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