1 SUBROUTINE CTPMV(UPLO,TRANS,DIAG,N,AP,X,INCX)
2 * .. Scalar Arguments ..
3 INTEGER INCX,N
4 CHARACTER DIAG,TRANS,UPLO
5 * ..
6 * .. Array Arguments ..
7 COMPLEX AP(*),X(*)
8 * ..
9 *
10 * Purpose
11 * =======
12 *
13 * CTPMV performs one of the matrix-vector operations
14 *
15 * x := A*x, or x := A**T*x, or x := A**H*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**T*x.
40 *
41 * TRANS = 'C' or 'c' x := A**H*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 - COMPLEX 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 - COMPLEX 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 * The vector and matrix arguments are not referenced when N = 0, or M = 0
93 *
94 * -- Written on 22-October-1986.
95 * Jack Dongarra, Argonne National Lab.
96 * Jeremy Du Croz, Nag Central Office.
97 * Sven Hammarling, Nag Central Office.
98 * Richard Hanson, Sandia National Labs.
99 *
100 * =====================================================================
101 *
102 * .. Parameters ..
103 COMPLEX ZERO
104 PARAMETER (ZERO= (0.0E+0,0.0E+0))
105 * ..
106 * .. Local Scalars ..
107 COMPLEX TEMP
108 INTEGER I,INFO,IX,J,JX,K,KK,KX
109 LOGICAL NOCONJ,NOUNIT
110 * ..
111 * .. External Functions ..
112 LOGICAL LSAME
113 EXTERNAL LSAME
114 * ..
115 * .. External Subroutines ..
116 EXTERNAL XERBLA
117 * ..
118 * .. Intrinsic Functions ..
119 INTRINSIC CONJG
120 * ..
121 *
122 * Test the input parameters.
123 *
124 INFO = 0
125 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
126 INFO = 1
127 ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
128 + .NOT.LSAME(TRANS,'C')) THEN
129 INFO = 2
130 ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
131 INFO = 3
132 ELSE IF (N.LT.0) THEN
133 INFO = 4
134 ELSE IF (INCX.EQ.0) THEN
135 INFO = 7
136 END IF
137 IF (INFO.NE.0) THEN
138 CALL XERBLA('CTPMV ',INFO)
139 RETURN
140 END IF
141 *
142 * Quick return if possible.
143 *
144 IF (N.EQ.0) RETURN
145 *
146 NOCONJ = LSAME(TRANS,'T')
147 NOUNIT = LSAME(DIAG,'N')
148 *
149 * Set up the start point in X if the increment is not unity. This
150 * will be ( N - 1 )*INCX too small for descending loops.
151 *
152 IF (INCX.LE.0) THEN
153 KX = 1 - (N-1)*INCX
154 ELSE IF (INCX.NE.1) THEN
155 KX = 1
156 END IF
157 *
158 * Start the operations. In this version the elements of AP are
159 * accessed sequentially with one pass through AP.
160 *
161 IF (LSAME(TRANS,'N')) THEN
162 *
163 * Form x:= A*x.
164 *
165 IF (LSAME(UPLO,'U')) THEN
166 KK = 1
167 IF (INCX.EQ.1) THEN
168 DO 20 J = 1,N
169 IF (X(J).NE.ZERO) THEN
170 TEMP = X(J)
171 K = KK
172 DO 10 I = 1,J - 1
173 X(I) = X(I) + TEMP*AP(K)
174 K = K + 1
175 10 CONTINUE
176 IF (NOUNIT) X(J) = X(J)*AP(KK+J-1)
177 END IF
178 KK = KK + J
179 20 CONTINUE
180 ELSE
181 JX = KX
182 DO 40 J = 1,N
183 IF (X(JX).NE.ZERO) THEN
184 TEMP = X(JX)
185 IX = KX
186 DO 30 K = KK,KK + J - 2
187 X(IX) = X(IX) + TEMP*AP(K)
188 IX = IX + INCX
189 30 CONTINUE
190 IF (NOUNIT) X(JX) = X(JX)*AP(KK+J-1)
191 END IF
192 JX = JX + INCX
193 KK = KK + J
194 40 CONTINUE
195 END IF
196 ELSE
197 KK = (N* (N+1))/2
198 IF (INCX.EQ.1) THEN
199 DO 60 J = N,1,-1
200 IF (X(J).NE.ZERO) THEN
201 TEMP = X(J)
202 K = KK
203 DO 50 I = N,J + 1,-1
204 X(I) = X(I) + TEMP*AP(K)
205 K = K - 1
206 50 CONTINUE
207 IF (NOUNIT) X(J) = X(J)*AP(KK-N+J)
208 END IF
209 KK = KK - (N-J+1)
210 60 CONTINUE
211 ELSE
212 KX = KX + (N-1)*INCX
213 JX = KX
214 DO 80 J = N,1,-1
215 IF (X(JX).NE.ZERO) THEN
216 TEMP = X(JX)
217 IX = KX
218 DO 70 K = KK,KK - (N- (J+1)),-1
219 X(IX) = X(IX) + TEMP*AP(K)
220 IX = IX - INCX
221 70 CONTINUE
222 IF (NOUNIT) X(JX) = X(JX)*AP(KK-N+J)
223 END IF
224 JX = JX - INCX
225 KK = KK - (N-J+1)
226 80 CONTINUE
227 END IF
228 END IF
229 ELSE
230 *
231 * Form x := A**T*x or x := A**H*x.
232 *
233 IF (LSAME(UPLO,'U')) THEN
234 KK = (N* (N+1))/2
235 IF (INCX.EQ.1) THEN
236 DO 110 J = N,1,-1
237 TEMP = X(J)
238 K = KK - 1
239 IF (NOCONJ) THEN
240 IF (NOUNIT) TEMP = TEMP*AP(KK)
241 DO 90 I = J - 1,1,-1
242 TEMP = TEMP + AP(K)*X(I)
243 K = K - 1
244 90 CONTINUE
245 ELSE
246 IF (NOUNIT) TEMP = TEMP*CONJG(AP(KK))
247 DO 100 I = J - 1,1,-1
248 TEMP = TEMP + CONJG(AP(K))*X(I)
249 K = K - 1
250 100 CONTINUE
251 END IF
252 X(J) = TEMP
253 KK = KK - J
254 110 CONTINUE
255 ELSE
256 JX = KX + (N-1)*INCX
257 DO 140 J = N,1,-1
258 TEMP = X(JX)
259 IX = JX
260 IF (NOCONJ) THEN
261 IF (NOUNIT) TEMP = TEMP*AP(KK)
262 DO 120 K = KK - 1,KK - J + 1,-1
263 IX = IX - INCX
264 TEMP = TEMP + AP(K)*X(IX)
265 120 CONTINUE
266 ELSE
267 IF (NOUNIT) TEMP = TEMP*CONJG(AP(KK))
268 DO 130 K = KK - 1,KK - J + 1,-1
269 IX = IX - INCX
270 TEMP = TEMP + CONJG(AP(K))*X(IX)
271 130 CONTINUE
272 END IF
273 X(JX) = TEMP
274 JX = JX - INCX
275 KK = KK - J
276 140 CONTINUE
277 END IF
278 ELSE
279 KK = 1
280 IF (INCX.EQ.1) THEN
281 DO 170 J = 1,N
282 TEMP = X(J)
283 K = KK + 1
284 IF (NOCONJ) THEN
285 IF (NOUNIT) TEMP = TEMP*AP(KK)
286 DO 150 I = J + 1,N
287 TEMP = TEMP + AP(K)*X(I)
288 K = K + 1
289 150 CONTINUE
290 ELSE
291 IF (NOUNIT) TEMP = TEMP*CONJG(AP(KK))
292 DO 160 I = J + 1,N
293 TEMP = TEMP + CONJG(AP(K))*X(I)
294 K = K + 1
295 160 CONTINUE
296 END IF
297 X(J) = TEMP
298 KK = KK + (N-J+1)
299 170 CONTINUE
300 ELSE
301 JX = KX
302 DO 200 J = 1,N
303 TEMP = X(JX)
304 IX = JX
305 IF (NOCONJ) THEN
306 IF (NOUNIT) TEMP = TEMP*AP(KK)
307 DO 180 K = KK + 1,KK + N - J
308 IX = IX + INCX
309 TEMP = TEMP + AP(K)*X(IX)
310 180 CONTINUE
311 ELSE
312 IF (NOUNIT) TEMP = TEMP*CONJG(AP(KK))
313 DO 190 K = KK + 1,KK + N - J
314 IX = IX + INCX
315 TEMP = TEMP + CONJG(AP(K))*X(IX)
316 190 CONTINUE
317 END IF
318 X(JX) = TEMP
319 JX = JX + INCX
320 KK = KK + (N-J+1)
321 200 CONTINUE
322 END IF
323 END IF
324 END IF
325 *
326 RETURN
327 *
328 * End of CTPMV .
329 *
330 END
2 * .. Scalar Arguments ..
3 INTEGER INCX,N
4 CHARACTER DIAG,TRANS,UPLO
5 * ..
6 * .. Array Arguments ..
7 COMPLEX AP(*),X(*)
8 * ..
9 *
10 * Purpose
11 * =======
12 *
13 * CTPMV performs one of the matrix-vector operations
14 *
15 * x := A*x, or x := A**T*x, or x := A**H*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**T*x.
40 *
41 * TRANS = 'C' or 'c' x := A**H*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 - COMPLEX 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 - COMPLEX 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 * The vector and matrix arguments are not referenced when N = 0, or M = 0
93 *
94 * -- Written on 22-October-1986.
95 * Jack Dongarra, Argonne National Lab.
96 * Jeremy Du Croz, Nag Central Office.
97 * Sven Hammarling, Nag Central Office.
98 * Richard Hanson, Sandia National Labs.
99 *
100 * =====================================================================
101 *
102 * .. Parameters ..
103 COMPLEX ZERO
104 PARAMETER (ZERO= (0.0E+0,0.0E+0))
105 * ..
106 * .. Local Scalars ..
107 COMPLEX TEMP
108 INTEGER I,INFO,IX,J,JX,K,KK,KX
109 LOGICAL NOCONJ,NOUNIT
110 * ..
111 * .. External Functions ..
112 LOGICAL LSAME
113 EXTERNAL LSAME
114 * ..
115 * .. External Subroutines ..
116 EXTERNAL XERBLA
117 * ..
118 * .. Intrinsic Functions ..
119 INTRINSIC CONJG
120 * ..
121 *
122 * Test the input parameters.
123 *
124 INFO = 0
125 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
126 INFO = 1
127 ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
128 + .NOT.LSAME(TRANS,'C')) THEN
129 INFO = 2
130 ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
131 INFO = 3
132 ELSE IF (N.LT.0) THEN
133 INFO = 4
134 ELSE IF (INCX.EQ.0) THEN
135 INFO = 7
136 END IF
137 IF (INFO.NE.0) THEN
138 CALL XERBLA('CTPMV ',INFO)
139 RETURN
140 END IF
141 *
142 * Quick return if possible.
143 *
144 IF (N.EQ.0) RETURN
145 *
146 NOCONJ = LSAME(TRANS,'T')
147 NOUNIT = LSAME(DIAG,'N')
148 *
149 * Set up the start point in X if the increment is not unity. This
150 * will be ( N - 1 )*INCX too small for descending loops.
151 *
152 IF (INCX.LE.0) THEN
153 KX = 1 - (N-1)*INCX
154 ELSE IF (INCX.NE.1) THEN
155 KX = 1
156 END IF
157 *
158 * Start the operations. In this version the elements of AP are
159 * accessed sequentially with one pass through AP.
160 *
161 IF (LSAME(TRANS,'N')) THEN
162 *
163 * Form x:= A*x.
164 *
165 IF (LSAME(UPLO,'U')) THEN
166 KK = 1
167 IF (INCX.EQ.1) THEN
168 DO 20 J = 1,N
169 IF (X(J).NE.ZERO) THEN
170 TEMP = X(J)
171 K = KK
172 DO 10 I = 1,J - 1
173 X(I) = X(I) + TEMP*AP(K)
174 K = K + 1
175 10 CONTINUE
176 IF (NOUNIT) X(J) = X(J)*AP(KK+J-1)
177 END IF
178 KK = KK + J
179 20 CONTINUE
180 ELSE
181 JX = KX
182 DO 40 J = 1,N
183 IF (X(JX).NE.ZERO) THEN
184 TEMP = X(JX)
185 IX = KX
186 DO 30 K = KK,KK + J - 2
187 X(IX) = X(IX) + TEMP*AP(K)
188 IX = IX + INCX
189 30 CONTINUE
190 IF (NOUNIT) X(JX) = X(JX)*AP(KK+J-1)
191 END IF
192 JX = JX + INCX
193 KK = KK + J
194 40 CONTINUE
195 END IF
196 ELSE
197 KK = (N* (N+1))/2
198 IF (INCX.EQ.1) THEN
199 DO 60 J = N,1,-1
200 IF (X(J).NE.ZERO) THEN
201 TEMP = X(J)
202 K = KK
203 DO 50 I = N,J + 1,-1
204 X(I) = X(I) + TEMP*AP(K)
205 K = K - 1
206 50 CONTINUE
207 IF (NOUNIT) X(J) = X(J)*AP(KK-N+J)
208 END IF
209 KK = KK - (N-J+1)
210 60 CONTINUE
211 ELSE
212 KX = KX + (N-1)*INCX
213 JX = KX
214 DO 80 J = N,1,-1
215 IF (X(JX).NE.ZERO) THEN
216 TEMP = X(JX)
217 IX = KX
218 DO 70 K = KK,KK - (N- (J+1)),-1
219 X(IX) = X(IX) + TEMP*AP(K)
220 IX = IX - INCX
221 70 CONTINUE
222 IF (NOUNIT) X(JX) = X(JX)*AP(KK-N+J)
223 END IF
224 JX = JX - INCX
225 KK = KK - (N-J+1)
226 80 CONTINUE
227 END IF
228 END IF
229 ELSE
230 *
231 * Form x := A**T*x or x := A**H*x.
232 *
233 IF (LSAME(UPLO,'U')) THEN
234 KK = (N* (N+1))/2
235 IF (INCX.EQ.1) THEN
236 DO 110 J = N,1,-1
237 TEMP = X(J)
238 K = KK - 1
239 IF (NOCONJ) THEN
240 IF (NOUNIT) TEMP = TEMP*AP(KK)
241 DO 90 I = J - 1,1,-1
242 TEMP = TEMP + AP(K)*X(I)
243 K = K - 1
244 90 CONTINUE
245 ELSE
246 IF (NOUNIT) TEMP = TEMP*CONJG(AP(KK))
247 DO 100 I = J - 1,1,-1
248 TEMP = TEMP + CONJG(AP(K))*X(I)
249 K = K - 1
250 100 CONTINUE
251 END IF
252 X(J) = TEMP
253 KK = KK - J
254 110 CONTINUE
255 ELSE
256 JX = KX + (N-1)*INCX
257 DO 140 J = N,1,-1
258 TEMP = X(JX)
259 IX = JX
260 IF (NOCONJ) THEN
261 IF (NOUNIT) TEMP = TEMP*AP(KK)
262 DO 120 K = KK - 1,KK - J + 1,-1
263 IX = IX - INCX
264 TEMP = TEMP + AP(K)*X(IX)
265 120 CONTINUE
266 ELSE
267 IF (NOUNIT) TEMP = TEMP*CONJG(AP(KK))
268 DO 130 K = KK - 1,KK - J + 1,-1
269 IX = IX - INCX
270 TEMP = TEMP + CONJG(AP(K))*X(IX)
271 130 CONTINUE
272 END IF
273 X(JX) = TEMP
274 JX = JX - INCX
275 KK = KK - J
276 140 CONTINUE
277 END IF
278 ELSE
279 KK = 1
280 IF (INCX.EQ.1) THEN
281 DO 170 J = 1,N
282 TEMP = X(J)
283 K = KK + 1
284 IF (NOCONJ) THEN
285 IF (NOUNIT) TEMP = TEMP*AP(KK)
286 DO 150 I = J + 1,N
287 TEMP = TEMP + AP(K)*X(I)
288 K = K + 1
289 150 CONTINUE
290 ELSE
291 IF (NOUNIT) TEMP = TEMP*CONJG(AP(KK))
292 DO 160 I = J + 1,N
293 TEMP = TEMP + CONJG(AP(K))*X(I)
294 K = K + 1
295 160 CONTINUE
296 END IF
297 X(J) = TEMP
298 KK = KK + (N-J+1)
299 170 CONTINUE
300 ELSE
301 JX = KX
302 DO 200 J = 1,N
303 TEMP = X(JX)
304 IX = JX
305 IF (NOCONJ) THEN
306 IF (NOUNIT) TEMP = TEMP*AP(KK)
307 DO 180 K = KK + 1,KK + N - J
308 IX = IX + INCX
309 TEMP = TEMP + AP(K)*X(IX)
310 180 CONTINUE
311 ELSE
312 IF (NOUNIT) TEMP = TEMP*CONJG(AP(KK))
313 DO 190 K = KK + 1,KK + N - J
314 IX = IX + INCX
315 TEMP = TEMP + CONJG(AP(K))*X(IX)
316 190 CONTINUE
317 END IF
318 X(JX) = TEMP
319 JX = JX + INCX
320 KK = KK + (N-J+1)
321 200 CONTINUE
322 END IF
323 END IF
324 END IF
325 *
326 RETURN
327 *
328 * End of CTPMV .
329 *
330 END