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1.8 bertrand 1: *> \brief \b DTPMV
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 DTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX)
12: *
13: * .. Scalar Arguments ..
14: * INTEGER INCX,N
15: * CHARACTER DIAG,TRANS,UPLO
16: * ..
17: * .. Array Arguments ..
18: * DOUBLE PRECISION AP(*),X(*)
19: * ..
20: *
21: *
22: *> \par Purpose:
23: * =============
24: *>
25: *> \verbatim
26: *>
27: *> DTPMV 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, supplied in packed form.
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] AP
82: *> \verbatim
83: *> AP is DOUBLE PRECISION array of DIMENSION at least
84: *> ( ( n*( n + 1 ) )/2 ).
85: *> Before entry with UPLO = 'U' or 'u', the array AP must
86: *> contain the upper triangular matrix packed sequentially,
87: *> column by column, so that AP( 1 ) contains a( 1, 1 ),
88: *> AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )
89: *> respectively, and so on.
90: *> Before entry with UPLO = 'L' or 'l', the array AP must
91: *> contain the lower triangular matrix packed sequentially,
92: *> column by column, so that AP( 1 ) contains a( 1, 1 ),
93: *> AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )
94: *> respectively, and so on.
95: *> Note that when DIAG = 'U' or 'u', the diagonal elements of
96: *> A are not referenced, but are assumed to be unity.
97: *> \endverbatim
98: *>
99: *> \param[in,out] X
100: *> \verbatim
101: *> X is DOUBLE PRECISION array of dimension at least
102: *> ( 1 + ( n - 1 )*abs( INCX ) ).
103: *> Before entry, the incremented array X must contain the n
104: *> element vector x. On exit, X is overwritten with the
105: *> tranformed vector x.
106: *> \endverbatim
107: *>
108: *> \param[in] INCX
109: *> \verbatim
110: *> INCX is INTEGER
111: *> On entry, INCX specifies the increment for the elements of
112: *> X. INCX must not be zero.
113: *> \endverbatim
114: *
115: * Authors:
116: * ========
117: *
118: *> \author Univ. of Tennessee
119: *> \author Univ. of California Berkeley
120: *> \author Univ. of Colorado Denver
121: *> \author NAG Ltd.
122: *
123: *> \date November 2011
124: *
125: *> \ingroup double_blas_level2
126: *
127: *> \par Further Details:
128: * =====================
129: *>
130: *> \verbatim
131: *>
132: *> Level 2 Blas routine.
133: *> The vector and matrix arguments are not referenced when N = 0, or M = 0
134: *>
135: *> -- Written on 22-October-1986.
136: *> Jack Dongarra, Argonne National Lab.
137: *> Jeremy Du Croz, Nag Central Office.
138: *> Sven Hammarling, Nag Central Office.
139: *> Richard Hanson, Sandia National Labs.
140: *> \endverbatim
141: *>
142: * =====================================================================
1.1 bertrand 143: SUBROUTINE DTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX)
1.8 bertrand 144: *
145: * -- Reference BLAS level2 routine (version 3.4.0) --
146: * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
147: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
148: * November 2011
149: *
1.1 bertrand 150: * .. Scalar Arguments ..
151: INTEGER INCX,N
152: CHARACTER DIAG,TRANS,UPLO
153: * ..
154: * .. Array Arguments ..
155: DOUBLE PRECISION AP(*),X(*)
156: * ..
157: *
158: * =====================================================================
159: *
160: * .. Parameters ..
161: DOUBLE PRECISION ZERO
162: PARAMETER (ZERO=0.0D+0)
163: * ..
164: * .. Local Scalars ..
165: DOUBLE PRECISION TEMP
166: INTEGER I,INFO,IX,J,JX,K,KK,KX
167: LOGICAL NOUNIT
168: * ..
169: * .. External Functions ..
170: LOGICAL LSAME
171: EXTERNAL LSAME
172: * ..
173: * .. External Subroutines ..
174: EXTERNAL XERBLA
175: * ..
176: *
177: * Test the input parameters.
178: *
179: INFO = 0
180: IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
181: INFO = 1
182: ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
183: + .NOT.LSAME(TRANS,'C')) THEN
184: INFO = 2
185: ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
186: INFO = 3
187: ELSE IF (N.LT.0) THEN
188: INFO = 4
189: ELSE IF (INCX.EQ.0) THEN
190: INFO = 7
191: END IF
192: IF (INFO.NE.0) THEN
193: CALL XERBLA('DTPMV ',INFO)
194: RETURN
195: END IF
196: *
197: * Quick return if possible.
198: *
199: IF (N.EQ.0) RETURN
200: *
201: NOUNIT = LSAME(DIAG,'N')
202: *
203: * Set up the start point in X if the increment is not unity. This
204: * will be ( N - 1 )*INCX too small for descending loops.
205: *
206: IF (INCX.LE.0) THEN
207: KX = 1 - (N-1)*INCX
208: ELSE IF (INCX.NE.1) THEN
209: KX = 1
210: END IF
211: *
212: * Start the operations. In this version the elements of AP are
213: * accessed sequentially with one pass through AP.
214: *
215: IF (LSAME(TRANS,'N')) THEN
216: *
217: * Form x:= A*x.
218: *
219: IF (LSAME(UPLO,'U')) THEN
220: KK = 1
221: IF (INCX.EQ.1) THEN
222: DO 20 J = 1,N
223: IF (X(J).NE.ZERO) THEN
224: TEMP = X(J)
225: K = KK
226: DO 10 I = 1,J - 1
227: X(I) = X(I) + TEMP*AP(K)
228: K = K + 1
229: 10 CONTINUE
230: IF (NOUNIT) X(J) = X(J)*AP(KK+J-1)
231: END IF
232: KK = KK + J
233: 20 CONTINUE
234: ELSE
235: JX = KX
236: DO 40 J = 1,N
237: IF (X(JX).NE.ZERO) THEN
238: TEMP = X(JX)
239: IX = KX
240: DO 30 K = KK,KK + J - 2
241: X(IX) = X(IX) + TEMP*AP(K)
242: IX = IX + INCX
243: 30 CONTINUE
244: IF (NOUNIT) X(JX) = X(JX)*AP(KK+J-1)
245: END IF
246: JX = JX + INCX
247: KK = KK + J
248: 40 CONTINUE
249: END IF
250: ELSE
251: KK = (N* (N+1))/2
252: IF (INCX.EQ.1) THEN
253: DO 60 J = N,1,-1
254: IF (X(J).NE.ZERO) THEN
255: TEMP = X(J)
256: K = KK
257: DO 50 I = N,J + 1,-1
258: X(I) = X(I) + TEMP*AP(K)
259: K = K - 1
260: 50 CONTINUE
261: IF (NOUNIT) X(J) = X(J)*AP(KK-N+J)
262: END IF
263: KK = KK - (N-J+1)
264: 60 CONTINUE
265: ELSE
266: KX = KX + (N-1)*INCX
267: JX = KX
268: DO 80 J = N,1,-1
269: IF (X(JX).NE.ZERO) THEN
270: TEMP = X(JX)
271: IX = KX
272: DO 70 K = KK,KK - (N- (J+1)),-1
273: X(IX) = X(IX) + TEMP*AP(K)
274: IX = IX - INCX
275: 70 CONTINUE
276: IF (NOUNIT) X(JX) = X(JX)*AP(KK-N+J)
277: END IF
278: JX = JX - INCX
279: KK = KK - (N-J+1)
280: 80 CONTINUE
281: END IF
282: END IF
283: ELSE
284: *
1.7 bertrand 285: * Form x := A**T*x.
1.1 bertrand 286: *
287: IF (LSAME(UPLO,'U')) THEN
288: KK = (N* (N+1))/2
289: IF (INCX.EQ.1) THEN
290: DO 100 J = N,1,-1
291: TEMP = X(J)
292: IF (NOUNIT) TEMP = TEMP*AP(KK)
293: K = KK - 1
294: DO 90 I = J - 1,1,-1
295: TEMP = TEMP + AP(K)*X(I)
296: K = K - 1
297: 90 CONTINUE
298: X(J) = TEMP
299: KK = KK - J
300: 100 CONTINUE
301: ELSE
302: JX = KX + (N-1)*INCX
303: DO 120 J = N,1,-1
304: TEMP = X(JX)
305: IX = JX
306: IF (NOUNIT) TEMP = TEMP*AP(KK)
307: DO 110 K = KK - 1,KK - J + 1,-1
308: IX = IX - INCX
309: TEMP = TEMP + AP(K)*X(IX)
310: 110 CONTINUE
311: X(JX) = TEMP
312: JX = JX - INCX
313: KK = KK - J
314: 120 CONTINUE
315: END IF
316: ELSE
317: KK = 1
318: IF (INCX.EQ.1) THEN
319: DO 140 J = 1,N
320: TEMP = X(J)
321: IF (NOUNIT) TEMP = TEMP*AP(KK)
322: K = KK + 1
323: DO 130 I = J + 1,N
324: TEMP = TEMP + AP(K)*X(I)
325: K = K + 1
326: 130 CONTINUE
327: X(J) = TEMP
328: KK = KK + (N-J+1)
329: 140 CONTINUE
330: ELSE
331: JX = KX
332: DO 160 J = 1,N
333: TEMP = X(JX)
334: IX = JX
335: IF (NOUNIT) TEMP = TEMP*AP(KK)
336: DO 150 K = KK + 1,KK + N - J
337: IX = IX + INCX
338: TEMP = TEMP + AP(K)*X(IX)
339: 150 CONTINUE
340: X(JX) = TEMP
341: JX = JX + INCX
342: KK = KK + (N-J+1)
343: 160 CONTINUE
344: END IF
345: END IF
346: END IF
347: *
348: RETURN
349: *
350: * End of DTPMV .
351: *
352: END