LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ 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)```

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 dlabad, dlaord, dlascl, xerbla, zdscal, zgemm,
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  CALL dlabad( smlnum, bignum )
203  eps = dlamch( 'Epsilon' )
204  smlnum = ( smlnum / eps ) / eps
205  bignum = one / smlnum
206 *
207 * Determine rank and (unscaled) singular values
208 *
209  IF( rksel.EQ.1 ) THEN
210  rank = mn
211  ELSE IF( rksel.EQ.2 ) THEN
212  rank = ( 3*mn ) / 4
213  DO 10 j = rank + 1, mn
214  s( j ) = zero
215  10 CONTINUE
216  ELSE
217  CALL xerbla( 'ZQRT15', 2 )
218  END IF
219 *
220  IF( rank.GT.0 ) THEN
221 *
222 * Nontrivial case
223 *
224  s( 1 ) = one
225  DO 30 j = 2, rank
226  20 CONTINUE
227  temp = dlarnd( 1, iseed )
228  IF( temp.GT.svmin ) THEN
229  s( j ) = abs( temp )
230  ELSE
231  GO TO 20
232  END IF
233  30 CONTINUE
234  CALL dlaord( 'Decreasing', rank, s, 1 )
235 *
236 * Generate 'rank' columns of a random orthogonal matrix in A
237 *
238  CALL zlarnv( 2, iseed, m, work )
239  CALL zdscal( m, one / dznrm2( m, work, 1 ), work, 1 )
240  CALL zlaset( 'Full', m, rank, czero, cone, a, lda )
241  CALL zlarf( 'Left', m, rank, work, 1, dcmplx( two ), a, lda,
242  \$ work( m+1 ) )
243 *
244 * workspace used: m+mn
245 *
246 * Generate consistent rhs in the range space of A
247 *
248  CALL zlarnv( 2, iseed, rank*nrhs, work )
249  CALL zgemm( 'No transpose', 'No transpose', m, nrhs, rank,
250  \$ cone, a, lda, work, rank, czero, b, ldb )
251 *
252 * work space used: <= mn *nrhs
253 *
254 * generate (unscaled) matrix A
255 *
256  DO 40 j = 1, rank
257  CALL zdscal( m, s( j ), a( 1, j ), 1 )
258  40 CONTINUE
259  IF( rank.LT.n )
260  \$ CALL zlaset( 'Full', m, n-rank, czero, czero,
261  \$ a( 1, rank+1 ), lda )
262  CALL zlaror( 'Right', 'No initialization', m, n, a, lda, iseed,
263  \$ work, info )
264 *
265  ELSE
266 *
267 * work space used 2*n+m
268 *
269 * Generate null matrix and rhs
270 *
271  DO 50 j = 1, mn
272  s( j ) = zero
273  50 CONTINUE
274  CALL zlaset( 'Full', m, n, czero, czero, a, lda )
275  CALL zlaset( 'Full', m, nrhs, czero, czero, b, ldb )
276 *
277  END IF
278 *
279 * Scale the matrix
280 *
281  IF( scale.NE.1 ) THEN
282  norma = zlange( 'Max', m, n, a, lda, dummy )
283  IF( norma.NE.zero ) THEN
284  IF( scale.EQ.2 ) THEN
285 *
286 * matrix scaled up
287 *
288  CALL zlascl( 'General', 0, 0, norma, bignum, m, n, a,
289  \$ lda, info )
290  CALL dlascl( 'General', 0, 0, norma, bignum, mn, 1, s,
291  \$ mn, info )
292  CALL zlascl( 'General', 0, 0, norma, bignum, m, nrhs, b,
293  \$ ldb, info )
294  ELSE IF( scale.EQ.3 ) THEN
295 *
296 * matrix scaled down
297 *
298  CALL zlascl( 'General', 0, 0, norma, smlnum, m, n, a,
299  \$ lda, info )
300  CALL dlascl( 'General', 0, 0, norma, smlnum, mn, 1, s,
301  \$ mn, info )
302  CALL zlascl( 'General', 0, 0, norma, smlnum, m, nrhs, b,
303  \$ ldb, info )
304  ELSE
305  CALL xerbla( 'ZQRT15', 1 )
306  RETURN
307  END IF
308  END IF
309  END IF
310 *
311  norma = dasum( mn, s, 1 )
312  normb = zlange( 'One-norm', m, nrhs, b, ldb, dummy )
313 *
314  RETURN
315 *
316 * End of ZQRT15
317 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
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
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine zdscal(N, DA, ZX, INCX)
ZDSCAL
Definition: zdscal.f:78
subroutine zgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZGEMM
Definition: zgemm.f:187
subroutine zlaror(SIDE, INIT, M, N, A, LDA, ISEED, X, INFO)
ZLAROR
Definition: zlaror.f:158
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
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
subroutine zlarnv(IDIST, ISEED, N, X)
ZLARNV returns a vector of random numbers from a uniform or normal distribution.
Definition: zlarnv.f:99
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
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
double precision function dasum(N, DX, INCX)
DASUM
Definition: dasum.f:71
subroutine dlaord(JOB, N, X, INCX)
DLAORD
Definition: dlaord.f:73
double precision function dlarnd(IDIST, ISEED)
DLARND
Definition: dlarnd.f:73
real(wp) function dznrm2(n, x, incx)
DZNRM2
Definition: dznrm2.f90:90
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