 LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ 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)```
Date
December 2016

Definition at line 150 of file dqrt15.f.

150 *
151 * -- LAPACK test routine (version 3.7.0) --
152 * -- LAPACK is a software package provided by Univ. of Tennessee, --
153 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
154 * December 2016
155 *
156 * .. Scalar Arguments ..
157  INTEGER lda, ldb, lwork, m, n, nrhs, rank, rksel, scale
158  DOUBLE PRECISION norma, normb
159 * ..
160 * .. Array Arguments ..
161  INTEGER iseed( 4 )
162  DOUBLE PRECISION a( lda, * ), b( ldb, * ), s( * ), work( lwork )
163 * ..
164 *
165 * =====================================================================
166 *
167 * .. Parameters ..
168  DOUBLE PRECISION zero, one, two, svmin
169  parameter( zero = 0.0d0, one = 1.0d0, two = 2.0d0,
170  \$ svmin = 0.1d0 )
171 * ..
172 * .. Local Scalars ..
173  INTEGER info, j, mn
174  DOUBLE PRECISION bignum, eps, smlnum, temp
175 * ..
176 * .. Local Arrays ..
177  DOUBLE PRECISION dummy( 1 )
178 * ..
179 * .. External Functions ..
180  DOUBLE PRECISION dasum, dlamch, dlange, dlarnd, dnrm2
181  EXTERNAL dasum, dlamch, dlange, dlarnd, dnrm2
182 * ..
183 * .. External Subroutines ..
184  EXTERNAL dgemm, dlaord, dlarf, dlarnv, dlaror, dlascl,
185  \$ dlaset, dscal, xerbla
186 * ..
187 * .. Intrinsic Functions ..
188  INTRINSIC abs, max, min
189 * ..
190 * .. Executable Statements ..
191 *
192  mn = min( m, n )
193  IF( lwork.LT.max( m+mn, mn*nrhs, 2*n+m ) ) THEN
194  CALL xerbla( 'DQRT15', 16 )
195  RETURN
196  END IF
197 *
198  smlnum = dlamch( 'Safe minimum' )
199  bignum = one / smlnum
200  eps = dlamch( 'Epsilon' )
201  smlnum = ( smlnum / eps ) / eps
202  bignum = one / smlnum
203 *
204 * Determine rank and (unscaled) singular values
205 *
206  IF( rksel.EQ.1 ) THEN
207  rank = mn
208  ELSE IF( rksel.EQ.2 ) THEN
209  rank = ( 3*mn ) / 4
210  DO 10 j = rank + 1, mn
211  s( j ) = zero
212  10 CONTINUE
213  ELSE
214  CALL xerbla( 'DQRT15', 2 )
215  END IF
216 *
217  IF( rank.GT.0 ) THEN
218 *
219 * Nontrivial case
220 *
221  s( 1 ) = one
222  DO 30 j = 2, rank
223  20 CONTINUE
224  temp = dlarnd( 1, iseed )
225  IF( temp.GT.svmin ) THEN
226  s( j ) = abs( temp )
227  ELSE
228  GO TO 20
229  END IF
230  30 CONTINUE
231  CALL dlaord( 'Decreasing', rank, s, 1 )
232 *
233 * Generate 'rank' columns of a random orthogonal matrix in A
234 *
235  CALL dlarnv( 2, iseed, m, work )
236  CALL dscal( m, one / dnrm2( m, work, 1 ), work, 1 )
237  CALL dlaset( 'Full', m, rank, zero, one, a, lda )
238  CALL dlarf( 'Left', m, rank, work, 1, two, a, lda,
239  \$ work( m+1 ) )
240 *
241 * workspace used: m+mn
242 *
243 * Generate consistent rhs in the range space of A
244 *
245  CALL dlarnv( 2, iseed, rank*nrhs, work )
246  CALL dgemm( 'No transpose', 'No transpose', m, nrhs, rank, one,
247  \$ a, lda, work, rank, zero, b, ldb )
248 *
249 * work space used: <= mn *nrhs
250 *
251 * generate (unscaled) matrix A
252 *
253  DO 40 j = 1, rank
254  CALL dscal( m, s( j ), a( 1, j ), 1 )
255  40 CONTINUE
256  IF( rank.LT.n )
257  \$ CALL dlaset( 'Full', m, n-rank, zero, zero, a( 1, rank+1 ),
258  \$ lda )
259  CALL dlaror( 'Right', 'No initialization', m, n, a, lda, iseed,
260  \$ work, info )
261 *
262  ELSE
263 *
264 * work space used 2*n+m
265 *
266 * Generate null matrix and rhs
267 *
268  DO 50 j = 1, mn
269  s( j ) = zero
270  50 CONTINUE
271  CALL dlaset( 'Full', m, n, zero, zero, a, lda )
272  CALL dlaset( 'Full', m, nrhs, zero, zero, b, ldb )
273 *
274  END IF
275 *
276 * Scale the matrix
277 *
278  IF( scale.NE.1 ) THEN
279  norma = dlange( 'Max', m, n, a, lda, dummy )
280  IF( norma.NE.zero ) THEN
281  IF( scale.EQ.2 ) THEN
282 *
283 * matrix scaled up
284 *
285  CALL dlascl( 'General', 0, 0, norma, bignum, m, n, a,
286  \$ lda, info )
287  CALL dlascl( 'General', 0, 0, norma, bignum, mn, 1, s,
288  \$ mn, info )
289  CALL dlascl( 'General', 0, 0, norma, bignum, m, nrhs, b,
290  \$ ldb, info )
291  ELSE IF( scale.EQ.3 ) THEN
292 *
293 * matrix scaled down
294 *
295  CALL dlascl( 'General', 0, 0, norma, smlnum, m, n, a,
296  \$ lda, info )
297  CALL dlascl( 'General', 0, 0, norma, smlnum, mn, 1, s,
298  \$ mn, info )
299  CALL dlascl( 'General', 0, 0, norma, smlnum, m, nrhs, b,
300  \$ ldb, info )
301  ELSE
302  CALL xerbla( 'DQRT15', 1 )
303  RETURN
304  END IF
305  END IF
306  END IF
307 *
308  norma = dasum( mn, s, 1 )
309  normb = dlange( 'One-norm', m, nrhs, b, ldb, dummy )
310 *
311  RETURN
312 *
313 * End of DQRT15
314 *
double precision function dnrm2(N, X, INCX)
DNRM2
Definition: dnrm2.f:76
double precision function dlarnd(IDIST, ISEED)
DLARND
Definition: dlarnd.f:75
subroutine dgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DGEMM
Definition: dgemm.f:189
double precision function dasum(N, DX, INCX)
DASUM
Definition: dasum.f:73
subroutine dscal(N, DA, DX, INCX)
DSCAL
Definition: dscal.f:81
subroutine dlaord(JOB, N, X, INCX)
DLAORD
Definition: dlaord.f:75
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:116
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
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:112
subroutine dlarnv(IDIST, ISEED, N, X)
DLARNV returns a vector of random numbers from a uniform or normal distribution.
Definition: dlarnv.f:99
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:65
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:145
subroutine dlaror(SIDE, INIT, M, N, A, LDA, ISEED, X, INFO)
DLAROR
Definition: dlaror.f:148
subroutine dlarf(SIDE, M, N, V, INCV, TAU, C, LDC, WORK)
DLARF applies an elementary reflector to a general rectangular matrix.
Definition: dlarf.f:126
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