1: SUBROUTINE DTBMV(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: DOUBLE PRECISION A(LDA,*),X(*)
8: * ..
9: *
10: * Purpose
11: * =======
12: *
13: * DTBMV performs one of the matrix-vector operations
14: *
15: * x := A*x, or x := A'*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'*x.
40: *
41: * TRANS = 'C' or 'c' x := A'*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 - DOUBLE PRECISION 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 - DOUBLE PRECISION 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: *
133: * -- Written on 22-October-1986.
134: * Jack Dongarra, Argonne National Lab.
135: * Jeremy Du Croz, Nag Central Office.
136: * Sven Hammarling, Nag Central Office.
137: * Richard Hanson, Sandia National Labs.
138: *
139: * =====================================================================
140: *
141: * .. Parameters ..
142: DOUBLE PRECISION ZERO
143: PARAMETER (ZERO=0.0D+0)
144: * ..
145: * .. Local Scalars ..
146: DOUBLE PRECISION TEMP
147: INTEGER I,INFO,IX,J,JX,KPLUS1,KX,L
148: LOGICAL NOUNIT
149: * ..
150: * .. External Functions ..
151: LOGICAL LSAME
152: EXTERNAL LSAME
153: * ..
154: * .. External Subroutines ..
155: EXTERNAL XERBLA
156: * ..
157: * .. Intrinsic Functions ..
158: INTRINSIC MAX,MIN
159: * ..
160: *
161: * Test the input parameters.
162: *
163: INFO = 0
164: IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
165: INFO = 1
166: ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
167: + .NOT.LSAME(TRANS,'C')) THEN
168: INFO = 2
169: ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
170: INFO = 3
171: ELSE IF (N.LT.0) THEN
172: INFO = 4
173: ELSE IF (K.LT.0) THEN
174: INFO = 5
175: ELSE IF (LDA.LT. (K+1)) THEN
176: INFO = 7
177: ELSE IF (INCX.EQ.0) THEN
178: INFO = 9
179: END IF
180: IF (INFO.NE.0) THEN
181: CALL XERBLA('DTBMV ',INFO)
182: RETURN
183: END IF
184: *
185: * Quick return if possible.
186: *
187: IF (N.EQ.0) RETURN
188: *
189: NOUNIT = LSAME(DIAG,'N')
190: *
191: * Set up the start point in X if the increment is not unity. This
192: * will be ( N - 1 )*INCX too small for descending loops.
193: *
194: IF (INCX.LE.0) THEN
195: KX = 1 - (N-1)*INCX
196: ELSE IF (INCX.NE.1) THEN
197: KX = 1
198: END IF
199: *
200: * Start the operations. In this version the elements of A are
201: * accessed sequentially with one pass through A.
202: *
203: IF (LSAME(TRANS,'N')) THEN
204: *
205: * Form x := A*x.
206: *
207: IF (LSAME(UPLO,'U')) THEN
208: KPLUS1 = K + 1
209: IF (INCX.EQ.1) THEN
210: DO 20 J = 1,N
211: IF (X(J).NE.ZERO) THEN
212: TEMP = X(J)
213: L = KPLUS1 - J
214: DO 10 I = MAX(1,J-K),J - 1
215: X(I) = X(I) + TEMP*A(L+I,J)
216: 10 CONTINUE
217: IF (NOUNIT) X(J) = X(J)*A(KPLUS1,J)
218: END IF
219: 20 CONTINUE
220: ELSE
221: JX = KX
222: DO 40 J = 1,N
223: IF (X(JX).NE.ZERO) THEN
224: TEMP = X(JX)
225: IX = KX
226: L = KPLUS1 - J
227: DO 30 I = MAX(1,J-K),J - 1
228: X(IX) = X(IX) + TEMP*A(L+I,J)
229: IX = IX + INCX
230: 30 CONTINUE
231: IF (NOUNIT) X(JX) = X(JX)*A(KPLUS1,J)
232: END IF
233: JX = JX + INCX
234: IF (J.GT.K) KX = KX + INCX
235: 40 CONTINUE
236: END IF
237: ELSE
238: IF (INCX.EQ.1) THEN
239: DO 60 J = N,1,-1
240: IF (X(J).NE.ZERO) THEN
241: TEMP = X(J)
242: L = 1 - J
243: DO 50 I = MIN(N,J+K),J + 1,-1
244: X(I) = X(I) + TEMP*A(L+I,J)
245: 50 CONTINUE
246: IF (NOUNIT) X(J) = X(J)*A(1,J)
247: END IF
248: 60 CONTINUE
249: ELSE
250: KX = KX + (N-1)*INCX
251: JX = KX
252: DO 80 J = N,1,-1
253: IF (X(JX).NE.ZERO) THEN
254: TEMP = X(JX)
255: IX = KX
256: L = 1 - J
257: DO 70 I = MIN(N,J+K),J + 1,-1
258: X(IX) = X(IX) + TEMP*A(L+I,J)
259: IX = IX - INCX
260: 70 CONTINUE
261: IF (NOUNIT) X(JX) = X(JX)*A(1,J)
262: END IF
263: JX = JX - INCX
264: IF ((N-J).GE.K) KX = KX - INCX
265: 80 CONTINUE
266: END IF
267: END IF
268: ELSE
269: *
270: * Form x := A'*x.
271: *
272: IF (LSAME(UPLO,'U')) THEN
273: KPLUS1 = K + 1
274: IF (INCX.EQ.1) THEN
275: DO 100 J = N,1,-1
276: TEMP = X(J)
277: L = KPLUS1 - J
278: IF (NOUNIT) TEMP = TEMP*A(KPLUS1,J)
279: DO 90 I = J - 1,MAX(1,J-K),-1
280: TEMP = TEMP + A(L+I,J)*X(I)
281: 90 CONTINUE
282: X(J) = TEMP
283: 100 CONTINUE
284: ELSE
285: KX = KX + (N-1)*INCX
286: JX = KX
287: DO 120 J = N,1,-1
288: TEMP = X(JX)
289: KX = KX - INCX
290: IX = KX
291: L = KPLUS1 - J
292: IF (NOUNIT) TEMP = TEMP*A(KPLUS1,J)
293: DO 110 I = J - 1,MAX(1,J-K),-1
294: TEMP = TEMP + A(L+I,J)*X(IX)
295: IX = IX - INCX
296: 110 CONTINUE
297: X(JX) = TEMP
298: JX = JX - INCX
299: 120 CONTINUE
300: END IF
301: ELSE
302: IF (INCX.EQ.1) THEN
303: DO 140 J = 1,N
304: TEMP = X(J)
305: L = 1 - J
306: IF (NOUNIT) TEMP = TEMP*A(1,J)
307: DO 130 I = J + 1,MIN(N,J+K)
308: TEMP = TEMP + A(L+I,J)*X(I)
309: 130 CONTINUE
310: X(J) = TEMP
311: 140 CONTINUE
312: ELSE
313: JX = KX
314: DO 160 J = 1,N
315: TEMP = X(JX)
316: KX = KX + INCX
317: IX = KX
318: L = 1 - J
319: IF (NOUNIT) TEMP = TEMP*A(1,J)
320: DO 150 I = J + 1,MIN(N,J+K)
321: TEMP = TEMP + A(L+I,J)*X(IX)
322: IX = IX + INCX
323: 150 CONTINUE
324: X(JX) = TEMP
325: JX = JX + INCX
326: 160 CONTINUE
327: END IF
328: END IF
329: END IF
330: *
331: RETURN
332: *
333: * End of DTBMV .
334: *
335: END
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