LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ zqrt15()

subroutine zqrt15 ( integer  scale,
integer  rksel,
integer  m,
integer  n,
integer  nrhs,
complex*16, dimension( lda, * )  a,
integer  lda,
complex*16, dimension( ldb, * )  b,
integer  ldb,
double precision, dimension( * )  s,
integer  rank,
double precision  norma,
double precision  normb,
integer, dimension( 4 )  iseed,
complex*16, dimension( lwork )  work,
integer  lwork 
)

ZQRT15

Purpose:
 ZQRT15 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 COMPLEX*16 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 COMPLEX*16 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 norm of A.
[out]NORMB
          NORMB is DOUBLE PRECISION
          one-norm norm of B.
[in,out]ISEED
          ISEED is integer array, dimension (4)
          seed for random number generator.
[out]WORK
          WORK is COMPLEX*16 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 147 of file zqrt15.f.

149*
150* -- LAPACK test routine --
151* -- LAPACK is a software package provided by Univ. of Tennessee, --
152* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
153*
154* .. Scalar Arguments ..
155 INTEGER LDA, LDB, LWORK, M, N, NRHS, RANK, RKSEL, SCALE
156 DOUBLE PRECISION NORMA, NORMB
157* ..
158* .. Array Arguments ..
159 INTEGER ISEED( 4 )
160 DOUBLE PRECISION S( * )
161 COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( LWORK )
162* ..
163*
164* =====================================================================
165*
166* .. Parameters ..
167 DOUBLE PRECISION ZERO, ONE, TWO, SVMIN
168 parameter( zero = 0.0d+0, one = 1.0d+0, two = 2.0d+0,
169 $ svmin = 0.1d+0 )
170 COMPLEX*16 CZERO, CONE
171 parameter( czero = ( 0.0d+0, 0.0d+0 ),
172 $ cone = ( 1.0d+0, 0.0d+0 ) )
173* ..
174* .. Local Scalars ..
175 INTEGER INFO, J, MN
176 DOUBLE PRECISION BIGNUM, EPS, SMLNUM, TEMP
177* ..
178* .. Local Arrays ..
179 DOUBLE PRECISION DUMMY( 1 )
180* ..
181* .. External Functions ..
182 DOUBLE PRECISION DASUM, DLAMCH, DLARND, DZNRM2, ZLANGE
183 EXTERNAL dasum, dlamch, dlarnd, dznrm2, zlange
184* ..
185* .. External Subroutines ..
186 EXTERNAL dlaord, dlascl, xerbla, zdscal, zgemm, zlarf,
187 $ zlarnv, zlaror, zlascl, zlaset
188* ..
189* .. Intrinsic Functions ..
190 INTRINSIC abs, dcmplx, max, min
191* ..
192* .. Executable Statements ..
193*
194 mn = min( m, n )
195 IF( lwork.LT.max( m+mn, mn*nrhs, 2*n+m ) ) THEN
196 CALL xerbla( 'ZQRT15', 16 )
197 RETURN
198 END IF
199*
200 smlnum = dlamch( 'Safe minimum' )
201 bignum = one / smlnum
202 eps = dlamch( 'Epsilon' )
203 smlnum = ( smlnum / eps ) / eps
204 bignum = one / smlnum
205*
206* Determine rank and (unscaled) singular values
207*
208 IF( rksel.EQ.1 ) THEN
209 rank = mn
210 ELSE IF( rksel.EQ.2 ) THEN
211 rank = ( 3*mn ) / 4
212 DO 10 j = rank + 1, mn
213 s( j ) = zero
214 10 CONTINUE
215 ELSE
216 CALL xerbla( 'ZQRT15', 2 )
217 END IF
218*
219 IF( rank.GT.0 ) THEN
220*
221* Nontrivial case
222*
223 s( 1 ) = one
224 DO 30 j = 2, rank
225 20 CONTINUE
226 temp = dlarnd( 1, iseed )
227 IF( temp.GT.svmin ) THEN
228 s( j ) = abs( temp )
229 ELSE
230 GO TO 20
231 END IF
232 30 CONTINUE
233 CALL dlaord( 'Decreasing', rank, s, 1 )
234*
235* Generate 'rank' columns of a random orthogonal matrix in A
236*
237 CALL zlarnv( 2, iseed, m, work )
238 CALL zdscal( m, one / dznrm2( m, work, 1 ), work, 1 )
239 CALL zlaset( 'Full', m, rank, czero, cone, a, lda )
240 CALL zlarf( 'Left', m, rank, work, 1, dcmplx( two ), a, lda,
241 $ work( m+1 ) )
242*
243* workspace used: m+mn
244*
245* Generate consistent rhs in the range space of A
246*
247 CALL zlarnv( 2, iseed, rank*nrhs, work )
248 CALL zgemm( 'No transpose', 'No transpose', m, nrhs, rank,
249 $ cone, a, lda, work, rank, czero, b, ldb )
250*
251* work space used: <= mn *nrhs
252*
253* generate (unscaled) matrix A
254*
255 DO 40 j = 1, rank
256 CALL zdscal( m, s( j ), a( 1, j ), 1 )
257 40 CONTINUE
258 IF( rank.LT.n )
259 $ CALL zlaset( 'Full', m, n-rank, czero, czero,
260 $ a( 1, rank+1 ), lda )
261 CALL zlaror( 'Right', 'No initialization', m, n, a, lda, iseed,
262 $ work, info )
263*
264 ELSE
265*
266* work space used 2*n+m
267*
268* Generate null matrix and rhs
269*
270 DO 50 j = 1, mn
271 s( j ) = zero
272 50 CONTINUE
273 CALL zlaset( 'Full', m, n, czero, czero, a, lda )
274 CALL zlaset( 'Full', m, nrhs, czero, czero, b, ldb )
275*
276 END IF
277*
278* Scale the matrix
279*
280 IF( scale.NE.1 ) THEN
281 norma = zlange( 'Max', m, n, a, lda, dummy )
282 IF( norma.NE.zero ) THEN
283 IF( scale.EQ.2 ) THEN
284*
285* matrix scaled up
286*
287 CALL zlascl( 'General', 0, 0, norma, bignum, m, n, a,
288 $ lda, info )
289 CALL dlascl( 'General', 0, 0, norma, bignum, mn, 1, s,
290 $ mn, info )
291 CALL zlascl( 'General', 0, 0, norma, bignum, m, nrhs, b,
292 $ ldb, info )
293 ELSE IF( scale.EQ.3 ) THEN
294*
295* matrix scaled down
296*
297 CALL zlascl( 'General', 0, 0, norma, smlnum, m, n, a,
298 $ lda, info )
299 CALL dlascl( 'General', 0, 0, norma, smlnum, mn, 1, s,
300 $ mn, info )
301 CALL zlascl( 'General', 0, 0, norma, smlnum, m, nrhs, b,
302 $ ldb, info )
303 ELSE
304 CALL xerbla( 'ZQRT15', 1 )
305 RETURN
306 END IF
307 END IF
308 END IF
309*
310 norma = dasum( mn, s, 1 )
311 normb = zlange( 'One-norm', m, nrhs, b, ldb, dummy )
312*
313 RETURN
314*
315* End of ZQRT15
316*
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
dasum
double precision function dasum(n, dx, incx)
DASUM
Definition dasum.f:71
zgemm
subroutine zgemm(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
ZGEMM
Definition zgemm.f:188
dlamch
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
zlange
double precision function zlange(norm, m, n, a, lda, work)
ZLANGE returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition zlange.f:115
zlarf
subroutine zlarf(side, m, n, v, incv, tau, c, ldc, work)
ZLARF applies an elementary reflector to a general rectangular matrix.
Definition zlarf.f:128
zlarnv
subroutine zlarnv(idist, iseed, n, x)
ZLARNV returns a vector of random numbers from a uniform or normal distribution.
Definition zlarnv.f:99
zlascl
subroutine zlascl(type, kl, ku, cfrom, cto, m, n, a, lda, info)
ZLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom.
Definition zlascl.f:143
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
zlaset
subroutine zlaset(uplo, m, n, alpha, beta, a, lda)
ZLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition zlaset.f:106
dznrm2
real(wp) function dznrm2(n, x, incx)
DZNRM2
Definition dznrm2.f90:90
zdscal
subroutine zdscal(n, da, zx, incx)
ZDSCAL
Definition zdscal.f:78
zlaror
subroutine zlaror(side, init, m, n, a, lda, iseed, x, info)
ZLAROR
Definition zlaror.f:158
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