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 = -k, the k-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 November 2011
205*
206*> \ingroup complex16_lin
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 3.4.0) --
213*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
214*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
215*     November 2011
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,
246     $                   ZLACPY, ZLARNV, ZSBMV, ZSPMV, ZSYMM, ZTBMV,
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
446