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1.1 bertrand 1: SUBROUTINE DTRMV(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 PRECISION A(LDA,*),X(*)
8: * ..
9: *
10: * Purpose
11: * =======
12: *
13: * DTRMV performs one of the matrix-vector operations
14: *
15: * x := A*x, or x := A'*x,
16: *
17: * where x is an n element vector and A is an n by n unit, or non-unit,
18: * upper or lower triangular matrix.
19: *
20: * Arguments
21: * ==========
22: *
23: * UPLO - CHARACTER*1.
24: * On entry, UPLO specifies whether the matrix is an upper or
25: * lower triangular matrix as follows:
26: *
27: * UPLO = 'U' or 'u' A is an upper triangular matrix.
28: *
29: * UPLO = 'L' or 'l' A is a lower triangular matrix.
30: *
31: * Unchanged on exit.
32: *
33: * TRANS - CHARACTER*1.
34: * On entry, TRANS specifies the operation to be performed as
35: * follows:
36: *
37: * TRANS = 'N' or 'n' x := A*x.
38: *
39: * TRANS = 'T' or 't' x := A'*x.
40: *
41: * TRANS = 'C' or 'c' x := A'*x.
42: *
43: * Unchanged on exit.
44: *
45: * DIAG - CHARACTER*1.
46: * On entry, DIAG specifies whether or not A is unit
47: * triangular as follows:
48: *
49: * DIAG = 'U' or 'u' A is assumed to be unit triangular.
50: *
51: * DIAG = 'N' or 'n' A is not assumed to be unit
52: * triangular.
53: *
54: * Unchanged on exit.
55: *
56: * N - INTEGER.
57: * On entry, N specifies the order of the matrix A.
58: * N must be at least zero.
59: * Unchanged on exit.
60: *
61: * A - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
62: * Before entry with UPLO = 'U' or 'u', the leading n by n
63: * upper triangular part of the array A must contain the upper
64: * triangular matrix and the strictly lower triangular part of
65: * A is not referenced.
66: * Before entry with UPLO = 'L' or 'l', the leading n by n
67: * lower triangular part of the array A must contain the lower
68: * triangular matrix and the strictly upper triangular part of
69: * A is not referenced.
70: * Note that when DIAG = 'U' or 'u', the diagonal elements of
71: * A are not referenced either, but are assumed to be unity.
72: * Unchanged on exit.
73: *
74: * LDA - INTEGER.
75: * On entry, LDA specifies the first dimension of A as declared
76: * in the calling (sub) program. LDA must be at least
77: * max( 1, n ).
78: * Unchanged on exit.
79: *
80: * X - DOUBLE PRECISION array of dimension at least
81: * ( 1 + ( n - 1 )*abs( INCX ) ).
82: * Before entry, the incremented array X must contain the n
83: * element vector x. On exit, X is overwritten with the
84: * tranformed 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 PRECISION ZERO
106: PARAMETER (ZERO=0.0D+0)
107: * ..
108: * .. Local Scalars ..
109: DOUBLE PRECISION TEMP
110: INTEGER I,INFO,IX,J,JX,KX
111: LOGICAL NOUNIT
112: * ..
113: * .. External Functions ..
114: LOGICAL LSAME
115: EXTERNAL LSAME
116: * ..
117: * .. External Subroutines ..
118: EXTERNAL XERBLA
119: * ..
120: * .. Intrinsic Functions ..
121: INTRINSIC MAX
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 (LDA.LT.MAX(1,N)) THEN
137: INFO = 6
138: ELSE IF (INCX.EQ.0) THEN
139: INFO = 8
140: END IF
141: IF (INFO.NE.0) THEN
142: CALL XERBLA('DTRMV ',INFO)
143: RETURN
144: END IF
145: *
146: * Quick return if possible.
147: *
148: IF (N.EQ.0) RETURN
149: *
150: NOUNIT = LSAME(DIAG,'N')
151: *
152: * Set up the start point in X if the increment is not unity. This
153: * will be ( N - 1 )*INCX too small for descending loops.
154: *
155: IF (INCX.LE.0) THEN
156: KX = 1 - (N-1)*INCX
157: ELSE IF (INCX.NE.1) THEN
158: KX = 1
159: END IF
160: *
161: * Start the operations. In this version the elements of A are
162: * accessed sequentially with one pass through A.
163: *
164: IF (LSAME(TRANS,'N')) THEN
165: *
166: * Form x := A*x.
167: *
168: IF (LSAME(UPLO,'U')) THEN
169: IF (INCX.EQ.1) THEN
170: DO 20 J = 1,N
171: IF (X(J).NE.ZERO) THEN
172: TEMP = X(J)
173: DO 10 I = 1,J - 1
174: X(I) = X(I) + TEMP*A(I,J)
175: 10 CONTINUE
176: IF (NOUNIT) X(J) = X(J)*A(J,J)
177: END IF
178: 20 CONTINUE
179: ELSE
180: JX = KX
181: DO 40 J = 1,N
182: IF (X(JX).NE.ZERO) THEN
183: TEMP = X(JX)
184: IX = KX
185: DO 30 I = 1,J - 1
186: X(IX) = X(IX) + TEMP*A(I,J)
187: IX = IX + INCX
188: 30 CONTINUE
189: IF (NOUNIT) X(JX) = X(JX)*A(J,J)
190: END IF
191: JX = JX + INCX
192: 40 CONTINUE
193: END IF
194: ELSE
195: IF (INCX.EQ.1) THEN
196: DO 60 J = N,1,-1
197: IF (X(J).NE.ZERO) THEN
198: TEMP = X(J)
199: DO 50 I = N,J + 1,-1
200: X(I) = X(I) + TEMP*A(I,J)
201: 50 CONTINUE
202: IF (NOUNIT) X(J) = X(J)*A(J,J)
203: END IF
204: 60 CONTINUE
205: ELSE
206: KX = KX + (N-1)*INCX
207: JX = KX
208: DO 80 J = N,1,-1
209: IF (X(JX).NE.ZERO) THEN
210: TEMP = X(JX)
211: IX = KX
212: DO 70 I = N,J + 1,-1
213: X(IX) = X(IX) + TEMP*A(I,J)
214: IX = IX - INCX
215: 70 CONTINUE
216: IF (NOUNIT) X(JX) = X(JX)*A(J,J)
217: END IF
218: JX = JX - INCX
219: 80 CONTINUE
220: END IF
221: END IF
222: ELSE
223: *
224: * Form x := A'*x.
225: *
226: IF (LSAME(UPLO,'U')) THEN
227: IF (INCX.EQ.1) THEN
228: DO 100 J = N,1,-1
229: TEMP = X(J)
230: IF (NOUNIT) TEMP = TEMP*A(J,J)
231: DO 90 I = J - 1,1,-1
232: TEMP = TEMP + A(I,J)*X(I)
233: 90 CONTINUE
234: X(J) = TEMP
235: 100 CONTINUE
236: ELSE
237: JX = KX + (N-1)*INCX
238: DO 120 J = N,1,-1
239: TEMP = X(JX)
240: IX = JX
241: IF (NOUNIT) TEMP = TEMP*A(J,J)
242: DO 110 I = J - 1,1,-1
243: IX = IX - INCX
244: TEMP = TEMP + A(I,J)*X(IX)
245: 110 CONTINUE
246: X(JX) = TEMP
247: JX = JX - INCX
248: 120 CONTINUE
249: END IF
250: ELSE
251: IF (INCX.EQ.1) THEN
252: DO 140 J = 1,N
253: TEMP = X(J)
254: IF (NOUNIT) TEMP = TEMP*A(J,J)
255: DO 130 I = J + 1,N
256: TEMP = TEMP + A(I,J)*X(I)
257: 130 CONTINUE
258: X(J) = TEMP
259: 140 CONTINUE
260: ELSE
261: JX = KX
262: DO 160 J = 1,N
263: TEMP = X(JX)
264: IX = JX
265: IF (NOUNIT) TEMP = TEMP*A(J,J)
266: DO 150 I = J + 1,N
267: IX = IX + INCX
268: TEMP = TEMP + A(I,J)*X(IX)
269: 150 CONTINUE
270: X(JX) = TEMP
271: JX = JX + INCX
272: 160 CONTINUE
273: END IF
274: END IF
275: END IF
276: *
277: RETURN
278: *
279: * End of DTRMV .
280: *
281: END