = zero
209 10 CONTINUE
210 ELSE
211 CALL xerbla( 'DQRT15', 2 )
212 END IF
213*
214 IF( rank.GT.0 ) THEN
215*
216* Nontrivial case
217*
218 s( 1 ) = one
219 DO 30 j = 2, rank
220 20 CONTINUE
221 temp = dlarnd( 1, iseed )
222 IF( temp.GT.svmin ) THEN
223 s( j ) = abs( temp )
224 ELSE
225 GO TO 20
226 END IF
227 30 CONTINUE
228 CALL dlaord( 'Decreasing', rank, s, 1 )
229*
230* Generate 'rank' columns of a random orthogonal matrix in A
231*
232 CALL dlarnv( 2, iseed, m, work )
233 CALL dscal( m, one / dnrm2( m, work, 1 ), work, 1 )
234 CALL dlaset( 'Full', m, rank, zero, one, a, lda )
235 CALL dlarf( 'Left', m, rank, work, 1, two, a, lda,
236 $ work( m+1 ) )
237*
238* workspace used: m+mn
239*
240* Generate consistent rhs in the range space of A
241*
242 CALL dlarnv( 2, iseed, rank*nrhs, work )
243 CALL dgemm( 'No transpose', 'No transpose', m, nrhs, rank, one,
244 $ a, lda, work, rank, zero, b, ldb )
245*
246* work space used: <= mn *nrhs
247*
248* generate (unscaled) matrix A
249*
250 DO 40 j = 1, rank
251 CALL dscal( m, s( j ), a( 1, j ), 1 )
252 40 CONTINUE
253 IF( rank.LT.n )
254 $ CALL dlaset( 'Full', m, n-rank, zero, zero, a( 1, rank+1 ),
255 $ lda )
256 CALL dlaror( 'Right', 'No initialization', m, n, a, lda, iseed,
257 $ work, info )
258*
259 ELSE
260*
261* work space used 2*n+m
262*
263* Generate null matrix and rhs
264*
265 DO 50 j = 1, mn
266 s( j ) = zero
267 50 CONTINUE
268 CALL dlaset( 'Full', m, n, zero, zero, a, lda )
269 CALL dlaset( 'Full', m, nrhs, zero, zero, b, ldb )
270*
271 END IF
272*
273* Scale the matrix
274*
275 IF( scale.NE.1 ) THEN
276 norma = dlange( 'Max', m, n, a, lda, dummy )
277 IF( norma.NE.zero ) THEN
278 IF( scale.EQ.2 ) THEN
279*
280* matrix scaled up
281*
282 CALL dlascl( 'General', 0, 0, norma, bignum, m, n, a,
283 $ lda, info )
284 CALL dlascl( 'General', 0, 0, norma, bignum, mn, 1, s,
285 $ mn, info )
286 CALL dlascl( 'General', 0, 0, norma, bignum, m, nrhs, b,
287 $ ldb, info )
288 ELSE IF( scale.EQ.3 ) THEN
289*
290* matrix scaled down
291*
292 CALL dlascl( 'General', 0, 0, norma, smlnum, m, n, a,
293 $ lda, info )
294 CALL dlascl( 'General', 0, 0, norma, smlnum, mn, 1, s,
295 $ mn, info )
296 CALL dlascl( 'General', 0, 0, norma, smlnum, m, nrhs, b,
297 $ ldb, info )
298 ELSE
299 CALL xerbla( 'DQRT15', 1 )
300 RETURN
301 END IF
302 END IF
303 END IF
304*
305 norma = dasum( mn, s, 1 )
306 normb = dlange( 'One-norm', m, nrhs, b, ldb, dummy )
307*
308 RETURN
309*
310* End of DQRT15
311*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
dlaord
subroutine dlaord(job, n, x, incx)
DLAORD
Definition dlaord.f:73
dlarnd
double precision function dlarnd(idist, iseed)
DLARND
Definition dlarnd.f:73
dlaror
subroutine dlaror(side, init, m, n, a, lda, iseed, x, info)
DLAROR
Definition dlaror.f:146
dasum
double precision function dasum(n, dx, incx)
DASUM
Definition dasum.f:71
dgemm
subroutine dgemm(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
DGEMM
Definition dgemm.f:188
dlamch
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
dlange
double precision function dlange(norm, m, n, a, lda, work)
DLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition dlange.f:114
dlarf
subroutine dlarf(side, m, n, v, incv, tau, c, ldc, work)
DLARF applies an elementary reflector to a general rectangular matrix.
Definition dlarf.f:124
dlarnv
subroutine dlarnv(idist, iseed, n, x)
DLARNV returns a vector of random numbers from a uniform or normal distribution.
Definition dlarnv.f:97
dlascl
subroutine dlascl(type, kl, ku, cfrom, cto, m, n, a, lda, info)
DLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom.
Definition dlascl.f:143
dlaset
subroutine dlaset(uplo, m, n, alpha, beta, a, lda)
DLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition dlaset.f:110
dnrm2
real(wp) function dnrm2(n, x, incx)
DNRM2
Definition dnrm2.f90:89
dscal
subroutine dscal(n, da, dx, incx)
DSCAL
Definition dscal.f:79
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