1: *> \brief \b ZTRMV
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: * Definition:
9: * ===========
10: *
11: * SUBROUTINE ZTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
12: *
13: * .. Scalar Arguments ..
14: * INTEGER INCX,LDA,N
15: * CHARACTER DIAG,TRANS,UPLO
16: * ..
17: * .. Array Arguments ..
18: * COMPLEX*16 A(LDA,*),X(*)
19: * ..
20: *
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
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] A
82: *> \verbatim
83: *> A is COMPLEX*16 array, dimension ( LDA, N ).
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: *>
104: *> \param[in,out] X
105: *> \verbatim
106: *> X is COMPLEX*16 array, dimension at least
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
110: *> transformed vector x.
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: *
123: *> \author Univ. of Tennessee
124: *> \author Univ. of California Berkeley
125: *> \author Univ. of Colorado Denver
126: *> \author NAG Ltd.
127: *
128: *> \date December 2016
129: *
130: *> \ingroup complex16_blas_level2
131: *
132: *> \par Further Details:
133: * =====================
134: *>
135: *> \verbatim
136: *>
137: *> Level 2 Blas routine.
138: *> The vector and matrix arguments are not referenced when N = 0, or M = 0
139: *>
140: *> -- Written on 22-October-1986.
141: *> Jack Dongarra, Argonne National Lab.
142: *> Jeremy Du Croz, Nag Central Office.
143: *> Sven Hammarling, Nag Central Office.
144: *> Richard Hanson, Sandia National Labs.
145: *> \endverbatim
146: *>
147: * =====================================================================
148: SUBROUTINE ZTRMV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX)
149: *
150: * -- Reference BLAS level2 routine (version 3.7.0) --
151: * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
152: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
153: * December 2016
154: *
155: * .. Scalar Arguments ..
156: INTEGER INCX,LDA,N
157: CHARACTER DIAG,TRANS,UPLO
158: * ..
159: * .. Array Arguments ..
160: COMPLEX*16 A(LDA,*),X(*)
161: * ..
162: *
163: * =====================================================================
164: *
165: * .. Parameters ..
166: COMPLEX*16 ZERO
167: PARAMETER (ZERO= (0.0D+0,0.0D+0))
168: * ..
169: * .. Local Scalars ..
170: COMPLEX*16 TEMP
171: INTEGER I,INFO,IX,J,JX,KX
172: LOGICAL NOCONJ,NOUNIT
173: * ..
174: * .. External Functions ..
175: LOGICAL LSAME
176: EXTERNAL LSAME
177: * ..
178: * .. External Subroutines ..
179: EXTERNAL XERBLA
180: * ..
181: * .. Intrinsic Functions ..
182: INTRINSIC DCONJG,MAX
183: * ..
184: *
185: * Test the input parameters.
186: *
187: INFO = 0
188: IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
189: INFO = 1
190: ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
191: + .NOT.LSAME(TRANS,'C')) THEN
192: INFO = 2
193: ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
194: INFO = 3
195: ELSE IF (N.LT.0) THEN
196: INFO = 4
197: ELSE IF (LDA.LT.MAX(1,N)) THEN
198: INFO = 6
199: ELSE IF (INCX.EQ.0) THEN
200: INFO = 8
201: END IF
202: IF (INFO.NE.0) THEN
203: CALL XERBLA('ZTRMV ',INFO)
204: RETURN
205: END IF
206: *
207: * Quick return if possible.
208: *
209: IF (N.EQ.0) RETURN
210: *
211: NOCONJ = LSAME(TRANS,'T')
212: NOUNIT = LSAME(DIAG,'N')
213: *
214: * Set up the start point in X if the increment is not unity. This
215: * will be ( N - 1 )*INCX too small for descending loops.
216: *
217: IF (INCX.LE.0) THEN
218: KX = 1 - (N-1)*INCX
219: ELSE IF (INCX.NE.1) THEN
220: KX = 1
221: END IF
222: *
223: * Start the operations. In this version the elements of A are
224: * accessed sequentially with one pass through A.
225: *
226: IF (LSAME(TRANS,'N')) THEN
227: *
228: * Form x := A*x.
229: *
230: IF (LSAME(UPLO,'U')) THEN
231: IF (INCX.EQ.1) THEN
232: DO 20 J = 1,N
233: IF (X(J).NE.ZERO) THEN
234: TEMP = X(J)
235: DO 10 I = 1,J - 1
236: X(I) = X(I) + TEMP*A(I,J)
237: 10 CONTINUE
238: IF (NOUNIT) X(J) = X(J)*A(J,J)
239: END IF
240: 20 CONTINUE
241: ELSE
242: JX = KX
243: DO 40 J = 1,N
244: IF (X(JX).NE.ZERO) THEN
245: TEMP = X(JX)
246: IX = KX
247: DO 30 I = 1,J - 1
248: X(IX) = X(IX) + TEMP*A(I,J)
249: IX = IX + INCX
250: 30 CONTINUE
251: IF (NOUNIT) X(JX) = X(JX)*A(J,J)
252: END IF
253: JX = JX + INCX
254: 40 CONTINUE
255: END IF
256: ELSE
257: IF (INCX.EQ.1) THEN
258: DO 60 J = N,1,-1
259: IF (X(J).NE.ZERO) THEN
260: TEMP = X(J)
261: DO 50 I = N,J + 1,-1
262: X(I) = X(I) + TEMP*A(I,J)
263: 50 CONTINUE
264: IF (NOUNIT) X(J) = X(J)*A(J,J)
265: END IF
266: 60 CONTINUE
267: ELSE
268: KX = KX + (N-1)*INCX
269: JX = KX
270: DO 80 J = N,1,-1
271: IF (X(JX).NE.ZERO) THEN
272: TEMP = X(JX)
273: IX = KX
274: DO 70 I = N,J + 1,-1
275: X(IX) = X(IX) + TEMP*A(I,J)
276: IX = IX - INCX
277: 70 CONTINUE
278: IF (NOUNIT) X(JX) = X(JX)*A(J,J)
279: END IF
280: JX = JX - INCX
281: 80 CONTINUE
282: END IF
283: END IF
284: ELSE
285: *
286: * Form x := A**T*x or x := A**H*x.
287: *
288: IF (LSAME(UPLO,'U')) THEN
289: IF (INCX.EQ.1) THEN
290: DO 110 J = N,1,-1
291: TEMP = X(J)
292: IF (NOCONJ) THEN
293: IF (NOUNIT) TEMP = TEMP*A(J,J)
294: DO 90 I = J - 1,1,-1
295: TEMP = TEMP + A(I,J)*X(I)
296: 90 CONTINUE
297: ELSE
298: IF (NOUNIT) TEMP = TEMP*DCONJG(A(J,J))
299: DO 100 I = J - 1,1,-1
300: TEMP = TEMP + DCONJG(A(I,J))*X(I)
301: 100 CONTINUE
302: END IF
303: X(J) = TEMP
304: 110 CONTINUE
305: ELSE
306: JX = KX + (N-1)*INCX
307: DO 140 J = N,1,-1
308: TEMP = X(JX)
309: IX = JX
310: IF (NOCONJ) THEN
311: IF (NOUNIT) TEMP = TEMP*A(J,J)
312: DO 120 I = J - 1,1,-1
313: IX = IX - INCX
314: TEMP = TEMP + A(I,J)*X(IX)
315: 120 CONTINUE
316: ELSE
317: IF (NOUNIT) TEMP = TEMP*DCONJG(A(J,J))
318: DO 130 I = J - 1,1,-1
319: IX = IX - INCX
320: TEMP = TEMP + DCONJG(A(I,J))*X(IX)
321: 130 CONTINUE
322: END IF
323: X(JX) = TEMP
324: JX = JX - INCX
325: 140 CONTINUE
326: END IF
327: ELSE
328: IF (INCX.EQ.1) THEN
329: DO 170 J = 1,N
330: TEMP = X(J)
331: IF (NOCONJ) THEN
332: IF (NOUNIT) TEMP = TEMP*A(J,J)
333: DO 150 I = J + 1,N
334: TEMP = TEMP + A(I,J)*X(I)
335: 150 CONTINUE
336: ELSE
337: IF (NOUNIT) TEMP = TEMP*DCONJG(A(J,J))
338: DO 160 I = J + 1,N
339: TEMP = TEMP + DCONJG(A(I,J))*X(I)
340: 160 CONTINUE
341: END IF
342: X(J) = TEMP
343: 170 CONTINUE
344: ELSE
345: JX = KX
346: DO 200 J = 1,N
347: TEMP = X(JX)
348: IX = JX
349: IF (NOCONJ) THEN
350: IF (NOUNIT) TEMP = TEMP*A(J,J)
351: DO 180 I = J + 1,N
352: IX = IX + INCX
353: TEMP = TEMP + A(I,J)*X(IX)
354: 180 CONTINUE
355: ELSE
356: IF (NOUNIT) TEMP = TEMP*DCONJG(A(J,J))
357: DO 190 I = J + 1,N
358: IX = IX + INCX
359: TEMP = TEMP + DCONJG(A(I,J))*X(IX)
360: 190 CONTINUE
361: END IF
362: X(JX) = TEMP
363: JX = JX + INCX
364: 200 CONTINUE
365: END IF
366: END IF
367: END IF
368: *
369: RETURN
370: *
371: * End of ZTRMV .
372: *
373: END
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