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1.8 bertrand 1: *> \brief \b ZTRMV
1.1 bertrand 2: *
1.8 bertrand 3: * =========== DOCUMENTATION ===========
1.1 bertrand 4: *
1.13 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 ZTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
1.13 bertrand 12: *
1.8 bertrand 13: * .. Scalar Arguments ..
14: * INTEGER INCX,LDA,N
15: * CHARACTER DIAG,TRANS,UPLO
16: * ..
17: * .. Array Arguments ..
18: * COMPLEX*16 A(LDA,*),X(*)
19: * ..
1.13 bertrand 20: *
1.8 bertrand 21: *
22: *> \par Purpose:
23: * =============
24: *>
25: *> \verbatim
26: *>
27: *> ZTRMV 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.
33: *> \endverbatim
1.1 bertrand 34: *
1.8 bertrand 35: * Arguments:
1.1 bertrand 36: * ==========
37: *
1.8 bertrand 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] A
82: *> \verbatim
1.14 bertrand 83: *> A is COMPLEX*16 array, dimension ( LDA, N ).
1.8 bertrand 84: *> Before entry with UPLO = 'U' or 'u', the leading n by n
85: *> upper triangular part of the array A must contain the upper
86: *> triangular matrix and the strictly lower triangular part of
87: *> A is not referenced.
88: *> Before entry with UPLO = 'L' or 'l', the leading n by n
89: *> lower triangular part of the array A must contain the lower
90: *> triangular matrix and the strictly upper triangular part of
91: *> A is not referenced.
92: *> Note that when DIAG = 'U' or 'u', the diagonal elements of
93: *> A are not referenced either, but are assumed to be unity.
94: *> \endverbatim
95: *>
96: *> \param[in] LDA
97: *> \verbatim
98: *> LDA is INTEGER
99: *> On entry, LDA specifies the first dimension of A as declared
100: *> in the calling (sub) program. LDA must be at least
101: *> max( 1, n ).
102: *> \endverbatim
103: *>
1.14 bertrand 104: *> \param[in,out] X
1.8 bertrand 105: *> \verbatim
1.14 bertrand 106: *> X is COMPLEX*16 array, dimension at least
1.8 bertrand 107: *> ( 1 + ( n - 1 )*abs( INCX ) ).
108: *> Before entry, the incremented array X must contain the n
109: *> element vector x. On exit, X is overwritten with the
1.13 bertrand 110: *> transformed vector x.
1.8 bertrand 111: *> \endverbatim
112: *>
113: *> \param[in] INCX
114: *> \verbatim
115: *> INCX is INTEGER
116: *> On entry, INCX specifies the increment for the elements of
117: *> X. INCX must not be zero.
118: *> \endverbatim
119: *
120: * Authors:
121: * ========
122: *
1.13 bertrand 123: *> \author Univ. of Tennessee
124: *> \author Univ. of California Berkeley
125: *> \author Univ. of Colorado Denver
126: *> \author NAG Ltd.
1.8 bertrand 127: *
128: *> \ingroup complex16_blas_level2
129: *
130: *> \par Further Details:
131: * =====================
132: *>
133: *> \verbatim
134: *>
135: *> Level 2 Blas routine.
136: *> The vector and matrix arguments are not referenced when N = 0, or M = 0
137: *>
138: *> -- Written on 22-October-1986.
139: *> Jack Dongarra, Argonne National Lab.
140: *> Jeremy Du Croz, Nag Central Office.
141: *> Sven Hammarling, Nag Central Office.
142: *> Richard Hanson, Sandia National Labs.
143: *> \endverbatim
144: *>
145: * =====================================================================
146: SUBROUTINE ZTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
1.1 bertrand 147: *
1.16 ! bertrand 148: * -- Reference BLAS level2 routine --
1.8 bertrand 149: * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
150: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.1 bertrand 151: *
1.8 bertrand 152: * .. Scalar Arguments ..
153: INTEGER INCX,LDA,N
154: CHARACTER DIAG,TRANS,UPLO
155: * ..
156: * .. Array Arguments ..
157: COMPLEX*16 A(LDA,*),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,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,MAX
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 (LDA.LT.MAX(1,N)) THEN
195: INFO = 6
196: ELSE IF (INCX.EQ.0) THEN
197: INFO = 8
198: END IF
199: IF (INFO.NE.0) THEN
200: CALL XERBLA('ZTRMV ',INFO)
201: RETURN
202: END IF
203: *
204: * Quick return if possible.
205: *
206: IF (N.EQ.0) RETURN
207: *
208: NOCONJ = LSAME(TRANS,'T')
209: NOUNIT = LSAME(DIAG,'N')
210: *
211: * Set up the start point in X if the increment is not unity. This
212: * will be ( N - 1 )*INCX too small for descending loops.
213: *
214: IF (INCX.LE.0) THEN
215: KX = 1 - (N-1)*INCX
216: ELSE IF (INCX.NE.1) THEN
217: KX = 1
218: END IF
219: *
220: * Start the operations. In this version the elements of A are
221: * accessed sequentially with one pass through A.
222: *
223: IF (LSAME(TRANS,'N')) THEN
224: *
225: * Form x := A*x.
226: *
227: IF (LSAME(UPLO,'U')) THEN
228: IF (INCX.EQ.1) THEN
229: DO 20 J = 1,N
230: IF (X(J).NE.ZERO) THEN
231: TEMP = X(J)
232: DO 10 I = 1,J - 1
233: X(I) = X(I) + TEMP*A(I,J)
234: 10 CONTINUE
235: IF (NOUNIT) X(J) = X(J)*A(J,J)
236: END IF
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 I = 1,J - 1
245: X(IX) = X(IX) + TEMP*A(I,J)
246: IX = IX + INCX
247: 30 CONTINUE
248: IF (NOUNIT) X(JX) = X(JX)*A(J,J)
249: END IF
250: JX = JX + INCX
251: 40 CONTINUE
252: END IF
253: ELSE
254: IF (INCX.EQ.1) THEN
255: DO 60 J = N,1,-1
256: IF (X(J).NE.ZERO) THEN
257: TEMP = X(J)
258: DO 50 I = N,J + 1,-1
259: X(I) = X(I) + TEMP*A(I,J)
260: 50 CONTINUE
261: IF (NOUNIT) X(J) = X(J)*A(J,J)
262: END IF
263: 60 CONTINUE
264: ELSE
265: KX = KX + (N-1)*INCX
266: JX = KX
267: DO 80 J = N,1,-1
268: IF (X(JX).NE.ZERO) THEN
269: TEMP = X(JX)
270: IX = KX
271: DO 70 I = N,J + 1,-1
272: X(IX) = X(IX) + TEMP*A(I,J)
273: IX = IX - INCX
274: 70 CONTINUE
275: IF (NOUNIT) X(JX) = X(JX)*A(J,J)
276: END IF
277: JX = JX - INCX
278: 80 CONTINUE
279: END IF
280: END IF
281: ELSE
282: *
1.7 bertrand 283: * Form x := A**T*x or x := A**H*x.
1.1 bertrand 284: *
285: IF (LSAME(UPLO,'U')) THEN
286: IF (INCX.EQ.1) THEN
287: DO 110 J = N,1,-1
288: TEMP = X(J)
289: IF (NOCONJ) THEN
290: IF (NOUNIT) TEMP = TEMP*A(J,J)
291: DO 90 I = J - 1,1,-1
292: TEMP = TEMP + A(I,J)*X(I)
293: 90 CONTINUE
294: ELSE
295: IF (NOUNIT) TEMP = TEMP*DCONJG(A(J,J))
296: DO 100 I = J - 1,1,-1
297: TEMP = TEMP + DCONJG(A(I,J))*X(I)
298: 100 CONTINUE
299: END IF
300: X(J) = TEMP
301: 110 CONTINUE
302: ELSE
303: JX = KX + (N-1)*INCX
304: DO 140 J = N,1,-1
305: TEMP = X(JX)
306: IX = JX
307: IF (NOCONJ) THEN
308: IF (NOUNIT) TEMP = TEMP*A(J,J)
309: DO 120 I = J - 1,1,-1
310: IX = IX - INCX
311: TEMP = TEMP + A(I,J)*X(IX)
312: 120 CONTINUE
313: ELSE
314: IF (NOUNIT) TEMP = TEMP*DCONJG(A(J,J))
315: DO 130 I = J - 1,1,-1
316: IX = IX - INCX
317: TEMP = TEMP + DCONJG(A(I,J))*X(IX)
318: 130 CONTINUE
319: END IF
320: X(JX) = TEMP
321: JX = JX - INCX
322: 140 CONTINUE
323: END IF
324: ELSE
325: IF (INCX.EQ.1) THEN
326: DO 170 J = 1,N
327: TEMP = X(J)
328: IF (NOCONJ) THEN
329: IF (NOUNIT) TEMP = TEMP*A(J,J)
330: DO 150 I = J + 1,N
331: TEMP = TEMP + A(I,J)*X(I)
332: 150 CONTINUE
333: ELSE
334: IF (NOUNIT) TEMP = TEMP*DCONJG(A(J,J))
335: DO 160 I = J + 1,N
336: TEMP = TEMP + DCONJG(A(I,J))*X(I)
337: 160 CONTINUE
338: END IF
339: X(J) = TEMP
340: 170 CONTINUE
341: ELSE
342: JX = KX
343: DO 200 J = 1,N
344: TEMP = X(JX)
345: IX = JX
346: IF (NOCONJ) THEN
347: IF (NOUNIT) TEMP = TEMP*A(J,J)
348: DO 180 I = J + 1,N
349: IX = IX + INCX
350: TEMP = TEMP + A(I,J)*X(IX)
351: 180 CONTINUE
352: ELSE
353: IF (NOUNIT) TEMP = TEMP*DCONJG(A(J,J))
354: DO 190 I = J + 1,N
355: IX = IX + INCX
356: TEMP = TEMP + DCONJG(A(I,J))*X(IX)
357: 190 CONTINUE
358: END IF
359: X(JX) = TEMP
360: JX = JX + INCX
361: 200 CONTINUE
362: END IF
363: END IF
364: END IF
365: *
366: RETURN
367: *
1.16 ! bertrand 368: * End of ZTRMV
1.1 bertrand 369: *
370: END