1 SUBROUTINE STPMV(UPLO,TRANS,DIAG,N,AP,X,INCX)
2 * .. Scalar Arguments ..
3 INTEGER INCX,N
4 CHARACTER DIAG,TRANS,UPLO
5 * ..
6 * .. Array Arguments ..
7 REAL AP(*),X(*)
8 * ..
9 *
10 * Purpose
11 * =======
12 *
13 * STPMV performs one of the matrix-vector operations
14 *
15 * x := A*x, or x := A**T*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**T*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 - REAL 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 - REAL 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 REAL ZERO
104 PARAMETER (ZERO=0.0E+0)
105 * ..
106 * .. Local Scalars ..
107 REAL TEMP
108 INTEGER I,INFO,IX,J,JX,K,KK,KX
109 LOGICAL NOUNIT
110 * ..
111 * .. External Functions ..
112 LOGICAL LSAME
113 EXTERNAL LSAME
114 * ..
115 * .. External Subroutines ..
116 EXTERNAL XERBLA
117 * ..
118 *
119 * Test the input parameters.
120 *
121 INFO = 0
122 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
123 INFO = 1
124 ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
125 + .NOT.LSAME(TRANS,'C')) THEN
126 INFO = 2
127 ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
128 INFO = 3
129 ELSE IF (N.LT.0) THEN
130 INFO = 4
131 ELSE IF (INCX.EQ.0) THEN
132 INFO = 7
133 END IF
134 IF (INFO.NE.0) THEN
135 CALL XERBLA('STPMV ',INFO)
136 RETURN
137 END IF
138 *
139 * Quick return if possible.
140 *
141 IF (N.EQ.0) RETURN
142 *
143 NOUNIT = LSAME(DIAG,'N')
144 *
145 * Set up the start point in X if the increment is not unity. This
146 * will be ( N - 1 )*INCX too small for descending loops.
147 *
148 IF (INCX.LE.0) THEN
149 KX = 1 - (N-1)*INCX
150 ELSE IF (INCX.NE.1) THEN
151 KX = 1
152 END IF
153 *
154 * Start the operations. In this version the elements of AP are
155 * accessed sequentially with one pass through AP.
156 *
157 IF (LSAME(TRANS,'N')) THEN
158 *
159 * Form x:= A*x.
160 *
161 IF (LSAME(UPLO,'U')) THEN
162 KK = 1
163 IF (INCX.EQ.1) THEN
164 DO 20 J = 1,N
165 IF (X(J).NE.ZERO) THEN
166 TEMP = X(J)
167 K = KK
168 DO 10 I = 1,J - 1
169 X(I) = X(I) + TEMP*AP(K)
170 K = K + 1
171 10 CONTINUE
172 IF (NOUNIT) X(J) = X(J)*AP(KK+J-1)
173 END IF
174 KK = KK + J
175 20 CONTINUE
176 ELSE
177 JX = KX
178 DO 40 J = 1,N
179 IF (X(JX).NE.ZERO) THEN
180 TEMP = X(JX)
181 IX = KX
182 DO 30 K = KK,KK + J - 2
183 X(IX) = X(IX) + TEMP*AP(K)
184 IX = IX + INCX
185 30 CONTINUE
186 IF (NOUNIT) X(JX) = X(JX)*AP(KK+J-1)
187 END IF
188 JX = JX + INCX
189 KK = KK + J
190 40 CONTINUE
191 END IF
192 ELSE
193 KK = (N* (N+1))/2
194 IF (INCX.EQ.1) THEN
195 DO 60 J = N,1,-1
196 IF (X(J).NE.ZERO) THEN
197 TEMP = X(J)
198 K = KK
199 DO 50 I = N,J + 1,-1
200 X(I) = X(I) + TEMP*AP(K)
201 K = K - 1
202 50 CONTINUE
203 IF (NOUNIT) X(J) = X(J)*AP(KK-N+J)
204 END IF
205 KK = KK - (N-J+1)
206 60 CONTINUE
207 ELSE
208 KX = KX + (N-1)*INCX
209 JX = KX
210 DO 80 J = N,1,-1
211 IF (X(JX).NE.ZERO) THEN
212 TEMP = X(JX)
213 IX = KX
214 DO 70 K = KK,KK - (N- (J+1)),-1
215 X(IX) = X(IX) + TEMP*AP(K)
216 IX = IX - INCX
217 70 CONTINUE
218 IF (NOUNIT) X(JX) = X(JX)*AP(KK-N+J)
219 END IF
220 JX = JX - INCX
221 KK = KK - (N-J+1)
222 80 CONTINUE
223 END IF
224 END IF
225 ELSE
226 *
227 * Form x := A**T*x.
228 *
229 IF (LSAME(UPLO,'U')) THEN
230 KK = (N* (N+1))/2
231 IF (INCX.EQ.1) THEN
232 DO 100 J = N,1,-1
233 TEMP = X(J)
234 IF (NOUNIT) TEMP = TEMP*AP(KK)
235 K = KK - 1
236 DO 90 I = J - 1,1,-1
237 TEMP = TEMP + AP(K)*X(I)
238 K = K - 1
239 90 CONTINUE
240 X(J) = TEMP
241 KK = KK - J
242 100 CONTINUE
243 ELSE
244 JX = KX + (N-1)*INCX
245 DO 120 J = N,1,-1
246 TEMP = X(JX)
247 IX = JX
248 IF (NOUNIT) TEMP = TEMP*AP(KK)
249 DO 110 K = KK - 1,KK - J + 1,-1
250 IX = IX - INCX
251 TEMP = TEMP + AP(K)*X(IX)
252 110 CONTINUE
253 X(JX) = TEMP
254 JX = JX - INCX
255 KK = KK - J
256 120 CONTINUE
257 END IF
258 ELSE
259 KK = 1
260 IF (INCX.EQ.1) THEN
261 DO 140 J = 1,N
262 TEMP = X(J)
263 IF (NOUNIT) TEMP = TEMP*AP(KK)
264 K = KK + 1
265 DO 130 I = J + 1,N
266 TEMP = TEMP + AP(K)*X(I)
267 K = K + 1
268 130 CONTINUE
269 X(J) = TEMP
270 KK = KK + (N-J+1)
271 140 CONTINUE
272 ELSE
273 JX = KX
274 DO 160 J = 1,N
275 TEMP = X(JX)
276 IX = JX
277 IF (NOUNIT) TEMP = TEMP*AP(KK)
278 DO 150 K = KK + 1,KK + N - J
279 IX = IX + INCX
280 TEMP = TEMP + AP(K)*X(IX)
281 150 CONTINUE
282 X(JX) = TEMP
283 JX = JX + INCX
284 KK = KK + (N-J+1)
285 160 CONTINUE
286 END IF
287 END IF
288 END IF
289 *
290 RETURN
291 *
292 * End of STPMV .
293 *
294 END
2 * .. Scalar Arguments ..
3 INTEGER INCX,N
4 CHARACTER DIAG,TRANS,UPLO
5 * ..
6 * .. Array Arguments ..
7 REAL AP(*),X(*)
8 * ..
9 *
10 * Purpose
11 * =======
12 *
13 * STPMV performs one of the matrix-vector operations
14 *
15 * x := A*x, or x := A**T*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**T*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 - REAL 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 - REAL 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 REAL ZERO
104 PARAMETER (ZERO=0.0E+0)
105 * ..
106 * .. Local Scalars ..
107 REAL TEMP
108 INTEGER I,INFO,IX,J,JX,K,KK,KX
109 LOGICAL NOUNIT
110 * ..
111 * .. External Functions ..
112 LOGICAL LSAME
113 EXTERNAL LSAME
114 * ..
115 * .. External Subroutines ..
116 EXTERNAL XERBLA
117 * ..
118 *
119 * Test the input parameters.
120 *
121 INFO = 0
122 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
123 INFO = 1
124 ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
125 + .NOT.LSAME(TRANS,'C')) THEN
126 INFO = 2
127 ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
128 INFO = 3
129 ELSE IF (N.LT.0) THEN
130 INFO = 4
131 ELSE IF (INCX.EQ.0) THEN
132 INFO = 7
133 END IF
134 IF (INFO.NE.0) THEN
135 CALL XERBLA('STPMV ',INFO)
136 RETURN
137 END IF
138 *
139 * Quick return if possible.
140 *
141 IF (N.EQ.0) RETURN
142 *
143 NOUNIT = LSAME(DIAG,'N')
144 *
145 * Set up the start point in X if the increment is not unity. This
146 * will be ( N - 1 )*INCX too small for descending loops.
147 *
148 IF (INCX.LE.0) THEN
149 KX = 1 - (N-1)*INCX
150 ELSE IF (INCX.NE.1) THEN
151 KX = 1
152 END IF
153 *
154 * Start the operations. In this version the elements of AP are
155 * accessed sequentially with one pass through AP.
156 *
157 IF (LSAME(TRANS,'N')) THEN
158 *
159 * Form x:= A*x.
160 *
161 IF (LSAME(UPLO,'U')) THEN
162 KK = 1
163 IF (INCX.EQ.1) THEN
164 DO 20 J = 1,N
165 IF (X(J).NE.ZERO) THEN
166 TEMP = X(J)
167 K = KK
168 DO 10 I = 1,J - 1
169 X(I) = X(I) + TEMP*AP(K)
170 K = K + 1
171 10 CONTINUE
172 IF (NOUNIT) X(J) = X(J)*AP(KK+J-1)
173 END IF
174 KK = KK + J
175 20 CONTINUE
176 ELSE
177 JX = KX
178 DO 40 J = 1,N
179 IF (X(JX).NE.ZERO) THEN
180 TEMP = X(JX)
181 IX = KX
182 DO 30 K = KK,KK + J - 2
183 X(IX) = X(IX) + TEMP*AP(K)
184 IX = IX + INCX
185 30 CONTINUE
186 IF (NOUNIT) X(JX) = X(JX)*AP(KK+J-1)
187 END IF
188 JX = JX + INCX
189 KK = KK + J
190 40 CONTINUE
191 END IF
192 ELSE
193 KK = (N* (N+1))/2
194 IF (INCX.EQ.1) THEN
195 DO 60 J = N,1,-1
196 IF (X(J).NE.ZERO) THEN
197 TEMP = X(J)
198 K = KK
199 DO 50 I = N,J + 1,-1
200 X(I) = X(I) + TEMP*AP(K)
201 K = K - 1
202 50 CONTINUE
203 IF (NOUNIT) X(J) = X(J)*AP(KK-N+J)
204 END IF
205 KK = KK - (N-J+1)
206 60 CONTINUE
207 ELSE
208 KX = KX + (N-1)*INCX
209 JX = KX
210 DO 80 J = N,1,-1
211 IF (X(JX).NE.ZERO) THEN
212 TEMP = X(JX)
213 IX = KX
214 DO 70 K = KK,KK - (N- (J+1)),-1
215 X(IX) = X(IX) + TEMP*AP(K)
216 IX = IX - INCX
217 70 CONTINUE
218 IF (NOUNIT) X(JX) = X(JX)*AP(KK-N+J)
219 END IF
220 JX = JX - INCX
221 KK = KK - (N-J+1)
222 80 CONTINUE
223 END IF
224 END IF
225 ELSE
226 *
227 * Form x := A**T*x.
228 *
229 IF (LSAME(UPLO,'U')) THEN
230 KK = (N* (N+1))/2
231 IF (INCX.EQ.1) THEN
232 DO 100 J = N,1,-1
233 TEMP = X(J)
234 IF (NOUNIT) TEMP = TEMP*AP(KK)
235 K = KK - 1
236 DO 90 I = J - 1,1,-1
237 TEMP = TEMP + AP(K)*X(I)
238 K = K - 1
239 90 CONTINUE
240 X(J) = TEMP
241 KK = KK - J
242 100 CONTINUE
243 ELSE
244 JX = KX + (N-1)*INCX
245 DO 120 J = N,1,-1
246 TEMP = X(JX)
247 IX = JX
248 IF (NOUNIT) TEMP = TEMP*AP(KK)
249 DO 110 K = KK - 1,KK - J + 1,-1
250 IX = IX - INCX
251 TEMP = TEMP + AP(K)*X(IX)
252 110 CONTINUE
253 X(JX) = TEMP
254 JX = JX - INCX
255 KK = KK - J
256 120 CONTINUE
257 END IF
258 ELSE
259 KK = 1
260 IF (INCX.EQ.1) THEN
261 DO 140 J = 1,N
262 TEMP = X(J)
263 IF (NOUNIT) TEMP = TEMP*AP(KK)
264 K = KK + 1
265 DO 130 I = J + 1,N
266 TEMP = TEMP + AP(K)*X(I)
267 K = K + 1
268 130 CONTINUE
269 X(J) = TEMP
270 KK = KK + (N-J+1)
271 140 CONTINUE
272 ELSE
273 JX = KX
274 DO 160 J = 1,N
275 TEMP = X(JX)
276 IX = JX
277 IF (NOUNIT) TEMP = TEMP*AP(KK)
278 DO 150 K = KK + 1,KK + N - J
279 IX = IX + INCX
280 TEMP = TEMP + AP(K)*X(IX)
281 150 CONTINUE
282 X(JX) = TEMP
283 JX = JX + INCX
284 KK = KK + (N-J+1)
285 160 CONTINUE
286 END IF
287 END IF
288 END IF
289 *
290 RETURN
291 *
292 * End of STPMV .
293 *
294 END