1*> \brief \b DTRMV
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 DTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
12*
13*       .. Scalar Arguments ..
14*       INTEGER INCX,LDA,N
15*       CHARACTER DIAG,TRANS,UPLO
16*       ..
17*       .. Array Arguments ..
18*       DOUBLE PRECISION A(LDA,*),X(*)
19*       ..
20*
21*
22*> \par Purpose:
23*  =============
24*>
25*> \verbatim
26*>
27*> DTRMV  performs one of the matrix-vector operations
28*>
29*>    x := A*x,   or   x := A**T*x,
30*>
31*> where x is an n element vector and  A is an n by n unit, or non-unit,
32*> upper or lower triangular matrix.
33*> \endverbatim
34*
35*  Arguments:
36*  ==========
37*
38*> \param[in] UPLO
39*> \verbatim
40*>          UPLO is CHARACTER*1
41*>           On entry, UPLO specifies whether the matrix is an upper or
42*>           lower triangular matrix as follows:
43*>
44*>              UPLO = 'U' or 'u'   A is an upper triangular matrix.
45*>
46*>              UPLO = 'L' or 'l'   A is a lower triangular matrix.
47*> \endverbatim
48*>
49*> \param[in] TRANS
50*> \verbatim
51*>          TRANS is CHARACTER*1
52*>           On entry, TRANS specifies the operation to be performed as
53*>           follows:
54*>
55*>              TRANS = 'N' or 'n'   x := A*x.
56*>
57*>              TRANS = 'T' or 't'   x := A**T*x.
58*>
59*>              TRANS = 'C' or 'c'   x := A**T*x.
60*> \endverbatim
61*>
62*> \param[in] DIAG
63*> \verbatim
64*>          DIAG is CHARACTER*1
65*>           On entry, DIAG specifies whether or not A is unit
66*>           triangular as follows:
67*>
68*>              DIAG = 'U' or 'u'   A is assumed to be unit triangular.
69*>
70*>              DIAG = 'N' or 'n'   A is not assumed to be unit
71*>                                  triangular.
72*> \endverbatim
73*>
74*> \param[in] N
75*> \verbatim
76*>          N is INTEGER
77*>           On entry, N specifies the order of the matrix A.
78*>           N must be at least zero.
79*> \endverbatim
80*>
81*> \param[in] A
82*> \verbatim
83*>          A is DOUBLE PRECISION array of DIMENSION ( LDA, n ).
84*>           Before entry with  UPLO = 'U' or 'u', the leading n by n
85*>           upper triangular part of the array A must contain the upper
86*>           triangular matrix and the strictly lower triangular part of
87*>           A is not referenced.
88*>           Before entry with UPLO = 'L' or 'l', the leading n by n
89*>           lower triangular part of the array A must contain the lower
90*>           triangular matrix and the strictly upper triangular part of
91*>           A is not referenced.
92*>           Note that when  DIAG = 'U' or 'u', the diagonal elements of
93*>           A are not referenced either, but are assumed to be unity.
94*> \endverbatim
95*>
96*> \param[in] LDA
97*> \verbatim
98*>          LDA is INTEGER
99*>           On entry, LDA specifies the first dimension of A as declared
100*>           in the calling (sub) program. LDA must be at least
101*>           max( 1, n ).
102*> \endverbatim
103*>
104*> \param[in,out] X
105*> \verbatim
106*>          X is DOUBLE PRECISION array of dimension at least
107*>           ( 1 + ( n - 1 )*abs( INCX ) ).
108*>           Before entry, the incremented array X must contain the n
109*>           element vector x. On exit, X is overwritten with the
110*>           tranformed vector x.
111*> \endverbatim
112*>
113*> \param[in] INCX
114*> \verbatim
115*>          INCX is INTEGER
116*>           On entry, INCX specifies the increment for the elements of
117*>           X. INCX must not be zero.
118*> \endverbatim
119*
120*  Authors:
121*  ========
122*
123*> \author Univ. of Tennessee
124*> \author Univ. of California Berkeley
125*> \author Univ. of Colorado Denver
126*> \author NAG Ltd.
127*
128*> \date November 2011
129*
130*> \ingroup double_blas_level2
131*
132*> \par Further Details:
133*  =====================
134*>
135*> \verbatim
136*>
137*>  Level 2 Blas routine.
138*>  The vector and matrix arguments are not referenced when N = 0, or M = 0
139*>
140*>  -- Written on 22-October-1986.
141*>     Jack Dongarra, Argonne National Lab.
142*>     Jeremy Du Croz, Nag Central Office.
143*>     Sven Hammarling, Nag Central Office.
144*>     Richard Hanson, Sandia National Labs.
145*> \endverbatim
146*>
147*  =====================================================================
148      SUBROUTINE DTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
149*
150*  -- Reference BLAS level2 routine (version 3.4.0) --
151*  -- Reference BLAS is a software package provided by Univ. of Tennessee,    --
152*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
153*     November 2011
154*
155*     .. Scalar Arguments ..
156      INTEGER INCX,LDA,N
157      CHARACTER DIAG,TRANS,UPLO
158*     ..
159*     .. Array Arguments ..
160      DOUBLE PRECISION A(LDA,*),X(*)
161*     ..
162*
163*  =====================================================================
164*
165*     .. Parameters ..
166      DOUBLE PRECISION ZERO
167      PARAMETER (ZERO=0.0D+0)
168*     ..
169*     .. Local Scalars ..
170      DOUBLE PRECISION TEMP
171      INTEGER I,INFO,IX,J,JX,KX
172      LOGICAL NOUNIT
173*     ..
174*     .. External Functions ..
175      LOGICAL LSAME
176      EXTERNAL LSAME
177*     ..
178*     .. External Subroutines ..
179      EXTERNAL XERBLA
180*     ..
181*     .. Intrinsic Functions ..
182      INTRINSIC MAX
183*     ..
184*
185*     Test the input parameters.
186*
187      INFO = 0
188      IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
189          INFO = 1
190      ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
191     +         .NOT.LSAME(TRANS,'C')) THEN
192          INFO = 2
193      ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
194          INFO = 3
195      ELSE IF (N.LT.0) THEN
196          INFO = 4
197      ELSE IF (LDA.LT.MAX(1,N)) THEN
198          INFO = 6
199      ELSE IF (INCX.EQ.0) THEN
200          INFO = 8
201      END IF
202      IF (INFO.NE.0) THEN
203          CALL XERBLA('DTRMV ',INFO)
204          RETURN
205      END IF
206*
207*     Quick return if possible.
208*
209      IF (N.EQ.0) RETURN
210*
211      NOUNIT = LSAME(DIAG,'N')
212*
213*     Set up the start point in X if the increment is not unity. This
214*     will be  ( N - 1 )*INCX  too small for descending loops.
215*
216      IF (INCX.LE.0) THEN
217          KX = 1 - (N-1)*INCX
218      ELSE IF (INCX.NE.1) THEN
219          KX = 1
220      END IF
221*
222*     Start the operations. In this version the elements of A are
223*     accessed sequentially with one pass through A.
224*
225      IF (LSAME(TRANS,'N')) THEN
226*
227*        Form  x := A*x.
228*
229          IF (LSAME(UPLO,'U')) THEN
230              IF (INCX.EQ.1) THEN
231                  DO 20 J = 1,N
232                      IF (X(J).NE.ZERO) THEN
233                          TEMP = X(J)
234                          DO 10 I = 1,J - 1
235                              X(I) = X(I) + TEMP*A(I,J)
236   10                     CONTINUE
237                          IF (NOUNIT) X(J) = X(J)*A(J,J)
238                      END IF
239   20             CONTINUE
240              ELSE
241                  JX = KX
242                  DO 40 J = 1,N
243                      IF (X(JX).NE.ZERO) THEN
244                          TEMP = X(JX)
245                          IX = KX
246                          DO 30 I = 1,J - 1
247                              X(IX) = X(IX) + TEMP*A(I,J)
248                              IX = IX + INCX
249   30                     CONTINUE
250                          IF (NOUNIT) X(JX) = X(JX)*A(J,J)
251                      END IF
252                      JX = JX + INCX
253   40             CONTINUE
254              END IF
255          ELSE
256              IF (INCX.EQ.1) THEN
257                  DO 60 J = N,1,-1
258                      IF (X(J).NE.ZERO) THEN
259                          TEMP = X(J)
260                          DO 50 I = N,J + 1,-1
261                              X(I) = X(I) + TEMP*A(I,J)
262   50                     CONTINUE
263                          IF (NOUNIT) X(J) = X(J)*A(J,J)
264                      END IF
265   60             CONTINUE
266              ELSE
267                  KX = KX + (N-1)*INCX
268                  JX = KX
269                  DO 80 J = N,1,-1
270                      IF (X(JX).NE.ZERO) THEN
271                          TEMP = X(JX)
272                          IX = KX
273                          DO 70 I = N,J + 1,-1
274                              X(IX) = X(IX) + TEMP*A(I,J)
275                              IX = IX - INCX
276   70                     CONTINUE
277                          IF (NOUNIT) X(JX) = X(JX)*A(J,J)
278                      END IF
279                      JX = JX - INCX
280   80             CONTINUE
281              END IF
282          END IF
283      ELSE
284*
285*        Form  x := A**T*x.
286*
287          IF (LSAME(UPLO,'U')) THEN
288              IF (INCX.EQ.1) THEN
289                  DO 100 J = N,1,-1
290                      TEMP = X(J)
291                      IF (NOUNIT) TEMP = TEMP*A(J,J)
292                      DO 90 I = J - 1,1,-1
293                          TEMP = TEMP + A(I,J)*X(I)
294   90                 CONTINUE
295                      X(J) = TEMP
296  100             CONTINUE
297              ELSE
298                  JX = KX + (N-1)*INCX
299                  DO 120 J = N,1,-1
300                      TEMP = X(JX)
301                      IX = JX
302                      IF (NOUNIT) TEMP = TEMP*A(J,J)
303                      DO 110 I = J - 1,1,-1
304                          IX = IX - INCX
305                          TEMP = TEMP + A(I,J)*X(IX)
306  110                 CONTINUE
307                      X(JX) = TEMP
308                      JX = JX - INCX
309  120             CONTINUE
310              END IF
311          ELSE
312              IF (INCX.EQ.1) THEN
313                  DO 140 J = 1,N
314                      TEMP = X(J)
315                      IF (NOUNIT) TEMP = TEMP*A(J,J)
316                      DO 130 I = J + 1,N
317                          TEMP = TEMP + A(I,J)*X(I)
318  130                 CONTINUE
319                      X(J) = TEMP
320  140             CONTINUE
321              ELSE
322                  JX = KX
323                  DO 160 J = 1,N
324                      TEMP = X(JX)
325                      IX = JX
326                      IF (NOUNIT) TEMP = TEMP*A(J,J)
327                      DO 150 I = J + 1,N
328                          IX = IX + INCX
329                          TEMP = TEMP + A(I,J)*X(IX)
330  150                 CONTINUE
331                      X(JX) = TEMP
332                      JX = JX + INCX
333  160             CONTINUE
334              END IF
335          END IF
336      END IF
337*
338      RETURN
339*
340*     End of DTRMV .
341*
342      END
343