1: SUBROUTINE DTBSV(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: * DTBSV solves one of the systems of equations
14: *
15: * A*x = b, or A'*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 band matrix, with ( k + 1 )
19: * diagonals.
20: *
21: * No test for singularity or near-singularity is included in this
22: * routine. Such tests must be performed before calling this routine.
23: *
24: * Arguments
25: * ==========
26: *
27: * UPLO - CHARACTER*1.
28: * On entry, UPLO specifies whether the matrix is an upper or
29: * lower triangular matrix as follows:
30: *
31: * UPLO = 'U' or 'u' A is an upper triangular matrix.
32: *
33: * UPLO = 'L' or 'l' A is a lower triangular matrix.
34: *
35: * Unchanged on exit.
36: *
37: * TRANS - CHARACTER*1.
38: * On entry, TRANS specifies the equations to be solved as
39: * follows:
40: *
41: * TRANS = 'N' or 'n' A*x = b.
42: *
43: * TRANS = 'T' or 't' A'*x = b.
44: *
45: * TRANS = 'C' or 'c' A'*x = b.
46: *
47: * Unchanged on exit.
48: *
49: * DIAG - CHARACTER*1.
50: * On entry, DIAG specifies whether or not A is unit
51: * triangular as follows:
52: *
53: * DIAG = 'U' or 'u' A is assumed to be unit triangular.
54: *
55: * DIAG = 'N' or 'n' A is not assumed to be unit
56: * triangular.
57: *
58: * Unchanged on exit.
59: *
60: * N - INTEGER.
61: * On entry, N specifies the order of the matrix A.
62: * N must be at least zero.
63: * Unchanged on exit.
64: *
65: * K - INTEGER.
66: * On entry with UPLO = 'U' or 'u', K specifies the number of
67: * super-diagonals of the matrix A.
68: * On entry with UPLO = 'L' or 'l', K specifies the number of
69: * sub-diagonals of the matrix A.
70: * K must satisfy 0 .le. K.
71: * Unchanged on exit.
72: *
73: * A - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
74: * Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
75: * by n part of the array A must contain the upper triangular
76: * band part of the matrix of coefficients, supplied column by
77: * column, with the leading diagonal of the matrix in row
78: * ( k + 1 ) of the array, the first super-diagonal starting at
79: * position 2 in row k, and so on. The top left k by k triangle
80: * of the array A is not referenced.
81: * The following program segment will transfer an upper
82: * triangular band matrix from conventional full matrix storage
83: * to band storage:
84: *
85: * DO 20, J = 1, N
86: * M = K + 1 - J
87: * DO 10, I = MAX( 1, J - K ), J
88: * A( M + I, J ) = matrix( I, J )
89: * 10 CONTINUE
90: * 20 CONTINUE
91: *
92: * Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
93: * by n part of the array A must contain the lower triangular
94: * band part of the matrix of coefficients, supplied column by
95: * column, with the leading diagonal of the matrix in row 1 of
96: * the array, the first sub-diagonal starting at position 1 in
97: * row 2, and so on. The bottom right k by k triangle of the
98: * array A is not referenced.
99: * The following program segment will transfer a lower
100: * triangular band matrix from conventional full matrix storage
101: * to band storage:
102: *
103: * DO 20, J = 1, N
104: * M = 1 - J
105: * DO 10, I = J, MIN( N, J + K )
106: * A( M + I, J ) = matrix( I, J )
107: * 10 CONTINUE
108: * 20 CONTINUE
109: *
110: * Note that when DIAG = 'U' or 'u' the elements of the array A
111: * corresponding to the diagonal elements of the matrix are not
112: * referenced, but are assumed to be unity.
113: * Unchanged on exit.
114: *
115: * LDA - INTEGER.
116: * On entry, LDA specifies the first dimension of A as declared
117: * in the calling (sub) program. LDA must be at least
118: * ( k + 1 ).
119: * Unchanged on exit.
120: *
121: * X - DOUBLE PRECISION array of dimension at least
122: * ( 1 + ( n - 1 )*abs( INCX ) ).
123: * Before entry, the incremented array X must contain the n
124: * element right-hand side vector b. On exit, X is overwritten
125: * with the solution vector x.
126: *
127: * INCX - INTEGER.
128: * On entry, INCX specifies the increment for the elements of
129: * X. INCX must not be zero.
130: * Unchanged on exit.
131: *
132: * Further Details
133: * ===============
134: *
135: * Level 2 Blas routine.
136: *
137: * -- Written on 22-October-1986.
138: * Jack Dongarra, Argonne National Lab.
139: * Jeremy Du Croz, Nag Central Office.
140: * Sven Hammarling, Nag Central Office.
141: * Richard Hanson, Sandia National Labs.
142: *
143: * =====================================================================
144: *
145: * .. Parameters ..
146: DOUBLE PRECISION ZERO
147: PARAMETER (ZERO=0.0D+0)
148: * ..
149: * .. Local Scalars ..
150: DOUBLE PRECISION TEMP
151: INTEGER I,INFO,IX,J,JX,KPLUS1,KX,L
152: LOGICAL NOUNIT
153: * ..
154: * .. External Functions ..
155: LOGICAL LSAME
156: EXTERNAL LSAME
157: * ..
158: * .. External Subroutines ..
159: EXTERNAL XERBLA
160: * ..
161: * .. Intrinsic Functions ..
162: INTRINSIC MAX,MIN
163: * ..
164: *
165: * Test the input parameters.
166: *
167: INFO = 0
168: IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
169: INFO = 1
170: ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
171: + .NOT.LSAME(TRANS,'C')) THEN
172: INFO = 2
173: ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
174: INFO = 3
175: ELSE IF (N.LT.0) THEN
176: INFO = 4
177: ELSE IF (K.LT.0) THEN
178: INFO = 5
179: ELSE IF (LDA.LT. (K+1)) THEN
180: INFO = 7
181: ELSE IF (INCX.EQ.0) THEN
182: INFO = 9
183: END IF
184: IF (INFO.NE.0) THEN
185: CALL XERBLA('DTBSV ',INFO)
186: RETURN
187: END IF
188: *
189: * Quick return if possible.
190: *
191: IF (N.EQ.0) RETURN
192: *
193: NOUNIT = LSAME(DIAG,'N')
194: *
195: * Set up the start point in X if the increment is not unity. This
196: * will be ( N - 1 )*INCX too small for descending loops.
197: *
198: IF (INCX.LE.0) THEN
199: KX = 1 - (N-1)*INCX
200: ELSE IF (INCX.NE.1) THEN
201: KX = 1
202: END IF
203: *
204: * Start the operations. In this version the elements of A are
205: * accessed by sequentially with one pass through A.
206: *
207: IF (LSAME(TRANS,'N')) THEN
208: *
209: * Form x := inv( A )*x.
210: *
211: IF (LSAME(UPLO,'U')) THEN
212: KPLUS1 = K + 1
213: IF (INCX.EQ.1) THEN
214: DO 20 J = N,1,-1
215: IF (X(J).NE.ZERO) THEN
216: L = KPLUS1 - J
217: IF (NOUNIT) X(J) = X(J)/A(KPLUS1,J)
218: TEMP = X(J)
219: DO 10 I = J - 1,MAX(1,J-K),-1
220: X(I) = X(I) - TEMP*A(L+I,J)
221: 10 CONTINUE
222: END IF
223: 20 CONTINUE
224: ELSE
225: KX = KX + (N-1)*INCX
226: JX = KX
227: DO 40 J = N,1,-1
228: KX = KX - INCX
229: IF (X(JX).NE.ZERO) THEN
230: IX = KX
231: L = KPLUS1 - J
232: IF (NOUNIT) X(JX) = X(JX)/A(KPLUS1,J)
233: TEMP = X(JX)
234: DO 30 I = J - 1,MAX(1,J-K),-1
235: X(IX) = X(IX) - TEMP*A(L+I,J)
236: IX = IX - INCX
237: 30 CONTINUE
238: END IF
239: JX = JX - INCX
240: 40 CONTINUE
241: END IF
242: ELSE
243: IF (INCX.EQ.1) THEN
244: DO 60 J = 1,N
245: IF (X(J).NE.ZERO) THEN
246: L = 1 - J
247: IF (NOUNIT) X(J) = X(J)/A(1,J)
248: TEMP = X(J)
249: DO 50 I = J + 1,MIN(N,J+K)
250: X(I) = X(I) - TEMP*A(L+I,J)
251: 50 CONTINUE
252: END IF
253: 60 CONTINUE
254: ELSE
255: JX = KX
256: DO 80 J = 1,N
257: KX = KX + INCX
258: IF (X(JX).NE.ZERO) THEN
259: IX = KX
260: L = 1 - J
261: IF (NOUNIT) X(JX) = X(JX)/A(1,J)
262: TEMP = X(JX)
263: DO 70 I = J + 1,MIN(N,J+K)
264: X(IX) = X(IX) - TEMP*A(L+I,J)
265: IX = IX + INCX
266: 70 CONTINUE
267: END IF
268: JX = JX + INCX
269: 80 CONTINUE
270: END IF
271: END IF
272: ELSE
273: *
274: * Form x := inv( A')*x.
275: *
276: IF (LSAME(UPLO,'U')) THEN
277: KPLUS1 = K + 1
278: IF (INCX.EQ.1) THEN
279: DO 100 J = 1,N
280: TEMP = X(J)
281: L = KPLUS1 - J
282: DO 90 I = MAX(1,J-K),J - 1
283: TEMP = TEMP - A(L+I,J)*X(I)
284: 90 CONTINUE
285: IF (NOUNIT) TEMP = TEMP/A(KPLUS1,J)
286: X(J) = TEMP
287: 100 CONTINUE
288: ELSE
289: JX = KX
290: DO 120 J = 1,N
291: TEMP = X(JX)
292: IX = KX
293: L = KPLUS1 - J
294: DO 110 I = MAX(1,J-K),J - 1
295: TEMP = TEMP - A(L+I,J)*X(IX)
296: IX = IX + INCX
297: 110 CONTINUE
298: IF (NOUNIT) TEMP = TEMP/A(KPLUS1,J)
299: X(JX) = TEMP
300: JX = JX + INCX
301: IF (J.GT.K) KX = KX + INCX
302: 120 CONTINUE
303: END IF
304: ELSE
305: IF (INCX.EQ.1) THEN
306: DO 140 J = N,1,-1
307: TEMP = X(J)
308: L = 1 - J
309: DO 130 I = MIN(N,J+K),J + 1,-1
310: TEMP = TEMP - A(L+I,J)*X(I)
311: 130 CONTINUE
312: IF (NOUNIT) TEMP = TEMP/A(1,J)
313: X(J) = TEMP
314: 140 CONTINUE
315: ELSE
316: KX = KX + (N-1)*INCX
317: JX = KX
318: DO 160 J = N,1,-1
319: TEMP = X(JX)
320: IX = KX
321: L = 1 - J
322: DO 150 I = MIN(N,J+K),J + 1,-1
323: TEMP = TEMP - A(L+I,J)*X(IX)
324: IX = IX - INCX
325: 150 CONTINUE
326: IF (NOUNIT) TEMP = TEMP/A(1,J)
327: X(JX) = TEMP
328: JX = JX - INCX
329: IF ((N-J).GE.K) KX = KX - INCX
330: 160 CONTINUE
331: END IF
332: END IF
333: END IF
334: *
335: RETURN
336: *
337: * End of DTBSV .
338: *
339: END
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