1 SUBROUTINE STPSV(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 * STPSV solves one of the systems of equations
14 *
15 * A*x = b, or A**T*x = b,
16 *
17 * where b and x are n element vectors and A is an n by n unit, or
18 * non-unit, upper or lower triangular matrix, supplied in packed form.
19 *
20 * No test for singularity or near-singularity is included in this
21 * routine. Such tests must be performed before calling this routine.
22 *
23 * Arguments
24 * ==========
25 *
26 * UPLO - CHARACTER*1.
27 * On entry, UPLO specifies whether the matrix is an upper or
28 * lower triangular matrix as follows:
29 *
30 * UPLO = 'U' or 'u' A is an upper triangular matrix.
31 *
32 * UPLO = 'L' or 'l' A is a lower triangular matrix.
33 *
34 * Unchanged on exit.
35 *
36 * TRANS - CHARACTER*1.
37 * On entry, TRANS specifies the equations to be solved as
38 * follows:
39 *
40 * TRANS = 'N' or 'n' A*x = b.
41 *
42 * TRANS = 'T' or 't' A**T*x = b.
43 *
44 * TRANS = 'C' or 'c' A**T*x = b.
45 *
46 * Unchanged on exit.
47 *
48 * DIAG - CHARACTER*1.
49 * On entry, DIAG specifies whether or not A is unit
50 * triangular as follows:
51 *
52 * DIAG = 'U' or 'u' A is assumed to be unit triangular.
53 *
54 * DIAG = 'N' or 'n' A is not assumed to be unit
55 * triangular.
56 *
57 * Unchanged on exit.
58 *
59 * N - INTEGER.
60 * On entry, N specifies the order of the matrix A.
61 * N must be at least zero.
62 * Unchanged on exit.
63 *
64 * AP - REAL array of DIMENSION at least
65 * ( ( n*( n + 1 ) )/2 ).
66 * Before entry with UPLO = 'U' or 'u', the array AP must
67 * contain the upper triangular matrix packed sequentially,
68 * column by column, so that AP( 1 ) contains a( 1, 1 ),
69 * AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )
70 * respectively, and so on.
71 * Before entry with UPLO = 'L' or 'l', the array AP must
72 * contain the lower triangular matrix packed sequentially,
73 * column by column, so that AP( 1 ) contains a( 1, 1 ),
74 * AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )
75 * respectively, and so on.
76 * Note that when DIAG = 'U' or 'u', the diagonal elements of
77 * A are not referenced, but are assumed to be unity.
78 * Unchanged on exit.
79 *
80 * X - REAL array of dimension at least
81 * ( 1 + ( n - 1 )*abs( INCX ) ).
82 * Before entry, the incremented array X must contain the n
83 * element right-hand side vector b. On exit, X is overwritten
84 * with the solution 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 REAL ZERO
106 PARAMETER (ZERO=0.0E+0)
107 * ..
108 * .. Local Scalars ..
109 REAL TEMP
110 INTEGER I,INFO,IX,J,JX,K,KK,KX
111 LOGICAL NOUNIT
112 * ..
113 * .. External Functions ..
114 LOGICAL LSAME
115 EXTERNAL LSAME
116 * ..
117 * .. External Subroutines ..
118 EXTERNAL XERBLA
119 * ..
120 *
121 * Test the input parameters.
122 *
123 INFO = 0
124 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
125 INFO = 1
126 ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
127 + .NOT.LSAME(TRANS,'C')) THEN
128 INFO = 2
129 ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
130 INFO = 3
131 ELSE IF (N.LT.0) THEN
132 INFO = 4
133 ELSE IF (INCX.EQ.0) THEN
134 INFO = 7
135 END IF
136 IF (INFO.NE.0) THEN
137 CALL XERBLA('STPSV ',INFO)
138 RETURN
139 END IF
140 *
141 * Quick return if possible.
142 *
143 IF (N.EQ.0) RETURN
144 *
145 NOUNIT = LSAME(DIAG,'N')
146 *
147 * Set up the start point in X if the increment is not unity. This
148 * will be ( N - 1 )*INCX too small for descending loops.
149 *
150 IF (INCX.LE.0) THEN
151 KX = 1 - (N-1)*INCX
152 ELSE IF (INCX.NE.1) THEN
153 KX = 1
154 END IF
155 *
156 * Start the operations. In this version the elements of AP are
157 * accessed sequentially with one pass through AP.
158 *
159 IF (LSAME(TRANS,'N')) THEN
160 *
161 * Form x := inv( A )*x.
162 *
163 IF (LSAME(UPLO,'U')) THEN
164 KK = (N* (N+1))/2
165 IF (INCX.EQ.1) THEN
166 DO 20 J = N,1,-1
167 IF (X(J).NE.ZERO) THEN
168 IF (NOUNIT) X(J) = X(J)/AP(KK)
169 TEMP = X(J)
170 K = KK - 1
171 DO 10 I = J - 1,1,-1
172 X(I) = X(I) - TEMP*AP(K)
173 K = K - 1
174 10 CONTINUE
175 END IF
176 KK = KK - J
177 20 CONTINUE
178 ELSE
179 JX = KX + (N-1)*INCX
180 DO 40 J = N,1,-1
181 IF (X(JX).NE.ZERO) THEN
182 IF (NOUNIT) X(JX) = X(JX)/AP(KK)
183 TEMP = X(JX)
184 IX = JX
185 DO 30 K = KK - 1,KK - J + 1,-1
186 IX = IX - INCX
187 X(IX) = X(IX) - TEMP*AP(K)
188 30 CONTINUE
189 END IF
190 JX = JX - INCX
191 KK = KK - J
192 40 CONTINUE
193 END IF
194 ELSE
195 KK = 1
196 IF (INCX.EQ.1) THEN
197 DO 60 J = 1,N
198 IF (X(J).NE.ZERO) THEN
199 IF (NOUNIT) X(J) = X(J)/AP(KK)
200 TEMP = X(J)
201 K = KK + 1
202 DO 50 I = J + 1,N
203 X(I) = X(I) - TEMP*AP(K)
204 K = K + 1
205 50 CONTINUE
206 END IF
207 KK = KK + (N-J+1)
208 60 CONTINUE
209 ELSE
210 JX = KX
211 DO 80 J = 1,N
212 IF (X(JX).NE.ZERO) THEN
213 IF (NOUNIT) X(JX) = X(JX)/AP(KK)
214 TEMP = X(JX)
215 IX = JX
216 DO 70 K = KK + 1,KK + N - J
217 IX = IX + INCX
218 X(IX) = X(IX) - TEMP*AP(K)
219 70 CONTINUE
220 END IF
221 JX = JX + INCX
222 KK = KK + (N-J+1)
223 80 CONTINUE
224 END IF
225 END IF
226 ELSE
227 *
228 * Form x := inv( A**T )*x.
229 *
230 IF (LSAME(UPLO,'U')) THEN
231 KK = 1
232 IF (INCX.EQ.1) THEN
233 DO 100 J = 1,N
234 TEMP = X(J)
235 K = KK
236 DO 90 I = 1,J - 1
237 TEMP = TEMP - AP(K)*X(I)
238 K = K + 1
239 90 CONTINUE
240 IF (NOUNIT) TEMP = TEMP/AP(KK+J-1)
241 X(J) = TEMP
242 KK = KK + J
243 100 CONTINUE
244 ELSE
245 JX = KX
246 DO 120 J = 1,N
247 TEMP = X(JX)
248 IX = KX
249 DO 110 K = KK,KK + J - 2
250 TEMP = TEMP - AP(K)*X(IX)
251 IX = IX + INCX
252 110 CONTINUE
253 IF (NOUNIT) TEMP = TEMP/AP(KK+J-1)
254 X(JX) = TEMP
255 JX = JX + INCX
256 KK = KK + J
257 120 CONTINUE
258 END IF
259 ELSE
260 KK = (N* (N+1))/2
261 IF (INCX.EQ.1) THEN
262 DO 140 J = N,1,-1
263 TEMP = X(J)
264 K = KK
265 DO 130 I = N,J + 1,-1
266 TEMP = TEMP - AP(K)*X(I)
267 K = K - 1
268 130 CONTINUE
269 IF (NOUNIT) TEMP = TEMP/AP(KK-N+J)
270 X(J) = TEMP
271 KK = KK - (N-J+1)
272 140 CONTINUE
273 ELSE
274 KX = KX + (N-1)*INCX
275 JX = KX
276 DO 160 J = N,1,-1
277 TEMP = X(JX)
278 IX = KX
279 DO 150 K = KK,KK - (N- (J+1)),-1
280 TEMP = TEMP - AP(K)*X(IX)
281 IX = IX - INCX
282 150 CONTINUE
283 IF (NOUNIT) TEMP = TEMP/AP(KK-N+J)
284 X(JX) = TEMP
285 JX = JX - INCX
286 KK = KK - (N-J+1)
287 160 CONTINUE
288 END IF
289 END IF
290 END IF
291 *
292 RETURN
293 *
294 * End of STPSV .
295 *
296 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 * STPSV solves one of the systems of equations
14 *
15 * A*x = b, or A**T*x = b,
16 *
17 * where b and x are n element vectors and A is an n by n unit, or
18 * non-unit, upper or lower triangular matrix, supplied in packed form.
19 *
20 * No test for singularity or near-singularity is included in this
21 * routine. Such tests must be performed before calling this routine.
22 *
23 * Arguments
24 * ==========
25 *
26 * UPLO - CHARACTER*1.
27 * On entry, UPLO specifies whether the matrix is an upper or
28 * lower triangular matrix as follows:
29 *
30 * UPLO = 'U' or 'u' A is an upper triangular matrix.
31 *
32 * UPLO = 'L' or 'l' A is a lower triangular matrix.
33 *
34 * Unchanged on exit.
35 *
36 * TRANS - CHARACTER*1.
37 * On entry, TRANS specifies the equations to be solved as
38 * follows:
39 *
40 * TRANS = 'N' or 'n' A*x = b.
41 *
42 * TRANS = 'T' or 't' A**T*x = b.
43 *
44 * TRANS = 'C' or 'c' A**T*x = b.
45 *
46 * Unchanged on exit.
47 *
48 * DIAG - CHARACTER*1.
49 * On entry, DIAG specifies whether or not A is unit
50 * triangular as follows:
51 *
52 * DIAG = 'U' or 'u' A is assumed to be unit triangular.
53 *
54 * DIAG = 'N' or 'n' A is not assumed to be unit
55 * triangular.
56 *
57 * Unchanged on exit.
58 *
59 * N - INTEGER.
60 * On entry, N specifies the order of the matrix A.
61 * N must be at least zero.
62 * Unchanged on exit.
63 *
64 * AP - REAL array of DIMENSION at least
65 * ( ( n*( n + 1 ) )/2 ).
66 * Before entry with UPLO = 'U' or 'u', the array AP must
67 * contain the upper triangular matrix packed sequentially,
68 * column by column, so that AP( 1 ) contains a( 1, 1 ),
69 * AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )
70 * respectively, and so on.
71 * Before entry with UPLO = 'L' or 'l', the array AP must
72 * contain the lower triangular matrix packed sequentially,
73 * column by column, so that AP( 1 ) contains a( 1, 1 ),
74 * AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )
75 * respectively, and so on.
76 * Note that when DIAG = 'U' or 'u', the diagonal elements of
77 * A are not referenced, but are assumed to be unity.
78 * Unchanged on exit.
79 *
80 * X - REAL array of dimension at least
81 * ( 1 + ( n - 1 )*abs( INCX ) ).
82 * Before entry, the incremented array X must contain the n
83 * element right-hand side vector b. On exit, X is overwritten
84 * with the solution 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 REAL ZERO
106 PARAMETER (ZERO=0.0E+0)
107 * ..
108 * .. Local Scalars ..
109 REAL TEMP
110 INTEGER I,INFO,IX,J,JX,K,KK,KX
111 LOGICAL NOUNIT
112 * ..
113 * .. External Functions ..
114 LOGICAL LSAME
115 EXTERNAL LSAME
116 * ..
117 * .. External Subroutines ..
118 EXTERNAL XERBLA
119 * ..
120 *
121 * Test the input parameters.
122 *
123 INFO = 0
124 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
125 INFO = 1
126 ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
127 + .NOT.LSAME(TRANS,'C')) THEN
128 INFO = 2
129 ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
130 INFO = 3
131 ELSE IF (N.LT.0) THEN
132 INFO = 4
133 ELSE IF (INCX.EQ.0) THEN
134 INFO = 7
135 END IF
136 IF (INFO.NE.0) THEN
137 CALL XERBLA('STPSV ',INFO)
138 RETURN
139 END IF
140 *
141 * Quick return if possible.
142 *
143 IF (N.EQ.0) RETURN
144 *
145 NOUNIT = LSAME(DIAG,'N')
146 *
147 * Set up the start point in X if the increment is not unity. This
148 * will be ( N - 1 )*INCX too small for descending loops.
149 *
150 IF (INCX.LE.0) THEN
151 KX = 1 - (N-1)*INCX
152 ELSE IF (INCX.NE.1) THEN
153 KX = 1
154 END IF
155 *
156 * Start the operations. In this version the elements of AP are
157 * accessed sequentially with one pass through AP.
158 *
159 IF (LSAME(TRANS,'N')) THEN
160 *
161 * Form x := inv( A )*x.
162 *
163 IF (LSAME(UPLO,'U')) THEN
164 KK = (N* (N+1))/2
165 IF (INCX.EQ.1) THEN
166 DO 20 J = N,1,-1
167 IF (X(J).NE.ZERO) THEN
168 IF (NOUNIT) X(J) = X(J)/AP(KK)
169 TEMP = X(J)
170 K = KK - 1
171 DO 10 I = J - 1,1,-1
172 X(I) = X(I) - TEMP*AP(K)
173 K = K - 1
174 10 CONTINUE
175 END IF
176 KK = KK - J
177 20 CONTINUE
178 ELSE
179 JX = KX + (N-1)*INCX
180 DO 40 J = N,1,-1
181 IF (X(JX).NE.ZERO) THEN
182 IF (NOUNIT) X(JX) = X(JX)/AP(KK)
183 TEMP = X(JX)
184 IX = JX
185 DO 30 K = KK - 1,KK - J + 1,-1
186 IX = IX - INCX
187 X(IX) = X(IX) - TEMP*AP(K)
188 30 CONTINUE
189 END IF
190 JX = JX - INCX
191 KK = KK - J
192 40 CONTINUE
193 END IF
194 ELSE
195 KK = 1
196 IF (INCX.EQ.1) THEN
197 DO 60 J = 1,N
198 IF (X(J).NE.ZERO) THEN
199 IF (NOUNIT) X(J) = X(J)/AP(KK)
200 TEMP = X(J)
201 K = KK + 1
202 DO 50 I = J + 1,N
203 X(I) = X(I) - TEMP*AP(K)
204 K = K + 1
205 50 CONTINUE
206 END IF
207 KK = KK + (N-J+1)
208 60 CONTINUE
209 ELSE
210 JX = KX
211 DO 80 J = 1,N
212 IF (X(JX).NE.ZERO) THEN
213 IF (NOUNIT) X(JX) = X(JX)/AP(KK)
214 TEMP = X(JX)
215 IX = JX
216 DO 70 K = KK + 1,KK + N - J
217 IX = IX + INCX
218 X(IX) = X(IX) - TEMP*AP(K)
219 70 CONTINUE
220 END IF
221 JX = JX + INCX
222 KK = KK + (N-J+1)
223 80 CONTINUE
224 END IF
225 END IF
226 ELSE
227 *
228 * Form x := inv( A**T )*x.
229 *
230 IF (LSAME(UPLO,'U')) THEN
231 KK = 1
232 IF (INCX.EQ.1) THEN
233 DO 100 J = 1,N
234 TEMP = X(J)
235 K = KK
236 DO 90 I = 1,J - 1
237 TEMP = TEMP - AP(K)*X(I)
238 K = K + 1
239 90 CONTINUE
240 IF (NOUNIT) TEMP = TEMP/AP(KK+J-1)
241 X(J) = TEMP
242 KK = KK + J
243 100 CONTINUE
244 ELSE
245 JX = KX
246 DO 120 J = 1,N
247 TEMP = X(JX)
248 IX = KX
249 DO 110 K = KK,KK + J - 2
250 TEMP = TEMP - AP(K)*X(IX)
251 IX = IX + INCX
252 110 CONTINUE
253 IF (NOUNIT) TEMP = TEMP/AP(KK+J-1)
254 X(JX) = TEMP
255 JX = JX + INCX
256 KK = KK + J
257 120 CONTINUE
258 END IF
259 ELSE
260 KK = (N* (N+1))/2
261 IF (INCX.EQ.1) THEN
262 DO 140 J = N,1,-1
263 TEMP = X(J)
264 K = KK
265 DO 130 I = N,J + 1,-1
266 TEMP = TEMP - AP(K)*X(I)
267 K = K - 1
268 130 CONTINUE
269 IF (NOUNIT) TEMP = TEMP/AP(KK-N+J)
270 X(J) = TEMP
271 KK = KK - (N-J+1)
272 140 CONTINUE
273 ELSE
274 KX = KX + (N-1)*INCX
275 JX = KX
276 DO 160 J = N,1,-1
277 TEMP = X(JX)
278 IX = KX
279 DO 150 K = KK,KK - (N- (J+1)),-1
280 TEMP = TEMP - AP(K)*X(IX)
281 IX = IX - INCX
282 150 CONTINUE
283 IF (NOUNIT) TEMP = TEMP/AP(KK-N+J)
284 X(JX) = TEMP
285 JX = JX - INCX
286 KK = KK - (N-J+1)
287 160 CONTINUE
288 END IF
289 END IF
290 END IF
291 *
292 RETURN
293 *
294 * End of STPSV .
295 *
296 END