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1.8 bertrand 1: *> \brief \b ZTPSV
1.1 bertrand 2: *
1.8 bertrand 3: * =========== DOCUMENTATION ===========
1.1 bertrand 4: *
1.8 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.1 bertrand 7: *
1.8 bertrand 8: * Definition:
9: * ===========
10: *
11: * SUBROUTINE ZTPSV(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: *> ZTPSV solves one of the systems of equations
28: *>
29: *> A*x = b, or A**T*x = b, or A**H*x = b,
30: *>
31: *> where b and x are n element vectors and A is an n by n unit, or
32: *> non-unit, upper or lower triangular matrix, supplied in packed form.
33: *>
34: *> No test for singularity or near-singularity is included in this
35: *> routine. Such tests must be performed before calling this routine.
36: *> \endverbatim
1.1 bertrand 37: *
1.8 bertrand 38: * Arguments:
1.1 bertrand 39: * ==========
40: *
1.8 bertrand 41: *> \param[in] UPLO
42: *> \verbatim
43: *> UPLO is CHARACTER*1
44: *> On entry, UPLO specifies whether the matrix is an upper or
45: *> lower triangular matrix as follows:
46: *>
47: *> UPLO = 'U' or 'u' A is an upper triangular matrix.
48: *>
49: *> UPLO = 'L' or 'l' A is a lower triangular matrix.
50: *> \endverbatim
51: *>
52: *> \param[in] TRANS
53: *> \verbatim
54: *> TRANS is CHARACTER*1
55: *> On entry, TRANS specifies the equations to be solved as
56: *> follows:
57: *>
58: *> TRANS = 'N' or 'n' A*x = b.
59: *>
60: *> TRANS = 'T' or 't' A**T*x = b.
61: *>
62: *> TRANS = 'C' or 'c' A**H*x = b.
63: *> \endverbatim
64: *>
65: *> \param[in] DIAG
66: *> \verbatim
67: *> DIAG is CHARACTER*1
68: *> On entry, DIAG specifies whether or not A is unit
69: *> triangular as follows:
70: *>
71: *> DIAG = 'U' or 'u' A is assumed to be unit triangular.
72: *>
73: *> DIAG = 'N' or 'n' A is not assumed to be unit
74: *> triangular.
75: *> \endverbatim
76: *>
77: *> \param[in] N
78: *> \verbatim
79: *> N is INTEGER
80: *> On entry, N specifies the order of the matrix A.
81: *> N must be at least zero.
82: *> \endverbatim
83: *>
84: *> \param[in] AP
85: *> \verbatim
86: *> AP is COMPLEX*16 array of DIMENSION at least
87: *> ( ( n*( n + 1 ) )/2 ).
88: *> Before entry with UPLO = 'U' or 'u', the array AP must
89: *> contain the upper triangular matrix packed sequentially,
90: *> column by column, so that AP( 1 ) contains a( 1, 1 ),
91: *> AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )
92: *> respectively, and so on.
93: *> Before entry with UPLO = 'L' or 'l', the array AP must
94: *> contain the lower triangular matrix packed sequentially,
95: *> column by column, so that AP( 1 ) contains a( 1, 1 ),
96: *> AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )
97: *> respectively, and so on.
98: *> Note that when DIAG = 'U' or 'u', the diagonal elements of
99: *> A are not referenced, but are assumed to be unity.
100: *> \endverbatim
101: *>
102: *> \param[in,out] X
103: *> \verbatim
104: *> X is COMPLEX*16 array of dimension at least
105: *> ( 1 + ( n - 1 )*abs( INCX ) ).
106: *> Before entry, the incremented array X must contain the n
107: *> element right-hand side vector b. On exit, X is overwritten
108: *> with the solution vector x.
109: *> \endverbatim
110: *>
111: *> \param[in] INCX
112: *> \verbatim
113: *> INCX is INTEGER
114: *> On entry, INCX specifies the increment for the elements of
115: *> X. INCX must not be zero.
116: *> \endverbatim
117: *
118: * Authors:
119: * ========
120: *
121: *> \author Univ. of Tennessee
122: *> \author Univ. of California Berkeley
123: *> \author Univ. of Colorado Denver
124: *> \author NAG Ltd.
125: *
126: *> \date November 2011
127: *
128: *> \ingroup complex16_blas_level2
129: *
130: *> \par Further Details:
131: * =====================
132: *>
133: *> \verbatim
134: *>
135: *> Level 2 Blas routine.
136: *>
137: *> -- Written on 22-October-1986.
138: *> Jack Dongarra, Argonne National Lab.
139: *> Jeremy Du Croz, Nag Central Office.
140: *> Sven Hammarling, Nag Central Office.
141: *> Richard Hanson, Sandia National Labs.
142: *> \endverbatim
143: *>
144: * =====================================================================
145: SUBROUTINE ZTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX)
1.1 bertrand 146: *
1.8 bertrand 147: * -- Reference BLAS level2 routine (version 3.4.0) --
148: * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
149: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
150: * November 2011
1.1 bertrand 151: *
1.8 bertrand 152: * .. Scalar Arguments ..
153: INTEGER INCX,N
154: CHARACTER DIAG,TRANS,UPLO
155: * ..
156: * .. Array Arguments ..
157: COMPLEX*16 AP(*),X(*)
158: * ..
1.1 bertrand 159: *
160: * =====================================================================
161: *
162: * .. Parameters ..
1.8 bertrand 163: COMPLEX*16 ZERO
1.1 bertrand 164: PARAMETER (ZERO= (0.0D+0,0.0D+0))
165: * ..
166: * .. Local Scalars ..
1.8 bertrand 167: COMPLEX*16 TEMP
1.1 bertrand 168: INTEGER I,INFO,IX,J,JX,K,KK,KX
169: LOGICAL NOCONJ,NOUNIT
170: * ..
171: * .. External Functions ..
172: LOGICAL LSAME
173: EXTERNAL LSAME
174: * ..
175: * .. External Subroutines ..
176: EXTERNAL XERBLA
177: * ..
178: * .. Intrinsic Functions ..
179: INTRINSIC DCONJG
180: * ..
181: *
182: * Test the input parameters.
183: *
184: INFO = 0
185: IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
186: INFO = 1
187: ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
188: + .NOT.LSAME(TRANS,'C')) THEN
189: INFO = 2
190: ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
191: INFO = 3
192: ELSE IF (N.LT.0) THEN
193: INFO = 4
194: ELSE IF (INCX.EQ.0) THEN
195: INFO = 7
196: END IF
197: IF (INFO.NE.0) THEN
198: CALL XERBLA('ZTPSV ',INFO)
199: RETURN
200: END IF
201: *
202: * Quick return if possible.
203: *
204: IF (N.EQ.0) RETURN
205: *
206: NOCONJ = LSAME(TRANS,'T')
207: NOUNIT = LSAME(DIAG,'N')
208: *
209: * Set up the start point in X if the increment is not unity. This
210: * will be ( N - 1 )*INCX too small for descending loops.
211: *
212: IF (INCX.LE.0) THEN
213: KX = 1 - (N-1)*INCX
214: ELSE IF (INCX.NE.1) THEN
215: KX = 1
216: END IF
217: *
218: * Start the operations. In this version the elements of AP are
219: * accessed sequentially with one pass through AP.
220: *
221: IF (LSAME(TRANS,'N')) THEN
222: *
223: * Form x := inv( A )*x.
224: *
225: IF (LSAME(UPLO,'U')) THEN
226: KK = (N* (N+1))/2
227: IF (INCX.EQ.1) THEN
228: DO 20 J = N,1,-1
229: IF (X(J).NE.ZERO) THEN
230: IF (NOUNIT) X(J) = X(J)/AP(KK)
231: TEMP = X(J)
232: K = KK - 1
233: DO 10 I = J - 1,1,-1
234: X(I) = X(I) - TEMP*AP(K)
235: K = K - 1
236: 10 CONTINUE
237: END IF
238: KK = KK - J
239: 20 CONTINUE
240: ELSE
241: JX = KX + (N-1)*INCX
242: DO 40 J = N,1,-1
243: IF (X(JX).NE.ZERO) THEN
244: IF (NOUNIT) X(JX) = X(JX)/AP(KK)
245: TEMP = X(JX)
246: IX = JX
247: DO 30 K = KK - 1,KK - J + 1,-1
248: IX = IX - INCX
249: X(IX) = X(IX) - TEMP*AP(K)
250: 30 CONTINUE
251: END IF
252: JX = JX - INCX
253: KK = KK - J
254: 40 CONTINUE
255: END IF
256: ELSE
257: KK = 1
258: IF (INCX.EQ.1) THEN
259: DO 60 J = 1,N
260: IF (X(J).NE.ZERO) THEN
261: IF (NOUNIT) X(J) = X(J)/AP(KK)
262: TEMP = X(J)
263: K = KK + 1
264: DO 50 I = J + 1,N
265: X(I) = X(I) - TEMP*AP(K)
266: K = K + 1
267: 50 CONTINUE
268: END IF
269: KK = KK + (N-J+1)
270: 60 CONTINUE
271: ELSE
272: JX = KX
273: DO 80 J = 1,N
274: IF (X(JX).NE.ZERO) THEN
275: IF (NOUNIT) X(JX) = X(JX)/AP(KK)
276: TEMP = X(JX)
277: IX = JX
278: DO 70 K = KK + 1,KK + N - J
279: IX = IX + INCX
280: X(IX) = X(IX) - TEMP*AP(K)
281: 70 CONTINUE
282: END IF
283: JX = JX + INCX
284: KK = KK + (N-J+1)
285: 80 CONTINUE
286: END IF
287: END IF
288: ELSE
289: *
1.7 bertrand 290: * Form x := inv( A**T )*x or x := inv( A**H )*x.
1.1 bertrand 291: *
292: IF (LSAME(UPLO,'U')) THEN
293: KK = 1
294: IF (INCX.EQ.1) THEN
295: DO 110 J = 1,N
296: TEMP = X(J)
297: K = KK
298: IF (NOCONJ) THEN
299: DO 90 I = 1,J - 1
300: TEMP = TEMP - AP(K)*X(I)
301: K = K + 1
302: 90 CONTINUE
303: IF (NOUNIT) TEMP = TEMP/AP(KK+J-1)
304: ELSE
305: DO 100 I = 1,J - 1
306: TEMP = TEMP - DCONJG(AP(K))*X(I)
307: K = K + 1
308: 100 CONTINUE
309: IF (NOUNIT) TEMP = TEMP/DCONJG(AP(KK+J-1))
310: END IF
311: X(J) = TEMP
312: KK = KK + J
313: 110 CONTINUE
314: ELSE
315: JX = KX
316: DO 140 J = 1,N
317: TEMP = X(JX)
318: IX = KX
319: IF (NOCONJ) THEN
320: DO 120 K = KK,KK + J - 2
321: TEMP = TEMP - AP(K)*X(IX)
322: IX = IX + INCX
323: 120 CONTINUE
324: IF (NOUNIT) TEMP = TEMP/AP(KK+J-1)
325: ELSE
326: DO 130 K = KK,KK + J - 2
327: TEMP = TEMP - DCONJG(AP(K))*X(IX)
328: IX = IX + INCX
329: 130 CONTINUE
330: IF (NOUNIT) TEMP = TEMP/DCONJG(AP(KK+J-1))
331: END IF
332: X(JX) = TEMP
333: JX = JX + INCX
334: KK = KK + J
335: 140 CONTINUE
336: END IF
337: ELSE
338: KK = (N* (N+1))/2
339: IF (INCX.EQ.1) THEN
340: DO 170 J = N,1,-1
341: TEMP = X(J)
342: K = KK
343: IF (NOCONJ) THEN
344: DO 150 I = N,J + 1,-1
345: TEMP = TEMP - AP(K)*X(I)
346: K = K - 1
347: 150 CONTINUE
348: IF (NOUNIT) TEMP = TEMP/AP(KK-N+J)
349: ELSE
350: DO 160 I = N,J + 1,-1
351: TEMP = TEMP - DCONJG(AP(K))*X(I)
352: K = K - 1
353: 160 CONTINUE
354: IF (NOUNIT) TEMP = TEMP/DCONJG(AP(KK-N+J))
355: END IF
356: X(J) = TEMP
357: KK = KK - (N-J+1)
358: 170 CONTINUE
359: ELSE
360: KX = KX + (N-1)*INCX
361: JX = KX
362: DO 200 J = N,1,-1
363: TEMP = X(JX)
364: IX = KX
365: IF (NOCONJ) THEN
366: DO 180 K = KK,KK - (N- (J+1)),-1
367: TEMP = TEMP - AP(K)*X(IX)
368: IX = IX - INCX
369: 180 CONTINUE
370: IF (NOUNIT) TEMP = TEMP/AP(KK-N+J)
371: ELSE
372: DO 190 K = KK,KK - (N- (J+1)),-1
373: TEMP = TEMP - DCONJG(AP(K))*X(IX)
374: IX = IX - INCX
375: 190 CONTINUE
376: IF (NOUNIT) TEMP = TEMP/DCONJG(AP(KK-N+J))
377: END IF
378: X(JX) = TEMP
379: JX = JX - INCX
380: KK = KK - (N-J+1)
381: 200 CONTINUE
382: END IF
383: END IF
384: END IF
385: *
386: RETURN
387: *
388: * End of ZTPSV .
389: *
390: END