LAPACK  3.8.0 LAPACK: Linear Algebra PACKage
zlarhs.f
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1 *> \brief \b ZLARHS
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 * Definition:
9 * ===========
10 *
11 * SUBROUTINE ZLARHS( PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS,
12 * A, LDA, X, LDX, B, LDB, ISEED, INFO )
13 *
14 * .. Scalar Arguments ..
15 * CHARACTER TRANS, UPLO, XTYPE
16 * CHARACTER*3 PATH
17 * INTEGER INFO, KL, KU, LDA, LDB, LDX, M, N, NRHS
18 * ..
19 * .. Array Arguments ..
20 * INTEGER ISEED( 4 )
21 * COMPLEX*16 A( LDA, * ), B( LDB, * ), X( LDX, * )
22 * ..
23 *
24 *
25 *> \par Purpose:
26 * =============
27 *>
28 *> \verbatim
29 *>
30 *> ZLARHS chooses a set of NRHS random solution vectors and sets
31 *> up the right hand sides for the linear system
32 *> op( A ) * X = B,
33 *> where op( A ) may be A, A**T (transpose of A), or A**H (conjugate
34 *> transpose of A).
35 *> \endverbatim
36 *
37 * Arguments:
38 * ==========
39 *
40 *> \param[in] PATH
41 *> \verbatim
42 *> PATH is CHARACTER*3
43 *> The type of the complex matrix A. PATH may be given in any
44 *> combination of upper and lower case. Valid paths include
45 *> xGE: General m x n matrix
46 *> xGB: General banded matrix
47 *> xPO: Hermitian positive definite, 2-D storage
48 *> xPP: Hermitian positive definite packed
49 *> xPB: Hermitian positive definite banded
50 *> xHE: Hermitian indefinite, 2-D storage
51 *> xHP: Hermitian indefinite packed
52 *> xHB: Hermitian indefinite banded
53 *> xSY: Symmetric indefinite, 2-D storage
54 *> xSP: Symmetric indefinite packed
55 *> xSB: Symmetric indefinite banded
56 *> xTR: Triangular
57 *> xTP: Triangular packed
58 *> xTB: Triangular banded
59 *> xQR: General m x n matrix
60 *> xLQ: General m x n matrix
61 *> xQL: General m x n matrix
62 *> xRQ: General m x n matrix
63 *> where the leading character indicates the precision.
64 *> \endverbatim
65 *>
66 *> \param[in] XTYPE
67 *> \verbatim
68 *> XTYPE is CHARACTER*1
69 *> Specifies how the exact solution X will be determined:
70 *> = 'N': New solution; generate a random X.
71 *> = 'C': Computed; use value of X on entry.
72 *> \endverbatim
73 *>
74 *> \param[in] UPLO
75 *> \verbatim
76 *> UPLO is CHARACTER*1
77 *> Used only if A is symmetric or triangular; specifies whether
78 *> the upper or lower triangular part of the matrix A is stored.
79 *> = 'U': Upper triangular
80 *> = 'L': Lower triangular
81 *> \endverbatim
82 *>
83 *> \param[in] TRANS
84 *> \verbatim
85 *> TRANS is CHARACTER*1
86 *> Used only if A is nonsymmetric; specifies the operation
87 *> applied to the matrix A.
88 *> = 'N': B := A * X
89 *> = 'T': B := A**T * X
90 *> = 'C': B := A**H * X
91 *> \endverbatim
92 *>
93 *> \param[in] M
94 *> \verbatim
95 *> M is INTEGER
96 *> The number of rows of the matrix A. M >= 0.
97 *> \endverbatim
98 *>
99 *> \param[in] N
100 *> \verbatim
101 *> N is INTEGER
102 *> The number of columns of the matrix A. N >= 0.
103 *> \endverbatim
104 *>
105 *> \param[in] KL
106 *> \verbatim
107 *> KL is INTEGER
108 *> Used only if A is a band matrix; specifies the number of
109 *> subdiagonals of A if A is a general band matrix or if A is
110 *> symmetric or triangular and UPLO = 'L'; specifies the number
111 *> of superdiagonals of A if A is symmetric or triangular and
112 *> UPLO = 'U'. 0 <= KL <= M-1.
113 *> \endverbatim
114 *>
115 *> \param[in] KU
116 *> \verbatim
117 *> KU is INTEGER
118 *> Used only if A is a general band matrix or if A is
119 *> triangular.
120 *>
121 *> If PATH = xGB, specifies the number of superdiagonals of A,
122 *> and 0 <= KU <= N-1.
123 *>
124 *> If PATH = xTR, xTP, or xTB, specifies whether or not the
125 *> matrix has unit diagonal:
126 *> = 1: matrix has non-unit diagonal (default)
127 *> = 2: matrix has unit diagonal
128 *> \endverbatim
129 *>
130 *> \param[in] NRHS
131 *> \verbatim
132 *> NRHS is INTEGER
133 *> The number of right hand side vectors in the system A*X = B.
134 *> \endverbatim
135 *>
136 *> \param[in] A
137 *> \verbatim
138 *> A is COMPLEX*16 array, dimension (LDA,N)
139 *> The test matrix whose type is given by PATH.
140 *> \endverbatim
141 *>
142 *> \param[in] LDA
143 *> \verbatim
144 *> LDA is INTEGER
145 *> The leading dimension of the array A.
146 *> If PATH = xGB, LDA >= KL+KU+1.
147 *> If PATH = xPB, xSB, xHB, or xTB, LDA >= KL+1.
148 *> Otherwise, LDA >= max(1,M).
149 *> \endverbatim
150 *>
151 *> \param[in,out] X
152 *> \verbatim
153 *> X is or output) COMPLEX*16 array, dimension (LDX,NRHS)
154 *> On entry, if XTYPE = 'C' (for 'Computed'), then X contains
155 *> the exact solution to the system of linear equations.
156 *> On exit, if XTYPE = 'N' (for 'New'), then X is initialized
157 *> with random values.
158 *> \endverbatim
159 *>
160 *> \param[in] LDX
161 *> \verbatim
162 *> LDX is INTEGER
163 *> The leading dimension of the array X. If TRANS = 'N',
164 *> LDX >= max(1,N); if TRANS = 'T', LDX >= max(1,M).
165 *> \endverbatim
166 *>
167 *> \param[out] B
168 *> \verbatim
169 *> B is COMPLEX*16 array, dimension (LDB,NRHS)
170 *> The right hand side vector(s) for the system of equations,
171 *> computed from B = op(A) * X, where op(A) is determined by
172 *> TRANS.
173 *> \endverbatim
174 *>
175 *> \param[in] LDB
176 *> \verbatim
177 *> LDB is INTEGER
178 *> The leading dimension of the array B. If TRANS = 'N',
179 *> LDB >= max(1,M); if TRANS = 'T', LDB >= max(1,N).
180 *> \endverbatim
181 *>
182 *> \param[in,out] ISEED
183 *> \verbatim
184 *> ISEED is INTEGER array, dimension (4)
185 *> The seed vector for the random number generator (used in
186 *> ZLATMS). Modified on exit.
187 *> \endverbatim
188 *>
189 *> \param[out] INFO
190 *> \verbatim
191 *> INFO is INTEGER
192 *> = 0: successful exit
193 *> < 0: if INFO = -i, the i-th argument had an illegal value
194 *> \endverbatim
195 *
196 * Authors:
197 * ========
198 *
199 *> \author Univ. of Tennessee
200 *> \author Univ. of California Berkeley
201 *> \author Univ. of Colorado Denver
202 *> \author NAG Ltd.
203 *
204 *> \date June 2017
205 *
206 *> \ingroup complex16_eig
207 *
208 * =====================================================================
209  SUBROUTINE zlarhs( PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS,
210  \$ A, LDA, X, LDX, B, LDB, ISEED, INFO )
211 *
212 * -- LAPACK test routine (version 3.7.1) --
213 * -- LAPACK is a software package provided by Univ. of Tennessee, --
214 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
215 * June 2017
216 *
217 * .. Scalar Arguments ..
218  CHARACTER TRANS, UPLO, XTYPE
219  CHARACTER*3 PATH
220  INTEGER INFO, KL, KU, LDA, LDB, LDX, M, N, NRHS
221 * ..
222 * .. Array Arguments ..
223  INTEGER ISEED( 4 )
224  COMPLEX*16 A( lda, * ), B( ldb, * ), X( ldx, * )
225 * ..
226 *
227 * =====================================================================
228 *
229 * .. Parameters ..
230  COMPLEX*16 ONE, ZERO
231  parameter( one = ( 1.0d+0, 0.0d+0 ),
232  \$ zero = ( 0.0d+0, 0.0d+0 ) )
233 * ..
234 * .. Local Scalars ..
235  LOGICAL BAND, GEN, NOTRAN, QRS, SYM, TRAN, TRI
236  CHARACTER C1, DIAG
237  CHARACTER*2 C2
238  INTEGER J, MB, NX
239 * ..
240 * .. External Functions ..
241  LOGICAL LSAME, LSAMEN
242  EXTERNAL lsame, lsamen
243 * ..
244 * .. External Subroutines ..
245  EXTERNAL xerbla, zgbmv, zgemm, zhbmv, zhemm, zhpmv,
247  \$ ztpmv, ztrmm
248 * ..
249 * .. Intrinsic Functions ..
250  INTRINSIC max
251 * ..
252 * .. Executable Statements ..
253 *
254 * Test the input parameters.
255 *
256  info = 0
257  c1 = path( 1: 1 )
258  c2 = path( 2: 3 )
259  tran = lsame( trans, 'T' ) .OR. lsame( trans, 'C' )
260  notran = .NOT.tran
261  gen = lsame( path( 2: 2 ), 'G' )
262  qrs = lsame( path( 2: 2 ), 'Q' ) .OR. lsame( path( 3: 3 ), 'Q' )
263  sym = lsame( path( 2: 2 ), 'P' ) .OR.
264  \$ lsame( path( 2: 2 ), 'S' ) .OR. lsame( path( 2: 2 ), 'H' )
265  tri = lsame( path( 2: 2 ), 'T' )
266  band = lsame( path( 3: 3 ), 'B' )
267  IF( .NOT.lsame( c1, 'Zomplex precision' ) ) THEN
268  info = -1
269  ELSE IF( .NOT.( lsame( xtype, 'N' ) .OR. lsame( xtype, 'C' ) ) )
270  \$ THEN
271  info = -2
272  ELSE IF( ( sym .OR. tri ) .AND. .NOT.
273  \$ ( lsame( uplo, 'U' ) .OR. lsame( uplo, 'L' ) ) ) THEN
274  info = -3
275  ELSE IF( ( gen .OR. qrs ) .AND. .NOT.
276  \$ ( tran .OR. lsame( trans, 'N' ) ) ) THEN
277  info = -4
278  ELSE IF( m.LT.0 ) THEN
279  info = -5
280  ELSE IF( n.LT.0 ) THEN
281  info = -6
282  ELSE IF( band .AND. kl.LT.0 ) THEN
283  info = -7
284  ELSE IF( band .AND. ku.LT.0 ) THEN
285  info = -8
286  ELSE IF( nrhs.LT.0 ) THEN
287  info = -9
288  ELSE IF( ( .NOT.band .AND. lda.LT.max( 1, m ) ) .OR.
289  \$ ( band .AND. ( sym .OR. tri ) .AND. lda.LT.kl+1 ) .OR.
290  \$ ( band .AND. gen .AND. lda.LT.kl+ku+1 ) ) THEN
291  info = -11
292  ELSE IF( ( notran .AND. ldx.LT.max( 1, n ) ) .OR.
293  \$ ( tran .AND. ldx.LT.max( 1, m ) ) ) THEN
294  info = -13
295  ELSE IF( ( notran .AND. ldb.LT.max( 1, m ) ) .OR.
296  \$ ( tran .AND. ldb.LT.max( 1, n ) ) ) THEN
297  info = -15
298  END IF
299  IF( info.NE.0 ) THEN
300  CALL xerbla( 'ZLARHS', -info )
301  RETURN
302  END IF
303 *
304 * Initialize X to NRHS random vectors unless XTYPE = 'C'.
305 *
306  IF( tran ) THEN
307  nx = m
308  mb = n
309  ELSE
310  nx = n
311  mb = m
312  END IF
313  IF( .NOT.lsame( xtype, 'C' ) ) THEN
314  DO 10 j = 1, nrhs
315  CALL zlarnv( 2, iseed, n, x( 1, j ) )
316  10 CONTINUE
317  END IF
318 *
319 * Multiply X by op( A ) using an appropriate
320 * matrix multiply routine.
321 *
322  IF( lsamen( 2, c2, 'GE' ) .OR. lsamen( 2, c2, 'QR' ) .OR.
323  \$ lsamen( 2, c2, 'LQ' ) .OR. lsamen( 2, c2, 'QL' ) .OR.
324  \$ lsamen( 2, c2, 'RQ' ) ) THEN
325 *
326 * General matrix
327 *
328  CALL zgemm( trans, 'N', mb, nrhs, nx, one, a, lda, x, ldx,
329  \$ zero, b, ldb )
330 *
331  ELSE IF( lsamen( 2, c2, 'PO' ) .OR. lsamen( 2, c2, 'HE' ) ) THEN
332 *
333 * Hermitian matrix, 2-D storage
334 *
335  CALL zhemm( 'Left', uplo, n, nrhs, one, a, lda, x, ldx, zero,
336  \$ b, ldb )
337 *
338  ELSE IF( lsamen( 2, c2, 'SY' ) ) THEN
339 *
340 * Symmetric matrix, 2-D storage
341 *
342  CALL zsymm( 'Left', uplo, n, nrhs, one, a, lda, x, ldx, zero,
343  \$ b, ldb )
344 *
345  ELSE IF( lsamen( 2, c2, 'GB' ) ) THEN
346 *
347 * General matrix, band storage
348 *
349  DO 20 j = 1, nrhs
350  CALL zgbmv( trans, m, n, kl, ku, one, a, lda, x( 1, j ), 1,
351  \$ zero, b( 1, j ), 1 )
352  20 CONTINUE
353 *
354  ELSE IF( lsamen( 2, c2, 'PB' ) .OR. lsamen( 2, c2, 'HB' ) ) THEN
355 *
356 * Hermitian matrix, band storage
357 *
358  DO 30 j = 1, nrhs
359  CALL zhbmv( uplo, n, kl, one, a, lda, x( 1, j ), 1, zero,
360  \$ b( 1, j ), 1 )
361  30 CONTINUE
362 *
363  ELSE IF( lsamen( 2, c2, 'SB' ) ) THEN
364 *
365 * Symmetric matrix, band storage
366 *
367  DO 40 j = 1, nrhs
368  CALL zsbmv( uplo, n, kl, one, a, lda, x( 1, j ), 1, zero,
369  \$ b( 1, j ), 1 )
370  40 CONTINUE
371 *
372  ELSE IF( lsamen( 2, c2, 'PP' ) .OR. lsamen( 2, c2, 'HP' ) ) THEN
373 *
374 * Hermitian matrix, packed storage
375 *
376  DO 50 j = 1, nrhs
377  CALL zhpmv( uplo, n, one, a, x( 1, j ), 1, zero, b( 1, j ),
378  \$ 1 )
379  50 CONTINUE
380 *
381  ELSE IF( lsamen( 2, c2, 'SP' ) ) THEN
382 *
383 * Symmetric matrix, packed storage
384 *
385  DO 60 j = 1, nrhs
386  CALL zspmv( uplo, n, one, a, x( 1, j ), 1, zero, b( 1, j ),
387  \$ 1 )
388  60 CONTINUE
389 *
390  ELSE IF( lsamen( 2, c2, 'TR' ) ) THEN
391 *
392 * Triangular matrix. Note that for triangular matrices,
393 * KU = 1 => non-unit triangular
394 * KU = 2 => unit triangular
395 *
396  CALL zlacpy( 'Full', n, nrhs, x, ldx, b, ldb )
397  IF( ku.EQ.2 ) THEN
398  diag = 'U'
399  ELSE
400  diag = 'N'
401  END IF
402  CALL ztrmm( 'Left', uplo, trans, diag, n, nrhs, one, a, lda, b,
403  \$ ldb )
404 *
405  ELSE IF( lsamen( 2, c2, 'TP' ) ) THEN
406 *
407 * Triangular matrix, packed storage
408 *
409  CALL zlacpy( 'Full', n, nrhs, x, ldx, b, ldb )
410  IF( ku.EQ.2 ) THEN
411  diag = 'U'
412  ELSE
413  diag = 'N'
414  END IF
415  DO 70 j = 1, nrhs
416  CALL ztpmv( uplo, trans, diag, n, a, b( 1, j ), 1 )
417  70 CONTINUE
418 *
419  ELSE IF( lsamen( 2, c2, 'TB' ) ) THEN
420 *
421 * Triangular matrix, banded storage
422 *
423  CALL zlacpy( 'Full', n, nrhs, x, ldx, b, ldb )
424  IF( ku.EQ.2 ) THEN
425  diag = 'U'
426  ELSE
427  diag = 'N'
428  END IF
429  DO 80 j = 1, nrhs
430  CALL ztbmv( uplo, trans, diag, n, kl, a, lda, b( 1, j ), 1 )
431  80 CONTINUE
432 *
433  ELSE
434 *
435 * If none of the above, set INFO = -1 and return
436 *
437  info = -1
438  CALL xerbla( 'ZLARHS', -info )
439  END IF
440 *
441  RETURN
442 *
443 * End of ZLARHS
444 *
445  END
subroutine zsymm(SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZSYMM
Definition: zsymm.f:191
subroutine zhpmv(UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY)
ZHPMV
Definition: zhpmv.f:151
subroutine zhemm(SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZHEMM
Definition: zhemm.f:193
subroutine zhbmv(UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
ZHBMV
Definition: zhbmv.f:189
subroutine zlarhs(PATH, XTYPE, UPLO, TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B, LDB, ISEED, INFO)
ZLARHS
Definition: zlarhs.f:211
subroutine zgbmv(TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
ZGBMV
Definition: zgbmv.f:189
subroutine zgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZGEMM
Definition: zgemm.f:189
subroutine ztpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
ZTPMV
Definition: ztpmv.f:144
subroutine zspmv(UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY)
ZSPMV computes a matrix-vector product for complex vectors using a complex symmetric packed matrix ...
Definition: zspmv.f:153
subroutine ztbmv(UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
ZTBMV
Definition: ztbmv.f:188
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine ztrmm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
ZTRMM
Definition: ztrmm.f:179
subroutine zlacpy(UPLO, M, N, A, LDA, B, LDB)
ZLACPY copies all or part of one two-dimensional array to another.
Definition: zlacpy.f:105
subroutine zlarnv(IDIST, ISEED, N, X)
ZLARNV returns a vector of random numbers from a uniform or normal distribution.
Definition: zlarnv.f:101
subroutine zsbmv(UPLO, N, K, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
ZSBMV
Definition: zsbmv.f:154