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1.1 bertrand 1: SUBROUTINE ZTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
2: * .. Scalar Arguments ..
3: INTEGER INCX,LDA,N
4: CHARACTER DIAG,TRANS,UPLO
5: * ..
6: * .. Array Arguments ..
7: DOUBLE COMPLEX A(LDA,*),X(*)
8: * ..
9: *
10: * Purpose
11: * =======
12: *
13: * ZTRSV solves one of the systems of equations
14: *
1.7 ! bertrand 15: * A*x = b, or A**T*x = b, or A**H*x = b,
1.1 bertrand 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.
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: *
1.7 ! bertrand 42: * TRANS = 'T' or 't' A**T*x = b.
1.1 bertrand 43: *
1.7 ! bertrand 44: * TRANS = 'C' or 'c' A**H*x = b.
1.1 bertrand 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: * A - COMPLEX*16 array of DIMENSION ( LDA, n ).
65: * Before entry with UPLO = 'U' or 'u', the leading n by n
66: * upper triangular part of the array A must contain the upper
67: * triangular matrix and the strictly lower triangular part of
68: * A is not referenced.
69: * Before entry with UPLO = 'L' or 'l', the leading n by n
70: * lower triangular part of the array A must contain the lower
71: * triangular matrix and the strictly upper triangular part of
72: * A is not referenced.
73: * Note that when DIAG = 'U' or 'u', the diagonal elements of
74: * A are not referenced either, but are assumed to be unity.
75: * Unchanged on exit.
76: *
77: * LDA - INTEGER.
78: * On entry, LDA specifies the first dimension of A as declared
79: * in the calling (sub) program. LDA must be at least
80: * max( 1, n ).
81: * Unchanged on exit.
82: *
83: * X - COMPLEX*16 array of dimension at least
84: * ( 1 + ( n - 1 )*abs( INCX ) ).
85: * Before entry, the incremented array X must contain the n
86: * element right-hand side vector b. On exit, X is overwritten
87: * with the solution vector x.
88: *
89: * INCX - INTEGER.
90: * On entry, INCX specifies the increment for the elements of
91: * X. INCX must not be zero.
92: * Unchanged on exit.
93: *
94: * Further Details
95: * ===============
96: *
97: * Level 2 Blas routine.
98: *
99: * -- Written on 22-October-1986.
100: * Jack Dongarra, Argonne National Lab.
101: * Jeremy Du Croz, Nag Central Office.
102: * Sven Hammarling, Nag Central Office.
103: * Richard Hanson, Sandia National Labs.
104: *
105: * =====================================================================
106: *
107: * .. Parameters ..
108: DOUBLE COMPLEX ZERO
109: PARAMETER (ZERO= (0.0D+0,0.0D+0))
110: * ..
111: * .. Local Scalars ..
112: DOUBLE COMPLEX TEMP
113: INTEGER I,INFO,IX,J,JX,KX
114: LOGICAL NOCONJ,NOUNIT
115: * ..
116: * .. External Functions ..
117: LOGICAL LSAME
118: EXTERNAL LSAME
119: * ..
120: * .. External Subroutines ..
121: EXTERNAL XERBLA
122: * ..
123: * .. Intrinsic Functions ..
124: INTRINSIC DCONJG,MAX
125: * ..
126: *
127: * Test the input parameters.
128: *
129: INFO = 0
130: IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
131: INFO = 1
132: ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
133: + .NOT.LSAME(TRANS,'C')) THEN
134: INFO = 2
135: ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
136: INFO = 3
137: ELSE IF (N.LT.0) THEN
138: INFO = 4
139: ELSE IF (LDA.LT.MAX(1,N)) THEN
140: INFO = 6
141: ELSE IF (INCX.EQ.0) THEN
142: INFO = 8
143: END IF
144: IF (INFO.NE.0) THEN
145: CALL XERBLA('ZTRSV ',INFO)
146: RETURN
147: END IF
148: *
149: * Quick return if possible.
150: *
151: IF (N.EQ.0) RETURN
152: *
153: NOCONJ = LSAME(TRANS,'T')
154: NOUNIT = LSAME(DIAG,'N')
155: *
156: * Set up the start point in X if the increment is not unity. This
157: * will be ( N - 1 )*INCX too small for descending loops.
158: *
159: IF (INCX.LE.0) THEN
160: KX = 1 - (N-1)*INCX
161: ELSE IF (INCX.NE.1) THEN
162: KX = 1
163: END IF
164: *
165: * Start the operations. In this version the elements of A are
166: * accessed sequentially with one pass through A.
167: *
168: IF (LSAME(TRANS,'N')) THEN
169: *
170: * Form x := inv( A )*x.
171: *
172: IF (LSAME(UPLO,'U')) THEN
173: IF (INCX.EQ.1) THEN
174: DO 20 J = N,1,-1
175: IF (X(J).NE.ZERO) THEN
176: IF (NOUNIT) X(J) = X(J)/A(J,J)
177: TEMP = X(J)
178: DO 10 I = J - 1,1,-1
179: X(I) = X(I) - TEMP*A(I,J)
180: 10 CONTINUE
181: END IF
182: 20 CONTINUE
183: ELSE
184: JX = KX + (N-1)*INCX
185: DO 40 J = N,1,-1
186: IF (X(JX).NE.ZERO) THEN
187: IF (NOUNIT) X(JX) = X(JX)/A(J,J)
188: TEMP = X(JX)
189: IX = JX
190: DO 30 I = J - 1,1,-1
191: IX = IX - INCX
192: X(IX) = X(IX) - TEMP*A(I,J)
193: 30 CONTINUE
194: END IF
195: JX = JX - INCX
196: 40 CONTINUE
197: END IF
198: ELSE
199: IF (INCX.EQ.1) THEN
200: DO 60 J = 1,N
201: IF (X(J).NE.ZERO) THEN
202: IF (NOUNIT) X(J) = X(J)/A(J,J)
203: TEMP = X(J)
204: DO 50 I = J + 1,N
205: X(I) = X(I) - TEMP*A(I,J)
206: 50 CONTINUE
207: END IF
208: 60 CONTINUE
209: ELSE
210: JX = KX
211: DO 80 J = 1,N
212: IF (X(JX).NE.ZERO) THEN
213: IF (NOUNIT) X(JX) = X(JX)/A(J,J)
214: TEMP = X(JX)
215: IX = JX
216: DO 70 I = J + 1,N
217: IX = IX + INCX
218: X(IX) = X(IX) - TEMP*A(I,J)
219: 70 CONTINUE
220: END IF
221: JX = JX + INCX
222: 80 CONTINUE
223: END IF
224: END IF
225: ELSE
226: *
1.7 ! bertrand 227: * Form x := inv( A**T )*x or x := inv( A**H )*x.
1.1 bertrand 228: *
229: IF (LSAME(UPLO,'U')) THEN
230: IF (INCX.EQ.1) THEN
231: DO 110 J = 1,N
232: TEMP = X(J)
233: IF (NOCONJ) THEN
234: DO 90 I = 1,J - 1
235: TEMP = TEMP - A(I,J)*X(I)
236: 90 CONTINUE
237: IF (NOUNIT) TEMP = TEMP/A(J,J)
238: ELSE
239: DO 100 I = 1,J - 1
240: TEMP = TEMP - DCONJG(A(I,J))*X(I)
241: 100 CONTINUE
242: IF (NOUNIT) TEMP = TEMP/DCONJG(A(J,J))
243: END IF
244: X(J) = TEMP
245: 110 CONTINUE
246: ELSE
247: JX = KX
248: DO 140 J = 1,N
249: IX = KX
250: TEMP = X(JX)
251: IF (NOCONJ) THEN
252: DO 120 I = 1,J - 1
253: TEMP = TEMP - A(I,J)*X(IX)
254: IX = IX + INCX
255: 120 CONTINUE
256: IF (NOUNIT) TEMP = TEMP/A(J,J)
257: ELSE
258: DO 130 I = 1,J - 1
259: TEMP = TEMP - DCONJG(A(I,J))*X(IX)
260: IX = IX + INCX
261: 130 CONTINUE
262: IF (NOUNIT) TEMP = TEMP/DCONJG(A(J,J))
263: END IF
264: X(JX) = TEMP
265: JX = JX + INCX
266: 140 CONTINUE
267: END IF
268: ELSE
269: IF (INCX.EQ.1) THEN
270: DO 170 J = N,1,-1
271: TEMP = X(J)
272: IF (NOCONJ) THEN
273: DO 150 I = N,J + 1,-1
274: TEMP = TEMP - A(I,J)*X(I)
275: 150 CONTINUE
276: IF (NOUNIT) TEMP = TEMP/A(J,J)
277: ELSE
278: DO 160 I = N,J + 1,-1
279: TEMP = TEMP - DCONJG(A(I,J))*X(I)
280: 160 CONTINUE
281: IF (NOUNIT) TEMP = TEMP/DCONJG(A(J,J))
282: END IF
283: X(J) = TEMP
284: 170 CONTINUE
285: ELSE
286: KX = KX + (N-1)*INCX
287: JX = KX
288: DO 200 J = N,1,-1
289: IX = KX
290: TEMP = X(JX)
291: IF (NOCONJ) THEN
292: DO 180 I = N,J + 1,-1
293: TEMP = TEMP - A(I,J)*X(IX)
294: IX = IX - INCX
295: 180 CONTINUE
296: IF (NOUNIT) TEMP = TEMP/A(J,J)
297: ELSE
298: DO 190 I = N,J + 1,-1
299: TEMP = TEMP - DCONJG(A(I,J))*X(IX)
300: IX = IX - INCX
301: 190 CONTINUE
302: IF (NOUNIT) TEMP = TEMP/DCONJG(A(J,J))
303: END IF
304: X(JX) = TEMP
305: JX = JX - INCX
306: 200 CONTINUE
307: END IF
308: END IF
309: END IF
310: *
311: RETURN
312: *
313: * End of ZTRSV .
314: *
315: END