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1.8 bertrand 1: *> \brief \b ZTPMV
2: *
3: * =========== DOCUMENTATION ===========
4: *
1.13 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.8 bertrand 7: *
8: * Definition:
9: * ===========
10: *
11: * SUBROUTINE ZTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX)
1.13 bertrand 12: *
1.8 bertrand 13: * .. Scalar Arguments ..
14: * INTEGER INCX,N
15: * CHARACTER DIAG,TRANS,UPLO
16: * ..
17: * .. Array Arguments ..
18: * COMPLEX*16 AP(*),X(*)
19: * ..
1.13 bertrand 20: *
1.8 bertrand 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
1.14 bertrand 83: *> AP is COMPLEX*16 array, dimension at least
1.8 bertrand 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: *>
1.14 bertrand 99: *> \param[in,out] X
1.8 bertrand 100: *> \verbatim
1.14 bertrand 101: *> X is COMPLEX*16 array, dimension at least
1.8 bertrand 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
1.13 bertrand 105: *> transformed vector x.
1.8 bertrand 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: *
1.13 bertrand 118: *> \author Univ. of Tennessee
119: *> \author Univ. of California Berkeley
120: *> \author Univ. of Colorado Denver
121: *> \author NAG Ltd.
1.8 bertrand 122: *
123: *> \ingroup complex16_blas_level2
124: *
125: *> \par Further Details:
126: * =====================
127: *>
128: *> \verbatim
129: *>
130: *> Level 2 Blas routine.
131: *> The vector and matrix arguments are not referenced when N = 0, or M = 0
132: *>
133: *> -- Written on 22-October-1986.
134: *> Jack Dongarra, Argonne National Lab.
135: *> Jeremy Du Croz, Nag Central Office.
136: *> Sven Hammarling, Nag Central Office.
137: *> Richard Hanson, Sandia National Labs.
138: *> \endverbatim
139: *>
140: * =====================================================================
1.1 bertrand 141: SUBROUTINE ZTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX)
1.8 bertrand 142: *
1.16 ! bertrand 143: * -- Reference BLAS level2 routine --
1.8 bertrand 144: * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
145: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
146: *
1.1 bertrand 147: * .. Scalar Arguments ..
148: INTEGER INCX,N
149: CHARACTER DIAG,TRANS,UPLO
150: * ..
151: * .. Array Arguments ..
1.8 bertrand 152: COMPLEX*16 AP(*),X(*)
1.1 bertrand 153: * ..
154: *
155: * =====================================================================
156: *
157: * .. Parameters ..
1.8 bertrand 158: COMPLEX*16 ZERO
1.1 bertrand 159: PARAMETER (ZERO= (0.0D+0,0.0D+0))
160: * ..
161: * .. Local Scalars ..
1.8 bertrand 162: COMPLEX*16 TEMP
1.1 bertrand 163: INTEGER I,INFO,IX,J,JX,K,KK,KX
164: LOGICAL NOCONJ,NOUNIT
165: * ..
166: * .. External Functions ..
167: LOGICAL LSAME
168: EXTERNAL LSAME
169: * ..
170: * .. External Subroutines ..
171: EXTERNAL XERBLA
172: * ..
173: * .. Intrinsic Functions ..
174: INTRINSIC DCONJG
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('ZTPMV ',INFO)
194: RETURN
195: END IF
196: *
197: * Quick return if possible.
198: *
199: IF (N.EQ.0) RETURN
200: *
201: NOCONJ = LSAME(TRANS,'T')
202: NOUNIT = LSAME(DIAG,'N')
203: *
204: * Set up the start point in X if the increment is not unity. This
205: * will be ( N - 1 )*INCX too small for descending loops.
206: *
207: IF (INCX.LE.0) THEN
208: KX = 1 - (N-1)*INCX
209: ELSE IF (INCX.NE.1) THEN
210: KX = 1
211: END IF
212: *
213: * Start the operations. In this version the elements of AP are
214: * accessed sequentially with one pass through AP.
215: *
216: IF (LSAME(TRANS,'N')) THEN
217: *
218: * Form x:= A*x.
219: *
220: IF (LSAME(UPLO,'U')) THEN
221: KK = 1
222: IF (INCX.EQ.1) THEN
223: DO 20 J = 1,N
224: IF (X(J).NE.ZERO) THEN
225: TEMP = X(J)
226: K = KK
227: DO 10 I = 1,J - 1
228: X(I) = X(I) + TEMP*AP(K)
229: K = K + 1
230: 10 CONTINUE
231: IF (NOUNIT) X(J) = X(J)*AP(KK+J-1)
232: END IF
233: KK = KK + J
234: 20 CONTINUE
235: ELSE
236: JX = KX
237: DO 40 J = 1,N
238: IF (X(JX).NE.ZERO) THEN
239: TEMP = X(JX)
240: IX = KX
241: DO 30 K = KK,KK + J - 2
242: X(IX) = X(IX) + TEMP*AP(K)
243: IX = IX + INCX
244: 30 CONTINUE
245: IF (NOUNIT) X(JX) = X(JX)*AP(KK+J-1)
246: END IF
247: JX = JX + INCX
248: KK = KK + J
249: 40 CONTINUE
250: END IF
251: ELSE
252: KK = (N* (N+1))/2
253: IF (INCX.EQ.1) THEN
254: DO 60 J = N,1,-1
255: IF (X(J).NE.ZERO) THEN
256: TEMP = X(J)
257: K = KK
258: DO 50 I = N,J + 1,-1
259: X(I) = X(I) + TEMP*AP(K)
260: K = K - 1
261: 50 CONTINUE
262: IF (NOUNIT) X(J) = X(J)*AP(KK-N+J)
263: END IF
264: KK = KK - (N-J+1)
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 K = KK,KK - (N- (J+1)),-1
274: X(IX) = X(IX) + TEMP*AP(K)
275: IX = IX - INCX
276: 70 CONTINUE
277: IF (NOUNIT) X(JX) = X(JX)*AP(KK-N+J)
278: END IF
279: JX = JX - INCX
280: KK = KK - (N-J+1)
281: 80 CONTINUE
282: END IF
283: END IF
284: ELSE
285: *
1.7 bertrand 286: * Form x := A**T*x or x := A**H*x.
1.1 bertrand 287: *
288: IF (LSAME(UPLO,'U')) THEN
289: KK = (N* (N+1))/2
290: IF (INCX.EQ.1) THEN
291: DO 110 J = N,1,-1
292: TEMP = X(J)
293: K = KK - 1
294: IF (NOCONJ) THEN
295: IF (NOUNIT) TEMP = TEMP*AP(KK)
296: DO 90 I = J - 1,1,-1
297: TEMP = TEMP + AP(K)*X(I)
298: K = K - 1
299: 90 CONTINUE
300: ELSE
301: IF (NOUNIT) TEMP = TEMP*DCONJG(AP(KK))
302: DO 100 I = J - 1,1,-1
303: TEMP = TEMP + DCONJG(AP(K))*X(I)
304: K = K - 1
305: 100 CONTINUE
306: END IF
307: X(J) = TEMP
308: KK = KK - J
309: 110 CONTINUE
310: ELSE
311: JX = KX + (N-1)*INCX
312: DO 140 J = N,1,-1
313: TEMP = X(JX)
314: IX = JX
315: IF (NOCONJ) THEN
316: IF (NOUNIT) TEMP = TEMP*AP(KK)
317: DO 120 K = KK - 1,KK - J + 1,-1
318: IX = IX - INCX
319: TEMP = TEMP + AP(K)*X(IX)
320: 120 CONTINUE
321: ELSE
322: IF (NOUNIT) TEMP = TEMP*DCONJG(AP(KK))
323: DO 130 K = KK - 1,KK - J + 1,-1
324: IX = IX - INCX
325: TEMP = TEMP + DCONJG(AP(K))*X(IX)
326: 130 CONTINUE
327: END IF
328: X(JX) = TEMP
329: JX = JX - INCX
330: KK = KK - J
331: 140 CONTINUE
332: END IF
333: ELSE
334: KK = 1
335: IF (INCX.EQ.1) THEN
336: DO 170 J = 1,N
337: TEMP = X(J)
338: K = KK + 1
339: IF (NOCONJ) THEN
340: IF (NOUNIT) TEMP = TEMP*AP(KK)
341: DO 150 I = J + 1,N
342: TEMP = TEMP + AP(K)*X(I)
343: K = K + 1
344: 150 CONTINUE
345: ELSE
346: IF (NOUNIT) TEMP = TEMP*DCONJG(AP(KK))
347: DO 160 I = J + 1,N
348: TEMP = TEMP + DCONJG(AP(K))*X(I)
349: K = K + 1
350: 160 CONTINUE
351: END IF
352: X(J) = TEMP
353: KK = KK + (N-J+1)
354: 170 CONTINUE
355: ELSE
356: JX = KX
357: DO 200 J = 1,N
358: TEMP = X(JX)
359: IX = JX
360: IF (NOCONJ) THEN
361: IF (NOUNIT) TEMP = TEMP*AP(KK)
362: DO 180 K = KK + 1,KK + N - J
363: IX = IX + INCX
364: TEMP = TEMP + AP(K)*X(IX)
365: 180 CONTINUE
366: ELSE
367: IF (NOUNIT) TEMP = TEMP*DCONJG(AP(KK))
368: DO 190 K = KK + 1,KK + N - J
369: IX = IX + INCX
370: TEMP = TEMP + DCONJG(AP(K))*X(IX)
371: 190 CONTINUE
372: END IF
373: X(JX) = TEMP
374: JX = JX + INCX
375: KK = KK + (N-J+1)
376: 200 CONTINUE
377: END IF
378: END IF
379: END IF
380: *
381: RETURN
382: *
1.16 ! bertrand 383: * End of ZTPMV
1.1 bertrand 384: *
385: END