trunk/blas/dgemv.f


      SUBROUTINE DGEMV ( TRANS, M, N, ALPHA, A, LDA, X, INCX,
*
************************************************************************
*
*     File of the DOUBLE PRECISION  Level-2 BLAS.
*     ===========================================
*
*     SUBROUTINE DGEMV ( TRANS, M, N, ALPHA, A, LDA, X, INCX,
*    $                   BETA, Y, INCY )
*
*     SUBROUTINE DGBMV ( TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX,
*    $                   BETA, Y, INCY )
*
*     SUBROUTINE DSYMV ( UPLO, N, ALPHA, A, LDA, X, INCX,
*    $                   BETA, Y, INCY )
*
*     SUBROUTINE DSBMV ( UPLO, N, K, ALPHA, A, LDA, X, INCX,
*    $                   BETA, Y, INCY )
*
*     SUBROUTINE DSPMV ( UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY )
*
*     SUBROUTINE DTRMV ( UPLO, TRANS, DIAG, N, A, LDA, X, INCX )
*
*     SUBROUTINE DTBMV ( UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX )
*
*     SUBROUTINE DTPMV ( UPLO, TRANS, DIAG, N, AP, X, INCX )
*
*     SUBROUTINE DTRSV ( UPLO, TRANS, DIAG, N, A, LDA, X, INCX )
*
*     SUBROUTINE DTBSV ( UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX )
*
*     SUBROUTINE DTPSV ( UPLO, TRANS, DIAG, N, AP, X, INCX )
*
*     SUBROUTINE DGER  ( M, N, ALPHA, X, INCX, Y, INCY, A, LDA )
*
*     SUBROUTINE DSYR  ( UPLO, N, ALPHA, X, INCX, A, LDA )
*
*     SUBROUTINE DSPR  ( UPLO, N, ALPHA, X, INCX, AP )
*
*     SUBROUTINE DSYR2 ( UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA )
*
*     SUBROUTINE DSPR2 ( UPLO, N, ALPHA, X, INCX, Y, INCY, AP )
*
*     See:
*
*        Dongarra J. J., Du Croz J. J., Hammarling S.  and Hanson R. J..
*        An  extended  set of Fortran  Basic Linear Algebra Subprograms.
*
*        Technical  Memoranda  Nos. 41 (revision 3) and 81,  Mathematics
*        and  Computer Science  Division,  Argonne  National Laboratory,
*        9700 South Cass Avenue, Argonne, Illinois 60439, US.
*
*        Or
*
*        NAG  Technical Reports TR3/87 and TR4/87,  Numerical Algorithms
*        Group  Ltd.,  NAG  Central  Office,  256  Banbury  Road, Oxford
*        OX2 7DE, UK,  and  Numerical Algorithms Group Inc.,  1101  31st
*        Street,  Suite 100,  Downers Grove,  Illinois 60515-1263,  USA.
*
************************************************************************
*
     $                   BETA, Y, INCY )
*     .. Scalar Arguments ..
      DOUBLE PRECISION   ALPHA, BETA
      INTEGER            INCX, INCY, LDA, M, N
      CHARACTER*1        TRANS
*     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * ), X( * ), Y( * )
*     ..
*
*  Purpose
*  =======
*
*  DGEMV  performs one of the matrix-vector operations
*
*     y := alpha*A*x + beta*y,   or   y := alpha*A'*x + beta*y,
*
*  where alpha and beta are scalars, x and y are vectors and A is an
*  m by n matrix.
*
*  Parameters
*  ==========
*
*  TRANS  - CHARACTER*1.
*           On entry, TRANS specifies the operation to be performed as
*           follows:
*
*              TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.
*
*              TRANS = 'T' or 't'   y := alpha*A'*x + beta*y.
*
*              TRANS = 'C' or 'c'   y := alpha*A'*x + beta*y.
*
*           Unchanged on exit.
*
*  M      - INTEGER.
*           On entry, M specifies the number of rows of the matrix A.
*           M must be at least zero.
*           Unchanged on exit.
*
*  N      - INTEGER.
*           On entry, N specifies the number of columns of the matrix A.
*           N must be at least zero.
*           Unchanged on exit.
*
*  ALPHA  - DOUBLE PRECISION.
*           On entry, ALPHA specifies the scalar alpha.
*           Unchanged on exit.
*
*  A      - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
*           Before entry, the leading m by n part of the array A must
*           contain the matrix of coefficients.
*           Unchanged on exit.
*
*  LDA    - INTEGER.
*           On entry, LDA specifies the first dimension of A as declared
*           in the calling (sub) program. LDA must be at least
*           max( 1, m ).
*           Unchanged on exit.
*
*  X      - DOUBLE PRECISION array of DIMENSION at least
*           ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
*           and at least
*           ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
*           Before entry, the incremented array X must contain the
*           vector x.
*           Unchanged on exit.
*
*  INCX   - INTEGER.
*           On entry, INCX specifies the increment for the elements of
*           X. INCX must not be zero.
*           Unchanged on exit.
*
*  BETA   - DOUBLE PRECISION.
*           On entry, BETA specifies the scalar beta. When BETA is
*           supplied as zero then Y need not be set on input.
*           Unchanged on exit.
*
*  Y      - DOUBLE PRECISION array of DIMENSION at least
*           ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
*           and at least
*           ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
*           Before entry with BETA non-zero, the incremented array Y
*           must contain the vector y. On exit, Y is overwritten by the
*           updated vector y.
*
*  INCY   - INTEGER.
*           On entry, INCY specifies the increment for the elements of
*           Y. INCY must not be zero.
*           Unchanged on exit.
*
*
*  Level 2 Blas routine.
*
*  -- Written on 22-October-1986.
*     Jack Dongarra, Argonne National Lab.
*     Jeremy Du Croz, Nag Central Office.
*     Sven Hammarling, Nag Central Office.
*     Richard Hanson, Sandia National Labs.
*
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE         , ZERO
      PARAMETER        ( ONE = 1.0D+0, ZERO = 0.0D+0 )
*     .. Local Scalars ..
      DOUBLE PRECISION   TEMP
      INTEGER            I, INFO, IX, IY, J, JX, JY, KX, KY, LENX, LENY
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     .. External Subroutines ..
      EXTERNAL           XERBLA
*     .. Intrinsic Functions ..
      INTRINSIC          MAX
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      INFO = 0
      IF     ( .NOT.LSAME( TRANS, 'N' ).AND.
     $         .NOT.LSAME( TRANS, 'T' ).AND.
     $         .NOT.LSAME( TRANS, 'C' )      )THEN
     INFO = 1
      ELSE IF( M.LT.0 )THEN
     INFO = 2
      ELSE IF( N.LT.0 )THEN
     INFO = 3
      ELSE IF( LDA.LT.MAX( 1, M ) )THEN
     INFO = 6
      ELSE IF( INCX.EQ.0 )THEN
     INFO = 8
      ELSE IF( INCY.EQ.0 )THEN
     INFO = 11
      END IF
      IF( INFO.NE.0 )THEN
     CALL XERBLA( 'DGEMV ', INFO )
     RETURN
      END IF
*
*     Quick return if possible.
*
      IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR.
     $    ( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) )
     $   RETURN
*
*     Set  LENX  and  LENY, the lengths of the vectors x and y, and set
*     up the start points in  X  and  Y.
*
      IF( LSAME( TRANS, 'N' ) )THEN
     LENX = N
     LENY = M
      ELSE
     LENX = M
     LENY = N
      END IF
      IF( INCX.GT.0 )THEN
     KX = 1
      ELSE
     KX = 1 - ( LENX - 1 )*INCX
      END IF
      IF( INCY.GT.0 )THEN
     KY = 1
      ELSE
     KY = 1 - ( LENY - 1 )*INCY
      END IF
*
*     Start the operations. In this version the elements of A are
*     accessed sequentially with one pass through A.
*
*     First form  y := beta*y.
*
      IF( BETA.NE.ONE )THEN
     IF( INCY.EQ.1 )THEN
        IF( BETA.EQ.ZERO )THEN
           DO 10, I = 1, LENY
          Y( I ) = ZERO
   10          CONTINUE
        ELSE
           DO 20, I = 1, LENY
          Y( I ) = BETA*Y( I )
   20          CONTINUE
        END IF
     ELSE
        IY = KY
        IF( BETA.EQ.ZERO )THEN
           DO 30, I = 1, LENY
          Y( IY ) = ZERO
          IY      = IY   + INCY
   30          CONTINUE
        ELSE
           DO 40, I = 1, LENY
          Y( IY ) = BETA*Y( IY )
          IY      = IY           + INCY
   40          CONTINUE
        END IF
     END IF
      END IF
      IF( ALPHA.EQ.ZERO )
     $   RETURN
      IF( LSAME( TRANS, 'N' ) )THEN
*
*        Form  y := alpha*A*x + y.
*
     JX = KX
     IF( INCY.EQ.1 )THEN
        DO 60, J = 1, N
           IF( X( JX ).NE.ZERO )THEN
          TEMP = ALPHA*X( JX )
          DO 50, I = 1, M
             Y( I ) = Y( I ) + TEMP*A( I, J )
   50             CONTINUE
           END IF
           JX = JX + INCX
   60       CONTINUE
     ELSE
        DO 80, J = 1, N
           IF( X( JX ).NE.ZERO )THEN
          TEMP = ALPHA*X( JX )
          IY   = KY
          DO 70, I = 1, M
             Y( IY ) = Y( IY ) + TEMP*A( I, J )
             IY      = IY      + INCY
   70             CONTINUE
           END IF
           JX = JX + INCX
   80       CONTINUE
     END IF
      ELSE
*
*        Form  y := alpha*A'*x + y.
*
     JY = KY
     IF( INCX.EQ.1 )THEN
        DO 100, J = 1, N
           TEMP = ZERO
           DO 90, I = 1, M
          TEMP = TEMP + A( I, J )*X( I )
   90          CONTINUE
           Y( JY ) = Y( JY ) + ALPHA*TEMP
           JY      = JY      + INCY
  100       CONTINUE
     ELSE
        DO 120, J = 1, N
           TEMP = ZERO
           IX   = KX
           DO 110, I = 1, M
          TEMP = TEMP + A( I, J )*X( IX )
          IX   = IX   + INCX
  110          CONTINUE
           Y( JY ) = Y( JY ) + ALPHA*TEMP
           JY      = JY      + INCY
  120       CONTINUE
     END IF
      END IF
*
      RETURN
*
*     End of DGEMV .
*
      END
1
2	SUBROUTINE DGEMV ( TRANS, M, N, ALPHA, A, LDA, X, INCX,
3	*
4	************************************************************************
5	*
6	* File of the DOUBLE PRECISION Level-2 BLAS.
7	* ===========================================
8	*
9	* SUBROUTINE DGEMV ( TRANS, M, N, ALPHA, A, LDA, X, INCX,
10	* $ BETA, Y, INCY )
11	*
12	* SUBROUTINE DGBMV ( TRANS, M, N, KL, KU, ALPHA, A, LDA, X, INCX,
13	* $ BETA, Y, INCY )
14	*
15	* SUBROUTINE DSYMV ( UPLO, N, ALPHA, A, LDA, X, INCX,
16	* $ BETA, Y, INCY )
17	*
18	* SUBROUTINE DSBMV ( UPLO, N, K, ALPHA, A, LDA, X, INCX,
19	* $ BETA, Y, INCY )
20	*
21	* SUBROUTINE DSPMV ( UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY )
22	*
23	* SUBROUTINE DTRMV ( UPLO, TRANS, DIAG, N, A, LDA, X, INCX )
24	*
25	* SUBROUTINE DTBMV ( UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX )
26	*
27	* SUBROUTINE DTPMV ( UPLO, TRANS, DIAG, N, AP, X, INCX )
28	*
29	* SUBROUTINE DTRSV ( UPLO, TRANS, DIAG, N, A, LDA, X, INCX )
30	*
31	* SUBROUTINE DTBSV ( UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX )
32	*
33	* SUBROUTINE DTPSV ( UPLO, TRANS, DIAG, N, AP, X, INCX )
34	*
35	* SUBROUTINE DGER ( M, N, ALPHA, X, INCX, Y, INCY, A, LDA )
36	*
37	* SUBROUTINE DSYR ( UPLO, N, ALPHA, X, INCX, A, LDA )
38	*
39	* SUBROUTINE DSPR ( UPLO, N, ALPHA, X, INCX, AP )
40	*
41	* SUBROUTINE DSYR2 ( UPLO, N, ALPHA, X, INCX, Y, INCY, A, LDA )
42	*
43	* SUBROUTINE DSPR2 ( UPLO, N, ALPHA, X, INCX, Y, INCY, AP )
44	*
45	* See:
46	*
47	* Dongarra J. J., Du Croz J. J., Hammarling S. and Hanson R. J..
48	* An extended set of Fortran Basic Linear Algebra Subprograms.
49	*
50	* Technical Memoranda Nos. 41 (revision 3) and 81, Mathematics
51	* and Computer Science Division, Argonne National Laboratory,
52	* 9700 South Cass Avenue, Argonne, Illinois 60439, US.
53	*
54	* Or
55	*
56	* NAG Technical Reports TR3/87 and TR4/87, Numerical Algorithms
57	* Group Ltd., NAG Central Office, 256 Banbury Road, Oxford
58	* OX2 7DE, UK, and Numerical Algorithms Group Inc., 1101 31st
59	* Street, Suite 100, Downers Grove, Illinois 60515-1263, USA.
60	*
61	************************************************************************
62	*
63	$ BETA, Y, INCY )
64	* .. Scalar Arguments ..
65	DOUBLE PRECISION ALPHA, BETA
66	INTEGER INCX, INCY, LDA, M, N
67	CHARACTER*1 TRANS
68	* .. Array Arguments ..
69	DOUBLE PRECISION A( LDA, * ), X( * ), Y( * )
70	* ..
71	*
72	* Purpose
73	* =======
74	*
75	* DGEMV performs one of the matrix-vector operations
76	*
77	* y := alphaAx + betay, or y := alphaA'x + betay,
78	*
79	* where alpha and beta are scalars, x and y are vectors and A is an
80	* m by n matrix.
81	*
82	* Parameters
83	* ==========
84	*
85	* TRANS - CHARACTER*1.
86	* On entry, TRANS specifies the operation to be performed as
87	* follows:
88	*
89	* TRANS = 'N' or 'n' y := alphaAx + beta*y.
90	*
91	* TRANS = 'T' or 't' y := alphaA'x + beta*y.
92	*
93	* TRANS = 'C' or 'c' y := alphaA'x + beta*y.
94	*
95	* Unchanged on exit.
96	*
97	* M - INTEGER.
98	* On entry, M specifies the number of rows of the matrix A.
99	* M must be at least zero.
100	* Unchanged on exit.
101	*
102	* N - INTEGER.
103	* On entry, N specifies the number of columns of the matrix A.
104	* N must be at least zero.
105	* Unchanged on exit.
106	*
107	* ALPHA - DOUBLE PRECISION.
108	* On entry, ALPHA specifies the scalar alpha.
109	* Unchanged on exit.
110	*
111	* A - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
112	* Before entry, the leading m by n part of the array A must
113	* contain the matrix of coefficients.
114	* Unchanged on exit.
115	*
116	* LDA - INTEGER.
117	* On entry, LDA specifies the first dimension of A as declared
118	* in the calling (sub) program. LDA must be at least
119	* max( 1, m ).
120	* Unchanged on exit.
121	*
122	* X - DOUBLE PRECISION array of DIMENSION at least
123	* ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
124	* and at least
125	* ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
126	* Before entry, the incremented array X must contain the
127	* vector x.
128	* Unchanged on exit.
129	*
130	* INCX - INTEGER.
131	* On entry, INCX specifies the increment for the elements of
132	* X. INCX must not be zero.
133	* Unchanged on exit.
134	*
135	* BETA - DOUBLE PRECISION.
136	* On entry, BETA specifies the scalar beta. When BETA is
137	* supplied as zero then Y need not be set on input.
138	* Unchanged on exit.
139	*
140	* Y - DOUBLE PRECISION array of DIMENSION at least
141	* ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
142	* and at least
143	* ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
144	* Before entry with BETA non-zero, the incremented array Y
145	* must contain the vector y. On exit, Y is overwritten by the
146	* updated vector y.
147	*
148	* INCY - INTEGER.
149	* On entry, INCY specifies the increment for the elements of
150	* Y. INCY must not be zero.
151	* Unchanged on exit.
152	*
153	*
154	* Level 2 Blas routine.
155	*
156	* -- Written on 22-October-1986.
157	* Jack Dongarra, Argonne National Lab.
158	* Jeremy Du Croz, Nag Central Office.
159	* Sven Hammarling, Nag Central Office.
160	* Richard Hanson, Sandia National Labs.
161	*
162	*
163	* .. Parameters ..
164	DOUBLE PRECISION ONE , ZERO
165	PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
166	* .. Local Scalars ..
167	DOUBLE PRECISION TEMP
168	INTEGER I, INFO, IX, IY, J, JX, JY, KX, KY, LENX, LENY
169	* .. External Functions ..
170	LOGICAL LSAME
171	EXTERNAL LSAME
172	* .. External Subroutines ..
173	EXTERNAL XERBLA
174	* .. Intrinsic Functions ..
175	INTRINSIC MAX
176	* ..
177	* .. Executable Statements ..
178	*
179	* Test the input parameters.
180	*
181	INFO = 0
182	IF ( .NOT.LSAME( TRANS, 'N' ).AND.
183	$ .NOT.LSAME( TRANS, 'T' ).AND.
184	$ .NOT.LSAME( TRANS, 'C' ) )THEN
185	INFO = 1
186	ELSE IF( M.LT.0 )THEN
187	INFO = 2
188	ELSE IF( N.LT.0 )THEN
189	INFO = 3
190	ELSE IF( LDA.LT.MAX( 1, M ) )THEN
191	INFO = 6
192	ELSE IF( INCX.EQ.0 )THEN
193	INFO = 8
194	ELSE IF( INCY.EQ.0 )THEN
195	INFO = 11
196	END IF
197	IF( INFO.NE.0 )THEN
198	CALL XERBLA( 'DGEMV ', INFO )
199	RETURN
200	END IF
201	*
202	* Quick return if possible.
203	*
204	IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR.
205	$ ( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) )
206	$ RETURN
207	*
208	* Set LENX and LENY, the lengths of the vectors x and y, and set
209	* up the start points in X and Y.
210	*
211	IF( LSAME( TRANS, 'N' ) )THEN
212	LENX = N
213	LENY = M
214	ELSE
215	LENX = M
216	LENY = N
217	END IF
218	IF( INCX.GT.0 )THEN
219	KX = 1
220	ELSE
221	KX = 1 - ( LENX - 1 )*INCX
222	END IF
223	IF( INCY.GT.0 )THEN
224	KY = 1
225	ELSE
226	KY = 1 - ( LENY - 1 )*INCY
227	END IF
228	*
229	* Start the operations. In this version the elements of A are
230	* accessed sequentially with one pass through A.
231	*
232	* First form y := beta*y.
233	*
234	IF( BETA.NE.ONE )THEN
235	IF( INCY.EQ.1 )THEN
236	IF( BETA.EQ.ZERO )THEN
237	DO 10, I = 1, LENY
238	Y( I ) = ZERO
239	10 CONTINUE
240	ELSE
241	DO 20, I = 1, LENY
242	Y( I ) = BETA*Y( I )
243	20 CONTINUE
244	END IF
245	ELSE
246	IY = KY
247	IF( BETA.EQ.ZERO )THEN
248	DO 30, I = 1, LENY
249	Y( IY ) = ZERO
250	IY = IY + INCY
251	30 CONTINUE
252	ELSE
253	DO 40, I = 1, LENY
254	Y( IY ) = BETA*Y( IY )
255	IY = IY + INCY
256	40 CONTINUE
257	END IF
258	END IF
259	END IF
260	IF( ALPHA.EQ.ZERO )
261	$ RETURN
262	IF( LSAME( TRANS, 'N' ) )THEN
263	*
264	* Form y := alphaAx + y.
265	*
266	JX = KX
267	IF( INCY.EQ.1 )THEN
268	DO 60, J = 1, N
269	IF( X( JX ).NE.ZERO )THEN
270	TEMP = ALPHA*X( JX )
271	DO 50, I = 1, M
272	Y( I ) = Y( I ) + TEMP*A( I, J )
273	50 CONTINUE
274	END IF
275	JX = JX + INCX
276	60 CONTINUE
277	ELSE
278	DO 80, J = 1, N
279	IF( X( JX ).NE.ZERO )THEN
280	TEMP = ALPHA*X( JX )
281	IY = KY
282	DO 70, I = 1, M
283	Y( IY ) = Y( IY ) + TEMP*A( I, J )
284	IY = IY + INCY
285	70 CONTINUE
286	END IF
287	JX = JX + INCX
288	80 CONTINUE
289	END IF
290	ELSE
291	*
292	* Form y := alphaA'x + y.
293	*
294	JY = KY
295	IF( INCX.EQ.1 )THEN
296	DO 100, J = 1, N
297	TEMP = ZERO
298	DO 90, I = 1, M
299	TEMP = TEMP + A( I, J )*X( I )
300	90 CONTINUE
301	Y( JY ) = Y( JY ) + ALPHA*TEMP
302	JY = JY + INCY
303	100 CONTINUE
304	ELSE
305	DO 120, J = 1, N
306	TEMP = ZERO
307	IX = KX
308	DO 110, I = 1, M
309	TEMP = TEMP + A( I, J )*X( IX )
310	IX = IX + INCX
311	110 CONTINUE
312	Y( JY ) = Y( JY ) + ALPHA*TEMP
313	JY = JY + INCY
314	120 CONTINUE
315	END IF
316	END IF
317	*
318	RETURN
319	*
320	* End of DGEMV .
321	*
322	END