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1.8 bertrand 1: *> \brief \b ZTPMV
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 ZTPMV(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: * COMPLEX*16 AP(*),X(*)
19: * ..
20: *
21: *
22: *> \par Purpose:
23: * =============
24: *>
25: *> \verbatim
26: *>
27: *> ZTPMV performs one of the matrix-vector operations
28: *>
29: *> x := A*x, or x := A**T*x, or x := A**H*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**H*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 COMPLEX*16 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] X
100: *> \verbatim
101: *> X is (input/output) COMPLEX*16 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 complex16_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 ZTPMV(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 ..
1.8 bertrand 155: COMPLEX*16 AP(*),X(*)
1.1 bertrand 156: * ..
157: *
158: * =====================================================================
159: *
160: * .. Parameters ..
1.8 bertrand 161: COMPLEX*16 ZERO
1.1 bertrand 162: PARAMETER (ZERO= (0.0D+0,0.0D+0))
163: * ..
164: * .. Local Scalars ..
1.8 bertrand 165: COMPLEX*16 TEMP
1.1 bertrand 166: INTEGER I,INFO,IX,J,JX,K,KK,KX
167: LOGICAL NOCONJ,NOUNIT
168: * ..
169: * .. External Functions ..
170: LOGICAL LSAME
171: EXTERNAL LSAME
172: * ..
173: * .. External Subroutines ..
174: EXTERNAL XERBLA
175: * ..
176: * .. Intrinsic Functions ..
177: INTRINSIC DCONJG
178: * ..
179: *
180: * Test the input parameters.
181: *
182: INFO = 0
183: IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
184: INFO = 1
185: ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
186: + .NOT.LSAME(TRANS,'C')) THEN
187: INFO = 2
188: ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
189: INFO = 3
190: ELSE IF (N.LT.0) THEN
191: INFO = 4
192: ELSE IF (INCX.EQ.0) THEN
193: INFO = 7
194: END IF
195: IF (INFO.NE.0) THEN
196: CALL XERBLA('ZTPMV ',INFO)
197: RETURN
198: END IF
199: *
200: * Quick return if possible.
201: *
202: IF (N.EQ.0) RETURN
203: *
204: NOCONJ = LSAME(TRANS,'T')
205: NOUNIT = LSAME(DIAG,'N')
206: *
207: * Set up the start point in X if the increment is not unity. This
208: * will be ( N - 1 )*INCX too small for descending loops.
209: *
210: IF (INCX.LE.0) THEN
211: KX = 1 - (N-1)*INCX
212: ELSE IF (INCX.NE.1) THEN
213: KX = 1
214: END IF
215: *
216: * Start the operations. In this version the elements of AP are
217: * accessed sequentially with one pass through AP.
218: *
219: IF (LSAME(TRANS,'N')) THEN
220: *
221: * Form x:= A*x.
222: *
223: IF (LSAME(UPLO,'U')) THEN
224: KK = 1
225: IF (INCX.EQ.1) THEN
226: DO 20 J = 1,N
227: IF (X(J).NE.ZERO) THEN
228: TEMP = X(J)
229: K = KK
230: DO 10 I = 1,J - 1
231: X(I) = X(I) + TEMP*AP(K)
232: K = K + 1
233: 10 CONTINUE
234: IF (NOUNIT) X(J) = X(J)*AP(KK+J-1)
235: END IF
236: KK = KK + J
237: 20 CONTINUE
238: ELSE
239: JX = KX
240: DO 40 J = 1,N
241: IF (X(JX).NE.ZERO) THEN
242: TEMP = X(JX)
243: IX = KX
244: DO 30 K = KK,KK + J - 2
245: X(IX) = X(IX) + TEMP*AP(K)
246: IX = IX + INCX
247: 30 CONTINUE
248: IF (NOUNIT) X(JX) = X(JX)*AP(KK+J-1)
249: END IF
250: JX = JX + INCX
251: KK = KK + J
252: 40 CONTINUE
253: END IF
254: ELSE
255: KK = (N* (N+1))/2
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: K = KK
261: DO 50 I = N,J + 1,-1
262: X(I) = X(I) + TEMP*AP(K)
263: K = K - 1
264: 50 CONTINUE
265: IF (NOUNIT) X(J) = X(J)*AP(KK-N+J)
266: END IF
267: KK = KK - (N-J+1)
268: 60 CONTINUE
269: ELSE
270: KX = KX + (N-1)*INCX
271: JX = KX
272: DO 80 J = N,1,-1
273: IF (X(JX).NE.ZERO) THEN
274: TEMP = X(JX)
275: IX = KX
276: DO 70 K = KK,KK - (N- (J+1)),-1
277: X(IX) = X(IX) + TEMP*AP(K)
278: IX = IX - INCX
279: 70 CONTINUE
280: IF (NOUNIT) X(JX) = X(JX)*AP(KK-N+J)
281: END IF
282: JX = JX - INCX
283: KK = KK - (N-J+1)
284: 80 CONTINUE
285: END IF
286: END IF
287: ELSE
288: *
1.7 bertrand 289: * Form x := A**T*x or x := A**H*x.
1.1 bertrand 290: *
291: IF (LSAME(UPLO,'U')) THEN
292: KK = (N* (N+1))/2
293: IF (INCX.EQ.1) THEN
294: DO 110 J = N,1,-1
295: TEMP = X(J)
296: K = KK - 1
297: IF (NOCONJ) THEN
298: IF (NOUNIT) TEMP = TEMP*AP(KK)
299: DO 90 I = J - 1,1,-1
300: TEMP = TEMP + AP(K)*X(I)
301: K = K - 1
302: 90 CONTINUE
303: ELSE
304: IF (NOUNIT) TEMP = TEMP*DCONJG(AP(KK))
305: DO 100 I = J - 1,1,-1
306: TEMP = TEMP + DCONJG(AP(K))*X(I)
307: K = K - 1
308: 100 CONTINUE
309: END IF
310: X(J) = TEMP
311: KK = KK - J
312: 110 CONTINUE
313: ELSE
314: JX = KX + (N-1)*INCX
315: DO 140 J = N,1,-1
316: TEMP = X(JX)
317: IX = JX
318: IF (NOCONJ) THEN
319: IF (NOUNIT) TEMP = TEMP*AP(KK)
320: DO 120 K = KK - 1,KK - J + 1,-1
321: IX = IX - INCX
322: TEMP = TEMP + AP(K)*X(IX)
323: 120 CONTINUE
324: ELSE
325: IF (NOUNIT) TEMP = TEMP*DCONJG(AP(KK))
326: DO 130 K = KK - 1,KK - J + 1,-1
327: IX = IX - INCX
328: TEMP = TEMP + DCONJG(AP(K))*X(IX)
329: 130 CONTINUE
330: END IF
331: X(JX) = TEMP
332: JX = JX - INCX
333: KK = KK - J
334: 140 CONTINUE
335: END IF
336: ELSE
337: KK = 1
338: IF (INCX.EQ.1) THEN
339: DO 170 J = 1,N
340: TEMP = X(J)
341: K = KK + 1
342: IF (NOCONJ) THEN
343: IF (NOUNIT) TEMP = TEMP*AP(KK)
344: DO 150 I = J + 1,N
345: TEMP = TEMP + AP(K)*X(I)
346: K = K + 1
347: 150 CONTINUE
348: ELSE
349: IF (NOUNIT) TEMP = TEMP*DCONJG(AP(KK))
350: DO 160 I = J + 1,N
351: TEMP = TEMP + DCONJG(AP(K))*X(I)
352: K = K + 1
353: 160 CONTINUE
354: END IF
355: X(J) = TEMP
356: KK = KK + (N-J+1)
357: 170 CONTINUE
358: ELSE
359: JX = KX
360: DO 200 J = 1,N
361: TEMP = X(JX)
362: IX = JX
363: IF (NOCONJ) THEN
364: IF (NOUNIT) TEMP = TEMP*AP(KK)
365: DO 180 K = KK + 1,KK + N - J
366: IX = IX + INCX
367: TEMP = TEMP + AP(K)*X(IX)
368: 180 CONTINUE
369: ELSE
370: IF (NOUNIT) TEMP = TEMP*DCONJG(AP(KK))
371: DO 190 K = KK + 1,KK + N - J
372: IX = IX + INCX
373: TEMP = TEMP + DCONJG(AP(K))*X(IX)
374: 190 CONTINUE
375: END IF
376: X(JX) = TEMP
377: JX = JX + INCX
378: KK = KK + (N-J+1)
379: 200 CONTINUE
380: END IF
381: END IF
382: END IF
383: *
384: RETURN
385: *
386: * End of ZTPMV .
387: *
388: END