1 SUBROUTINE STRMV(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 REAL A(LDA,*),X(*)
8 * ..
9 *
10 * Purpose
11 * =======
12 *
13 * STRMV 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.
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 * A - REAL 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 - 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 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 * The vector and matrix arguments are not referenced when N = 0, or M = 0
96 *
97 * -- Written on 22-October-1986.
98 * Jack Dongarra, Argonne National Lab.
99 * Jeremy Du Croz, Nag Central Office.
100 * Sven Hammarling, Nag Central Office.
101 * Richard Hanson, Sandia National Labs.
102 *
103 * =====================================================================
104 *
105 * .. Parameters ..
106 REAL ZERO
107 PARAMETER (ZERO=0.0E+0)
108 * ..
109 * .. Local Scalars ..
110 REAL TEMP
111 INTEGER I,INFO,IX,J,JX,KX
112 LOGICAL NOUNIT
113 * ..
114 * .. External Functions ..
115 LOGICAL LSAME
116 EXTERNAL LSAME
117 * ..
118 * .. External Subroutines ..
119 EXTERNAL XERBLA
120 * ..
121 * .. Intrinsic Functions ..
122 INTRINSIC MAX
123 * ..
124 *
125 * Test the input parameters.
126 *
127 INFO = 0
128 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
129 INFO = 1
130 ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
131 + .NOT.LSAME(TRANS,'C')) THEN
132 INFO = 2
133 ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
134 INFO = 3
135 ELSE IF (N.LT.0) THEN
136 INFO = 4
137 ELSE IF (LDA.LT.MAX(1,N)) THEN
138 INFO = 6
139 ELSE IF (INCX.EQ.0) THEN
140 INFO = 8
141 END IF
142 IF (INFO.NE.0) THEN
143 CALL XERBLA('STRMV ',INFO)
144 RETURN
145 END IF
146 *
147 * Quick return if possible.
148 *
149 IF (N.EQ.0) RETURN
150 *
151 NOUNIT = LSAME(DIAG,'N')
152 *
153 * Set up the start point in X if the increment is not unity. This
154 * will be ( N - 1 )*INCX too small for descending loops.
155 *
156 IF (INCX.LE.0) THEN
157 KX = 1 - (N-1)*INCX
158 ELSE IF (INCX.NE.1) THEN
159 KX = 1
160 END IF
161 *
162 * Start the operations. In this version the elements of A are
163 * accessed sequentially with one pass through A.
164 *
165 IF (LSAME(TRANS,'N')) THEN
166 *
167 * Form x := A*x.
168 *
169 IF (LSAME(UPLO,'U')) THEN
170 IF (INCX.EQ.1) THEN
171 DO 20 J = 1,N
172 IF (X(J).NE.ZERO) THEN
173 TEMP = X(J)
174 DO 10 I = 1,J - 1
175 X(I) = X(I) + TEMP*A(I,J)
176 10 CONTINUE
177 IF (NOUNIT) X(J) = X(J)*A(J,J)
178 END IF
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 I = 1,J - 1
187 X(IX) = X(IX) + TEMP*A(I,J)
188 IX = IX + INCX
189 30 CONTINUE
190 IF (NOUNIT) X(JX) = X(JX)*A(J,J)
191 END IF
192 JX = JX + INCX
193 40 CONTINUE
194 END IF
195 ELSE
196 IF (INCX.EQ.1) THEN
197 DO 60 J = N,1,-1
198 IF (X(J).NE.ZERO) THEN
199 TEMP = X(J)
200 DO 50 I = N,J + 1,-1
201 X(I) = X(I) + TEMP*A(I,J)
202 50 CONTINUE
203 IF (NOUNIT) X(J) = X(J)*A(J,J)
204 END IF
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 I = N,J + 1,-1
214 X(IX) = X(IX) + TEMP*A(I,J)
215 IX = IX - INCX
216 70 CONTINUE
217 IF (NOUNIT) X(JX) = X(JX)*A(J,J)
218 END IF
219 JX = JX - INCX
220 80 CONTINUE
221 END IF
222 END IF
223 ELSE
224 *
225 * Form x := A**T*x.
226 *
227 IF (LSAME(UPLO,'U')) THEN
228 IF (INCX.EQ.1) THEN
229 DO 100 J = N,1,-1
230 TEMP = X(J)
231 IF (NOUNIT) TEMP = TEMP*A(J,J)
232 DO 90 I = J - 1,1,-1
233 TEMP = TEMP + A(I,J)*X(I)
234 90 CONTINUE
235 X(J) = TEMP
236 100 CONTINUE
237 ELSE
238 JX = KX + (N-1)*INCX
239 DO 120 J = N,1,-1
240 TEMP = X(JX)
241 IX = JX
242 IF (NOUNIT) TEMP = TEMP*A(J,J)
243 DO 110 I = J - 1,1,-1
244 IX = IX - INCX
245 TEMP = TEMP + A(I,J)*X(IX)
246 110 CONTINUE
247 X(JX) = TEMP
248 JX = JX - INCX
249 120 CONTINUE
250 END IF
251 ELSE
252 IF (INCX.EQ.1) THEN
253 DO 140 J = 1,N
254 TEMP = X(J)
255 IF (NOUNIT) TEMP = TEMP*A(J,J)
256 DO 130 I = J + 1,N
257 TEMP = TEMP + A(I,J)*X(I)
258 130 CONTINUE
259 X(J) = TEMP
260 140 CONTINUE
261 ELSE
262 JX = KX
263 DO 160 J = 1,N
264 TEMP = X(JX)
265 IX = JX
266 IF (NOUNIT) TEMP = TEMP*A(J,J)
267 DO 150 I = J + 1,N
268 IX = IX + INCX
269 TEMP = TEMP + A(I,J)*X(IX)
270 150 CONTINUE
271 X(JX) = TEMP
272 JX = JX + INCX
273 160 CONTINUE
274 END IF
275 END IF
276 END IF
277 *
278 RETURN
279 *
280 * End of STRMV .
281 *
282 END
2 * .. Scalar Arguments ..
3 INTEGER INCX,LDA,N
4 CHARACTER DIAG,TRANS,UPLO
5 * ..
6 * .. Array Arguments ..
7 REAL A(LDA,*),X(*)
8 * ..
9 *
10 * Purpose
11 * =======
12 *
13 * STRMV 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.
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 * A - REAL 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 - 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 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 * The vector and matrix arguments are not referenced when N = 0, or M = 0
96 *
97 * -- Written on 22-October-1986.
98 * Jack Dongarra, Argonne National Lab.
99 * Jeremy Du Croz, Nag Central Office.
100 * Sven Hammarling, Nag Central Office.
101 * Richard Hanson, Sandia National Labs.
102 *
103 * =====================================================================
104 *
105 * .. Parameters ..
106 REAL ZERO
107 PARAMETER (ZERO=0.0E+0)
108 * ..
109 * .. Local Scalars ..
110 REAL TEMP
111 INTEGER I,INFO,IX,J,JX,KX
112 LOGICAL NOUNIT
113 * ..
114 * .. External Functions ..
115 LOGICAL LSAME
116 EXTERNAL LSAME
117 * ..
118 * .. External Subroutines ..
119 EXTERNAL XERBLA
120 * ..
121 * .. Intrinsic Functions ..
122 INTRINSIC MAX
123 * ..
124 *
125 * Test the input parameters.
126 *
127 INFO = 0
128 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
129 INFO = 1
130 ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
131 + .NOT.LSAME(TRANS,'C')) THEN
132 INFO = 2
133 ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
134 INFO = 3
135 ELSE IF (N.LT.0) THEN
136 INFO = 4
137 ELSE IF (LDA.LT.MAX(1,N)) THEN
138 INFO = 6
139 ELSE IF (INCX.EQ.0) THEN
140 INFO = 8
141 END IF
142 IF (INFO.NE.0) THEN
143 CALL XERBLA('STRMV ',INFO)
144 RETURN
145 END IF
146 *
147 * Quick return if possible.
148 *
149 IF (N.EQ.0) RETURN
150 *
151 NOUNIT = LSAME(DIAG,'N')
152 *
153 * Set up the start point in X if the increment is not unity. This
154 * will be ( N - 1 )*INCX too small for descending loops.
155 *
156 IF (INCX.LE.0) THEN
157 KX = 1 - (N-1)*INCX
158 ELSE IF (INCX.NE.1) THEN
159 KX = 1
160 END IF
161 *
162 * Start the operations. In this version the elements of A are
163 * accessed sequentially with one pass through A.
164 *
165 IF (LSAME(TRANS,'N')) THEN
166 *
167 * Form x := A*x.
168 *
169 IF (LSAME(UPLO,'U')) THEN
170 IF (INCX.EQ.1) THEN
171 DO 20 J = 1,N
172 IF (X(J).NE.ZERO) THEN
173 TEMP = X(J)
174 DO 10 I = 1,J - 1
175 X(I) = X(I) + TEMP*A(I,J)
176 10 CONTINUE
177 IF (NOUNIT) X(J) = X(J)*A(J,J)
178 END IF
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 I = 1,J - 1
187 X(IX) = X(IX) + TEMP*A(I,J)
188 IX = IX + INCX
189 30 CONTINUE
190 IF (NOUNIT) X(JX) = X(JX)*A(J,J)
191 END IF
192 JX = JX + INCX
193 40 CONTINUE
194 END IF
195 ELSE
196 IF (INCX.EQ.1) THEN
197 DO 60 J = N,1,-1
198 IF (X(J).NE.ZERO) THEN
199 TEMP = X(J)
200 DO 50 I = N,J + 1,-1
201 X(I) = X(I) + TEMP*A(I,J)
202 50 CONTINUE
203 IF (NOUNIT) X(J) = X(J)*A(J,J)
204 END IF
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 I = N,J + 1,-1
214 X(IX) = X(IX) + TEMP*A(I,J)
215 IX = IX - INCX
216 70 CONTINUE
217 IF (NOUNIT) X(JX) = X(JX)*A(J,J)
218 END IF
219 JX = JX - INCX
220 80 CONTINUE
221 END IF
222 END IF
223 ELSE
224 *
225 * Form x := A**T*x.
226 *
227 IF (LSAME(UPLO,'U')) THEN
228 IF (INCX.EQ.1) THEN
229 DO 100 J = N,1,-1
230 TEMP = X(J)
231 IF (NOUNIT) TEMP = TEMP*A(J,J)
232 DO 90 I = J - 1,1,-1
233 TEMP = TEMP + A(I,J)*X(I)
234 90 CONTINUE
235 X(J) = TEMP
236 100 CONTINUE
237 ELSE
238 JX = KX + (N-1)*INCX
239 DO 120 J = N,1,-1
240 TEMP = X(JX)
241 IX = JX
242 IF (NOUNIT) TEMP = TEMP*A(J,J)
243 DO 110 I = J - 1,1,-1
244 IX = IX - INCX
245 TEMP = TEMP + A(I,J)*X(IX)
246 110 CONTINUE
247 X(JX) = TEMP
248 JX = JX - INCX
249 120 CONTINUE
250 END IF
251 ELSE
252 IF (INCX.EQ.1) THEN
253 DO 140 J = 1,N
254 TEMP = X(J)
255 IF (NOUNIT) TEMP = TEMP*A(J,J)
256 DO 130 I = J + 1,N
257 TEMP = TEMP + A(I,J)*X(I)
258 130 CONTINUE
259 X(J) = TEMP
260 140 CONTINUE
261 ELSE
262 JX = KX
263 DO 160 J = 1,N
264 TEMP = X(JX)
265 IX = JX
266 IF (NOUNIT) TEMP = TEMP*A(J,J)
267 DO 150 I = J + 1,N
268 IX = IX + INCX
269 TEMP = TEMP + A(I,J)*X(IX)
270 150 CONTINUE
271 X(JX) = TEMP
272 JX = JX + INCX
273 160 CONTINUE
274 END IF
275 END IF
276 END IF
277 *
278 RETURN
279 *
280 * End of STRMV .
281 *
282 END