1 SUBROUTINE STBMV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
2 * .. Scalar Arguments ..
3 INTEGER INCX,K,LDA,N
4 CHARACTER DIAG,TRANS,UPLO
5 * ..
6 * .. Array Arguments ..
7 REAL A(LDA,*),X(*)
8 * ..
9 *
10 * Purpose
11 * =======
12 *
13 * STBMV 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 band matrix, with ( k + 1 ) diagonals.
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 * K - INTEGER.
62 * On entry with UPLO = 'U' or 'u', K specifies the number of
63 * super-diagonals of the matrix A.
64 * On entry with UPLO = 'L' or 'l', K specifies the number of
65 * sub-diagonals of the matrix A.
66 * K must satisfy 0 .le. K.
67 * Unchanged on exit.
68 *
69 * A - REAL array of DIMENSION ( LDA, n ).
70 * Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
71 * by n part of the array A must contain the upper triangular
72 * band part of the matrix of coefficients, supplied column by
73 * column, with the leading diagonal of the matrix in row
74 * ( k + 1 ) of the array, the first super-diagonal starting at
75 * position 2 in row k, and so on. The top left k by k triangle
76 * of the array A is not referenced.
77 * The following program segment will transfer an upper
78 * triangular band matrix from conventional full matrix storage
79 * to band storage:
80 *
81 * DO 20, J = 1, N
82 * M = K + 1 - J
83 * DO 10, I = MAX( 1, J - K ), J
84 * A( M + I, J ) = matrix( I, J )
85 * 10 CONTINUE
86 * 20 CONTINUE
87 *
88 * Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
89 * by n part of the array A must contain the lower triangular
90 * band part of the matrix of coefficients, supplied column by
91 * column, with the leading diagonal of the matrix in row 1 of
92 * the array, the first sub-diagonal starting at position 1 in
93 * row 2, and so on. The bottom right k by k triangle of the
94 * array A is not referenced.
95 * The following program segment will transfer a lower
96 * triangular band matrix from conventional full matrix storage
97 * to band storage:
98 *
99 * DO 20, J = 1, N
100 * M = 1 - J
101 * DO 10, I = J, MIN( N, J + K )
102 * A( M + I, J ) = matrix( I, J )
103 * 10 CONTINUE
104 * 20 CONTINUE
105 *
106 * Note that when DIAG = 'U' or 'u' the elements of the array A
107 * corresponding to the diagonal elements of the matrix are not
108 * referenced, but are assumed to be unity.
109 * Unchanged on exit.
110 *
111 * LDA - INTEGER.
112 * On entry, LDA specifies the first dimension of A as declared
113 * in the calling (sub) program. LDA must be at least
114 * ( k + 1 ).
115 * Unchanged on exit.
116 *
117 * X - REAL array of dimension at least
118 * ( 1 + ( n - 1 )*abs( INCX ) ).
119 * Before entry, the incremented array X must contain the n
120 * element vector x. On exit, X is overwritten with the
121 * tranformed vector x.
122 *
123 * INCX - INTEGER.
124 * On entry, INCX specifies the increment for the elements of
125 * X. INCX must not be zero.
126 * Unchanged on exit.
127 *
128 * Further Details
129 * ===============
130 *
131 * Level 2 Blas routine.
132 * The vector and matrix arguments are not referenced when N = 0, or M = 0
133 *
134 * -- Written on 22-October-1986.
135 * Jack Dongarra, Argonne National Lab.
136 * Jeremy Du Croz, Nag Central Office.
137 * Sven Hammarling, Nag Central Office.
138 * Richard Hanson, Sandia National Labs.
139 *
140 * =====================================================================
141 *
142 * .. Parameters ..
143 REAL ZERO
144 PARAMETER (ZERO=0.0E+0)
145 * ..
146 * .. Local Scalars ..
147 REAL TEMP
148 INTEGER I,INFO,IX,J,JX,KPLUS1,KX,L
149 LOGICAL NOUNIT
150 * ..
151 * .. External Functions ..
152 LOGICAL LSAME
153 EXTERNAL LSAME
154 * ..
155 * .. External Subroutines ..
156 EXTERNAL XERBLA
157 * ..
158 * .. Intrinsic Functions ..
159 INTRINSIC MAX,MIN
160 * ..
161 *
162 * Test the input parameters.
163 *
164 INFO = 0
165 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
166 INFO = 1
167 ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
168 + .NOT.LSAME(TRANS,'C')) THEN
169 INFO = 2
170 ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
171 INFO = 3
172 ELSE IF (N.LT.0) THEN
173 INFO = 4
174 ELSE IF (K.LT.0) THEN
175 INFO = 5
176 ELSE IF (LDA.LT. (K+1)) THEN
177 INFO = 7
178 ELSE IF (INCX.EQ.0) THEN
179 INFO = 9
180 END IF
181 IF (INFO.NE.0) THEN
182 CALL XERBLA('STBMV ',INFO)
183 RETURN
184 END IF
185 *
186 * Quick return if possible.
187 *
188 IF (N.EQ.0) RETURN
189 *
190 NOUNIT = LSAME(DIAG,'N')
191 *
192 * Set up the start point in X if the increment is not unity. This
193 * will be ( N - 1 )*INCX too small for descending loops.
194 *
195 IF (INCX.LE.0) THEN
196 KX = 1 - (N-1)*INCX
197 ELSE IF (INCX.NE.1) THEN
198 KX = 1
199 END IF
200 *
201 * Start the operations. In this version the elements of A are
202 * accessed sequentially with one pass through A.
203 *
204 IF (LSAME(TRANS,'N')) THEN
205 *
206 * Form x := A*x.
207 *
208 IF (LSAME(UPLO,'U')) THEN
209 KPLUS1 = K + 1
210 IF (INCX.EQ.1) THEN
211 DO 20 J = 1,N
212 IF (X(J).NE.ZERO) THEN
213 TEMP = X(J)
214 L = KPLUS1 - J
215 DO 10 I = MAX(1,J-K),J - 1
216 X(I) = X(I) + TEMP*A(L+I,J)
217 10 CONTINUE
218 IF (NOUNIT) X(J) = X(J)*A(KPLUS1,J)
219 END IF
220 20 CONTINUE
221 ELSE
222 JX = KX
223 DO 40 J = 1,N
224 IF (X(JX).NE.ZERO) THEN
225 TEMP = X(JX)
226 IX = KX
227 L = KPLUS1 - J
228 DO 30 I = MAX(1,J-K),J - 1
229 X(IX) = X(IX) + TEMP*A(L+I,J)
230 IX = IX + INCX
231 30 CONTINUE
232 IF (NOUNIT) X(JX) = X(JX)*A(KPLUS1,J)
233 END IF
234 JX = JX + INCX
235 IF (J.GT.K) KX = KX + INCX
236 40 CONTINUE
237 END IF
238 ELSE
239 IF (INCX.EQ.1) THEN
240 DO 60 J = N,1,-1
241 IF (X(J).NE.ZERO) THEN
242 TEMP = X(J)
243 L = 1 - J
244 DO 50 I = MIN(N,J+K),J + 1,-1
245 X(I) = X(I) + TEMP*A(L+I,J)
246 50 CONTINUE
247 IF (NOUNIT) X(J) = X(J)*A(1,J)
248 END IF
249 60 CONTINUE
250 ELSE
251 KX = KX + (N-1)*INCX
252 JX = KX
253 DO 80 J = N,1,-1
254 IF (X(JX).NE.ZERO) THEN
255 TEMP = X(JX)
256 IX = KX
257 L = 1 - J
258 DO 70 I = MIN(N,J+K),J + 1,-1
259 X(IX) = X(IX) + TEMP*A(L+I,J)
260 IX = IX - INCX
261 70 CONTINUE
262 IF (NOUNIT) X(JX) = X(JX)*A(1,J)
263 END IF
264 JX = JX - INCX
265 IF ((N-J).GE.K) KX = KX - INCX
266 80 CONTINUE
267 END IF
268 END IF
269 ELSE
270 *
271 * Form x := A**T*x.
272 *
273 IF (LSAME(UPLO,'U')) THEN
274 KPLUS1 = K + 1
275 IF (INCX.EQ.1) THEN
276 DO 100 J = N,1,-1
277 TEMP = X(J)
278 L = KPLUS1 - J
279 IF (NOUNIT) TEMP = TEMP*A(KPLUS1,J)
280 DO 90 I = J - 1,MAX(1,J-K),-1
281 TEMP = TEMP + A(L+I,J)*X(I)
282 90 CONTINUE
283 X(J) = TEMP
284 100 CONTINUE
285 ELSE
286 KX = KX + (N-1)*INCX
287 JX = KX
288 DO 120 J = N,1,-1
289 TEMP = X(JX)
290 KX = KX - INCX
291 IX = KX
292 L = KPLUS1 - J
293 IF (NOUNIT) TEMP = TEMP*A(KPLUS1,J)
294 DO 110 I = J - 1,MAX(1,J-K),-1
295 TEMP = TEMP + A(L+I,J)*X(IX)
296 IX = IX - INCX
297 110 CONTINUE
298 X(JX) = TEMP
299 JX = JX - INCX
300 120 CONTINUE
301 END IF
302 ELSE
303 IF (INCX.EQ.1) THEN
304 DO 140 J = 1,N
305 TEMP = X(J)
306 L = 1 - J
307 IF (NOUNIT) TEMP = TEMP*A(1,J)
308 DO 130 I = J + 1,MIN(N,J+K)
309 TEMP = TEMP + A(L+I,J)*X(I)
310 130 CONTINUE
311 X(J) = TEMP
312 140 CONTINUE
313 ELSE
314 JX = KX
315 DO 160 J = 1,N
316 TEMP = X(JX)
317 KX = KX + INCX
318 IX = KX
319 L = 1 - J
320 IF (NOUNIT) TEMP = TEMP*A(1,J)
321 DO 150 I = J + 1,MIN(N,J+K)
322 TEMP = TEMP + A(L+I,J)*X(IX)
323 IX = IX + INCX
324 150 CONTINUE
325 X(JX) = TEMP
326 JX = JX + INCX
327 160 CONTINUE
328 END IF
329 END IF
330 END IF
331 *
332 RETURN
333 *
334 * End of STBMV .
335 *
336 END
2 * .. Scalar Arguments ..
3 INTEGER INCX,K,LDA,N
4 CHARACTER DIAG,TRANS,UPLO
5 * ..
6 * .. Array Arguments ..
7 REAL A(LDA,*),X(*)
8 * ..
9 *
10 * Purpose
11 * =======
12 *
13 * STBMV 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 band matrix, with ( k + 1 ) diagonals.
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 * K - INTEGER.
62 * On entry with UPLO = 'U' or 'u', K specifies the number of
63 * super-diagonals of the matrix A.
64 * On entry with UPLO = 'L' or 'l', K specifies the number of
65 * sub-diagonals of the matrix A.
66 * K must satisfy 0 .le. K.
67 * Unchanged on exit.
68 *
69 * A - REAL array of DIMENSION ( LDA, n ).
70 * Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
71 * by n part of the array A must contain the upper triangular
72 * band part of the matrix of coefficients, supplied column by
73 * column, with the leading diagonal of the matrix in row
74 * ( k + 1 ) of the array, the first super-diagonal starting at
75 * position 2 in row k, and so on. The top left k by k triangle
76 * of the array A is not referenced.
77 * The following program segment will transfer an upper
78 * triangular band matrix from conventional full matrix storage
79 * to band storage:
80 *
81 * DO 20, J = 1, N
82 * M = K + 1 - J
83 * DO 10, I = MAX( 1, J - K ), J
84 * A( M + I, J ) = matrix( I, J )
85 * 10 CONTINUE
86 * 20 CONTINUE
87 *
88 * Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
89 * by n part of the array A must contain the lower triangular
90 * band part of the matrix of coefficients, supplied column by
91 * column, with the leading diagonal of the matrix in row 1 of
92 * the array, the first sub-diagonal starting at position 1 in
93 * row 2, and so on. The bottom right k by k triangle of the
94 * array A is not referenced.
95 * The following program segment will transfer a lower
96 * triangular band matrix from conventional full matrix storage
97 * to band storage:
98 *
99 * DO 20, J = 1, N
100 * M = 1 - J
101 * DO 10, I = J, MIN( N, J + K )
102 * A( M + I, J ) = matrix( I, J )
103 * 10 CONTINUE
104 * 20 CONTINUE
105 *
106 * Note that when DIAG = 'U' or 'u' the elements of the array A
107 * corresponding to the diagonal elements of the matrix are not
108 * referenced, but are assumed to be unity.
109 * Unchanged on exit.
110 *
111 * LDA - INTEGER.
112 * On entry, LDA specifies the first dimension of A as declared
113 * in the calling (sub) program. LDA must be at least
114 * ( k + 1 ).
115 * Unchanged on exit.
116 *
117 * X - REAL array of dimension at least
118 * ( 1 + ( n - 1 )*abs( INCX ) ).
119 * Before entry, the incremented array X must contain the n
120 * element vector x. On exit, X is overwritten with the
121 * tranformed vector x.
122 *
123 * INCX - INTEGER.
124 * On entry, INCX specifies the increment for the elements of
125 * X. INCX must not be zero.
126 * Unchanged on exit.
127 *
128 * Further Details
129 * ===============
130 *
131 * Level 2 Blas routine.
132 * The vector and matrix arguments are not referenced when N = 0, or M = 0
133 *
134 * -- Written on 22-October-1986.
135 * Jack Dongarra, Argonne National Lab.
136 * Jeremy Du Croz, Nag Central Office.
137 * Sven Hammarling, Nag Central Office.
138 * Richard Hanson, Sandia National Labs.
139 *
140 * =====================================================================
141 *
142 * .. Parameters ..
143 REAL ZERO
144 PARAMETER (ZERO=0.0E+0)
145 * ..
146 * .. Local Scalars ..
147 REAL TEMP
148 INTEGER I,INFO,IX,J,JX,KPLUS1,KX,L
149 LOGICAL NOUNIT
150 * ..
151 * .. External Functions ..
152 LOGICAL LSAME
153 EXTERNAL LSAME
154 * ..
155 * .. External Subroutines ..
156 EXTERNAL XERBLA
157 * ..
158 * .. Intrinsic Functions ..
159 INTRINSIC MAX,MIN
160 * ..
161 *
162 * Test the input parameters.
163 *
164 INFO = 0
165 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
166 INFO = 1
167 ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
168 + .NOT.LSAME(TRANS,'C')) THEN
169 INFO = 2
170 ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
171 INFO = 3
172 ELSE IF (N.LT.0) THEN
173 INFO = 4
174 ELSE IF (K.LT.0) THEN
175 INFO = 5
176 ELSE IF (LDA.LT. (K+1)) THEN
177 INFO = 7
178 ELSE IF (INCX.EQ.0) THEN
179 INFO = 9
180 END IF
181 IF (INFO.NE.0) THEN
182 CALL XERBLA('STBMV ',INFO)
183 RETURN
184 END IF
185 *
186 * Quick return if possible.
187 *
188 IF (N.EQ.0) RETURN
189 *
190 NOUNIT = LSAME(DIAG,'N')
191 *
192 * Set up the start point in X if the increment is not unity. This
193 * will be ( N - 1 )*INCX too small for descending loops.
194 *
195 IF (INCX.LE.0) THEN
196 KX = 1 - (N-1)*INCX
197 ELSE IF (INCX.NE.1) THEN
198 KX = 1
199 END IF
200 *
201 * Start the operations. In this version the elements of A are
202 * accessed sequentially with one pass through A.
203 *
204 IF (LSAME(TRANS,'N')) THEN
205 *
206 * Form x := A*x.
207 *
208 IF (LSAME(UPLO,'U')) THEN
209 KPLUS1 = K + 1
210 IF (INCX.EQ.1) THEN
211 DO 20 J = 1,N
212 IF (X(J).NE.ZERO) THEN
213 TEMP = X(J)
214 L = KPLUS1 - J
215 DO 10 I = MAX(1,J-K),J - 1
216 X(I) = X(I) + TEMP*A(L+I,J)
217 10 CONTINUE
218 IF (NOUNIT) X(J) = X(J)*A(KPLUS1,J)
219 END IF
220 20 CONTINUE
221 ELSE
222 JX = KX
223 DO 40 J = 1,N
224 IF (X(JX).NE.ZERO) THEN
225 TEMP = X(JX)
226 IX = KX
227 L = KPLUS1 - J
228 DO 30 I = MAX(1,J-K),J - 1
229 X(IX) = X(IX) + TEMP*A(L+I,J)
230 IX = IX + INCX
231 30 CONTINUE
232 IF (NOUNIT) X(JX) = X(JX)*A(KPLUS1,J)
233 END IF
234 JX = JX + INCX
235 IF (J.GT.K) KX = KX + INCX
236 40 CONTINUE
237 END IF
238 ELSE
239 IF (INCX.EQ.1) THEN
240 DO 60 J = N,1,-1
241 IF (X(J).NE.ZERO) THEN
242 TEMP = X(J)
243 L = 1 - J
244 DO 50 I = MIN(N,J+K),J + 1,-1
245 X(I) = X(I) + TEMP*A(L+I,J)
246 50 CONTINUE
247 IF (NOUNIT) X(J) = X(J)*A(1,J)
248 END IF
249 60 CONTINUE
250 ELSE
251 KX = KX + (N-1)*INCX
252 JX = KX
253 DO 80 J = N,1,-1
254 IF (X(JX).NE.ZERO) THEN
255 TEMP = X(JX)
256 IX = KX
257 L = 1 - J
258 DO 70 I = MIN(N,J+K),J + 1,-1
259 X(IX) = X(IX) + TEMP*A(L+I,J)
260 IX = IX - INCX
261 70 CONTINUE
262 IF (NOUNIT) X(JX) = X(JX)*A(1,J)
263 END IF
264 JX = JX - INCX
265 IF ((N-J).GE.K) KX = KX - INCX
266 80 CONTINUE
267 END IF
268 END IF
269 ELSE
270 *
271 * Form x := A**T*x.
272 *
273 IF (LSAME(UPLO,'U')) THEN
274 KPLUS1 = K + 1
275 IF (INCX.EQ.1) THEN
276 DO 100 J = N,1,-1
277 TEMP = X(J)
278 L = KPLUS1 - J
279 IF (NOUNIT) TEMP = TEMP*A(KPLUS1,J)
280 DO 90 I = J - 1,MAX(1,J-K),-1
281 TEMP = TEMP + A(L+I,J)*X(I)
282 90 CONTINUE
283 X(J) = TEMP
284 100 CONTINUE
285 ELSE
286 KX = KX + (N-1)*INCX
287 JX = KX
288 DO 120 J = N,1,-1
289 TEMP = X(JX)
290 KX = KX - INCX
291 IX = KX
292 L = KPLUS1 - J
293 IF (NOUNIT) TEMP = TEMP*A(KPLUS1,J)
294 DO 110 I = J - 1,MAX(1,J-K),-1
295 TEMP = TEMP + A(L+I,J)*X(IX)
296 IX = IX - INCX
297 110 CONTINUE
298 X(JX) = TEMP
299 JX = JX - INCX
300 120 CONTINUE
301 END IF
302 ELSE
303 IF (INCX.EQ.1) THEN
304 DO 140 J = 1,N
305 TEMP = X(J)
306 L = 1 - J
307 IF (NOUNIT) TEMP = TEMP*A(1,J)
308 DO 130 I = J + 1,MIN(N,J+K)
309 TEMP = TEMP + A(L+I,J)*X(I)
310 130 CONTINUE
311 X(J) = TEMP
312 140 CONTINUE
313 ELSE
314 JX = KX
315 DO 160 J = 1,N
316 TEMP = X(JX)
317 KX = KX + INCX
318 IX = KX
319 L = 1 - J
320 IF (NOUNIT) TEMP = TEMP*A(1,J)
321 DO 150 I = J + 1,MIN(N,J+K)
322 TEMP = TEMP + A(L+I,J)*X(IX)
323 IX = IX + INCX
324 150 CONTINUE
325 X(JX) = TEMP
326 JX = JX + INCX
327 160 CONTINUE
328 END IF
329 END IF
330 END IF
331 *
332 RETURN
333 *
334 * End of STBMV .
335 *
336 END