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1.1 bertrand 1: SUBROUTINE ZTPSV(UPLO,TRANS,DIAG,N,AP,X,INCX)
2: * .. Scalar Arguments ..
3: INTEGER INCX,N
4: CHARACTER DIAG,TRANS,UPLO
5: * ..
6: * .. Array Arguments ..
7: DOUBLE COMPLEX AP(*),X(*)
8: * ..
9: *
10: * Purpose
11: * =======
12: *
13: * ZTPSV solves one of the systems of equations
14: *
15: * A*x = b, or A'*x = b, or conjg( A' )*x = b,
16: *
17: * where b and x are n element vectors and A is an n by n unit, or
18: * non-unit, upper or lower triangular matrix, supplied in packed form.
19: *
20: * No test for singularity or near-singularity is included in this
21: * routine. Such tests must be performed before calling this routine.
22: *
23: * Arguments
24: * ==========
25: *
26: * UPLO - CHARACTER*1.
27: * On entry, UPLO specifies whether the matrix is an upper or
28: * lower triangular matrix as follows:
29: *
30: * UPLO = 'U' or 'u' A is an upper triangular matrix.
31: *
32: * UPLO = 'L' or 'l' A is a lower triangular matrix.
33: *
34: * Unchanged on exit.
35: *
36: * TRANS - CHARACTER*1.
37: * On entry, TRANS specifies the equations to be solved as
38: * follows:
39: *
40: * TRANS = 'N' or 'n' A*x = b.
41: *
42: * TRANS = 'T' or 't' A'*x = b.
43: *
44: * TRANS = 'C' or 'c' conjg( A' )*x = b.
45: *
46: * Unchanged on exit.
47: *
48: * DIAG - CHARACTER*1.
49: * On entry, DIAG specifies whether or not A is unit
50: * triangular as follows:
51: *
52: * DIAG = 'U' or 'u' A is assumed to be unit triangular.
53: *
54: * DIAG = 'N' or 'n' A is not assumed to be unit
55: * triangular.
56: *
57: * Unchanged on exit.
58: *
59: * N - INTEGER.
60: * On entry, N specifies the order of the matrix A.
61: * N must be at least zero.
62: * Unchanged on exit.
63: *
64: * AP - COMPLEX*16 array of DIMENSION at least
65: * ( ( n*( n + 1 ) )/2 ).
66: * Before entry with UPLO = 'U' or 'u', the array AP must
67: * contain the upper triangular matrix packed sequentially,
68: * column by column, so that AP( 1 ) contains a( 1, 1 ),
69: * AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )
70: * respectively, and so on.
71: * Before entry with UPLO = 'L' or 'l', the array AP must
72: * contain the lower triangular matrix packed sequentially,
73: * column by column, so that AP( 1 ) contains a( 1, 1 ),
74: * AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )
75: * respectively, and so on.
76: * Note that when DIAG = 'U' or 'u', the diagonal elements of
77: * A are not referenced, but are assumed to be unity.
78: * Unchanged on exit.
79: *
80: * X - COMPLEX*16 array of dimension at least
81: * ( 1 + ( n - 1 )*abs( INCX ) ).
82: * Before entry, the incremented array X must contain the n
83: * element right-hand side vector b. On exit, X is overwritten
84: * with the solution vector x.
85: *
86: * INCX - INTEGER.
87: * On entry, INCX specifies the increment for the elements of
88: * X. INCX must not be zero.
89: * Unchanged on exit.
90: *
91: * Further Details
92: * ===============
93: *
94: * Level 2 Blas routine.
95: *
96: * -- Written on 22-October-1986.
97: * Jack Dongarra, Argonne National Lab.
98: * Jeremy Du Croz, Nag Central Office.
99: * Sven Hammarling, Nag Central Office.
100: * Richard Hanson, Sandia National Labs.
101: *
102: * =====================================================================
103: *
104: * .. Parameters ..
105: DOUBLE COMPLEX ZERO
106: PARAMETER (ZERO= (0.0D+0,0.0D+0))
107: * ..
108: * .. Local Scalars ..
109: DOUBLE COMPLEX TEMP
110: INTEGER I,INFO,IX,J,JX,K,KK,KX
111: LOGICAL NOCONJ,NOUNIT
112: * ..
113: * .. External Functions ..
114: LOGICAL LSAME
115: EXTERNAL LSAME
116: * ..
117: * .. External Subroutines ..
118: EXTERNAL XERBLA
119: * ..
120: * .. Intrinsic Functions ..
121: INTRINSIC DCONJG
122: * ..
123: *
124: * Test the input parameters.
125: *
126: INFO = 0
127: IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
128: INFO = 1
129: ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
130: + .NOT.LSAME(TRANS,'C')) THEN
131: INFO = 2
132: ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
133: INFO = 3
134: ELSE IF (N.LT.0) THEN
135: INFO = 4
136: ELSE IF (INCX.EQ.0) THEN
137: INFO = 7
138: END IF
139: IF (INFO.NE.0) THEN
140: CALL XERBLA('ZTPSV ',INFO)
141: RETURN
142: END IF
143: *
144: * Quick return if possible.
145: *
146: IF (N.EQ.0) RETURN
147: *
148: NOCONJ = LSAME(TRANS,'T')
149: NOUNIT = LSAME(DIAG,'N')
150: *
151: * Set up the start point in X if the increment is not unity. This
152: * will be ( N - 1 )*INCX too small for descending loops.
153: *
154: IF (INCX.LE.0) THEN
155: KX = 1 - (N-1)*INCX
156: ELSE IF (INCX.NE.1) THEN
157: KX = 1
158: END IF
159: *
160: * Start the operations. In this version the elements of AP are
161: * accessed sequentially with one pass through AP.
162: *
163: IF (LSAME(TRANS,'N')) THEN
164: *
165: * Form x := inv( A )*x.
166: *
167: IF (LSAME(UPLO,'U')) THEN
168: KK = (N* (N+1))/2
169: IF (INCX.EQ.1) THEN
170: DO 20 J = N,1,-1
171: IF (X(J).NE.ZERO) THEN
172: IF (NOUNIT) X(J) = X(J)/AP(KK)
173: TEMP = X(J)
174: K = KK - 1
175: DO 10 I = J - 1,1,-1
176: X(I) = X(I) - TEMP*AP(K)
177: K = K - 1
178: 10 CONTINUE
179: END IF
180: KK = KK - J
181: 20 CONTINUE
182: ELSE
183: JX = KX + (N-1)*INCX
184: DO 40 J = N,1,-1
185: IF (X(JX).NE.ZERO) THEN
186: IF (NOUNIT) X(JX) = X(JX)/AP(KK)
187: TEMP = X(JX)
188: IX = JX
189: DO 30 K = KK - 1,KK - J + 1,-1
190: IX = IX - INCX
191: X(IX) = X(IX) - TEMP*AP(K)
192: 30 CONTINUE
193: END IF
194: JX = JX - INCX
195: KK = KK - J
196: 40 CONTINUE
197: END IF
198: ELSE
199: KK = 1
200: IF (INCX.EQ.1) THEN
201: DO 60 J = 1,N
202: IF (X(J).NE.ZERO) THEN
203: IF (NOUNIT) X(J) = X(J)/AP(KK)
204: TEMP = X(J)
205: K = KK + 1
206: DO 50 I = J + 1,N
207: X(I) = X(I) - TEMP*AP(K)
208: K = K + 1
209: 50 CONTINUE
210: END IF
211: KK = KK + (N-J+1)
212: 60 CONTINUE
213: ELSE
214: JX = KX
215: DO 80 J = 1,N
216: IF (X(JX).NE.ZERO) THEN
217: IF (NOUNIT) X(JX) = X(JX)/AP(KK)
218: TEMP = X(JX)
219: IX = JX
220: DO 70 K = KK + 1,KK + N - J
221: IX = IX + INCX
222: X(IX) = X(IX) - TEMP*AP(K)
223: 70 CONTINUE
224: END IF
225: JX = JX + INCX
226: KK = KK + (N-J+1)
227: 80 CONTINUE
228: END IF
229: END IF
230: ELSE
231: *
232: * Form x := inv( A' )*x or x := inv( conjg( A' ) )*x.
233: *
234: IF (LSAME(UPLO,'U')) THEN
235: KK = 1
236: IF (INCX.EQ.1) THEN
237: DO 110 J = 1,N
238: TEMP = X(J)
239: K = KK
240: IF (NOCONJ) THEN
241: DO 90 I = 1,J - 1
242: TEMP = TEMP - AP(K)*X(I)
243: K = K + 1
244: 90 CONTINUE
245: IF (NOUNIT) TEMP = TEMP/AP(KK+J-1)
246: ELSE
247: DO 100 I = 1,J - 1
248: TEMP = TEMP - DCONJG(AP(K))*X(I)
249: K = K + 1
250: 100 CONTINUE
251: IF (NOUNIT) TEMP = TEMP/DCONJG(AP(KK+J-1))
252: END IF
253: X(J) = TEMP
254: KK = KK + J
255: 110 CONTINUE
256: ELSE
257: JX = KX
258: DO 140 J = 1,N
259: TEMP = X(JX)
260: IX = KX
261: IF (NOCONJ) THEN
262: DO 120 K = KK,KK + J - 2
263: TEMP = TEMP - AP(K)*X(IX)
264: IX = IX + INCX
265: 120 CONTINUE
266: IF (NOUNIT) TEMP = TEMP/AP(KK+J-1)
267: ELSE
268: DO 130 K = KK,KK + J - 2
269: TEMP = TEMP - DCONJG(AP(K))*X(IX)
270: IX = IX + INCX
271: 130 CONTINUE
272: IF (NOUNIT) TEMP = TEMP/DCONJG(AP(KK+J-1))
273: END IF
274: X(JX) = TEMP
275: JX = JX + INCX
276: KK = KK + J
277: 140 CONTINUE
278: END IF
279: ELSE
280: KK = (N* (N+1))/2
281: IF (INCX.EQ.1) THEN
282: DO 170 J = N,1,-1
283: TEMP = X(J)
284: K = KK
285: IF (NOCONJ) THEN
286: DO 150 I = N,J + 1,-1
287: TEMP = TEMP - AP(K)*X(I)
288: K = K - 1
289: 150 CONTINUE
290: IF (NOUNIT) TEMP = TEMP/AP(KK-N+J)
291: ELSE
292: DO 160 I = N,J + 1,-1
293: TEMP = TEMP - DCONJG(AP(K))*X(I)
294: K = K - 1
295: 160 CONTINUE
296: IF (NOUNIT) TEMP = TEMP/DCONJG(AP(KK-N+J))
297: END IF
298: X(J) = TEMP
299: KK = KK - (N-J+1)
300: 170 CONTINUE
301: ELSE
302: KX = KX + (N-1)*INCX
303: JX = KX
304: DO 200 J = N,1,-1
305: TEMP = X(JX)
306: IX = KX
307: IF (NOCONJ) THEN
308: DO 180 K = KK,KK - (N- (J+1)),-1
309: TEMP = TEMP - AP(K)*X(IX)
310: IX = IX - INCX
311: 180 CONTINUE
312: IF (NOUNIT) TEMP = TEMP/AP(KK-N+J)
313: ELSE
314: DO 190 K = KK,KK - (N- (J+1)),-1
315: TEMP = TEMP - DCONJG(AP(K))*X(IX)
316: IX = IX - INCX
317: 190 CONTINUE
318: IF (NOUNIT) TEMP = TEMP/DCONJG(AP(KK-N+J))
319: END IF
320: X(JX) = TEMP
321: JX = JX - INCX
322: KK = KK - (N-J+1)
323: 200 CONTINUE
324: END IF
325: END IF
326: END IF
327: *
328: RETURN
329: *
330: * End of ZTPSV .
331: *
332: END