1: *> \brief \b ZTBSV
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: * Definition:
9: * ===========
10: *
11: * SUBROUTINE ZTBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
12: *
13: * .. Scalar Arguments ..
14: * INTEGER INCX,K,LDA,N
15: * CHARACTER DIAG,TRANS,UPLO
16: * ..
17: * .. Array Arguments ..
18: * COMPLEX*16 A(LDA,*),X(*)
19: * ..
20: *
21: *
22: *> \par Purpose:
23: * =============
24: *>
25: *> \verbatim
26: *>
27: *> ZTBSV solves one of the systems of equations
28: *>
29: *> A*x = b, or A**T*x = b, or A**H*x = b,
30: *>
31: *> where b and x are n element vectors and A is an n by n unit, or
32: *> non-unit, upper or lower triangular band matrix, with ( k + 1 )
33: *> diagonals.
34: *>
35: *> No test for singularity or near-singularity is included in this
36: *> routine. Such tests must be performed before calling this routine.
37: *> \endverbatim
38: *
39: * Arguments:
40: * ==========
41: *
42: *> \param[in] UPLO
43: *> \verbatim
44: *> UPLO is CHARACTER*1
45: *> On entry, UPLO specifies whether the matrix is an upper or
46: *> lower triangular matrix as follows:
47: *>
48: *> UPLO = 'U' or 'u' A is an upper triangular matrix.
49: *>
50: *> UPLO = 'L' or 'l' A is a lower triangular matrix.
51: *> \endverbatim
52: *>
53: *> \param[in] TRANS
54: *> \verbatim
55: *> TRANS is CHARACTER*1
56: *> On entry, TRANS specifies the equations to be solved as
57: *> follows:
58: *>
59: *> TRANS = 'N' or 'n' A*x = b.
60: *>
61: *> TRANS = 'T' or 't' A**T*x = b.
62: *>
63: *> TRANS = 'C' or 'c' A**H*x = b.
64: *> \endverbatim
65: *>
66: *> \param[in] DIAG
67: *> \verbatim
68: *> DIAG is CHARACTER*1
69: *> On entry, DIAG specifies whether or not A is unit
70: *> triangular as follows:
71: *>
72: *> DIAG = 'U' or 'u' A is assumed to be unit triangular.
73: *>
74: *> DIAG = 'N' or 'n' A is not assumed to be unit
75: *> triangular.
76: *> \endverbatim
77: *>
78: *> \param[in] N
79: *> \verbatim
80: *> N is INTEGER
81: *> On entry, N specifies the order of the matrix A.
82: *> N must be at least zero.
83: *> \endverbatim
84: *>
85: *> \param[in] K
86: *> \verbatim
87: *> K is INTEGER
88: *> On entry with UPLO = 'U' or 'u', K specifies the number of
89: *> super-diagonals of the matrix A.
90: *> On entry with UPLO = 'L' or 'l', K specifies the number of
91: *> sub-diagonals of the matrix A.
92: *> K must satisfy 0 .le. K.
93: *> \endverbatim
94: *>
95: *> \param[in] A
96: *> \verbatim
97: *> A is COMPLEX*16 array of DIMENSION ( LDA, n ).
98: *> Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
99: *> by n part of the array A must contain the upper triangular
100: *> band part of the matrix of coefficients, supplied column by
101: *> column, with the leading diagonal of the matrix in row
102: *> ( k + 1 ) of the array, the first super-diagonal starting at
103: *> position 2 in row k, and so on. The top left k by k triangle
104: *> of the array A is not referenced.
105: *> The following program segment will transfer an upper
106: *> triangular band matrix from conventional full matrix storage
107: *> to band storage:
108: *>
109: *> DO 20, J = 1, N
110: *> M = K + 1 - J
111: *> DO 10, I = MAX( 1, J - K ), J
112: *> A( M + I, J ) = matrix( I, J )
113: *> 10 CONTINUE
114: *> 20 CONTINUE
115: *>
116: *> Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
117: *> by n part of the array A must contain the lower triangular
118: *> band part of the matrix of coefficients, supplied column by
119: *> column, with the leading diagonal of the matrix in row 1 of
120: *> the array, the first sub-diagonal starting at position 1 in
121: *> row 2, and so on. The bottom right k by k triangle of the
122: *> array A is not referenced.
123: *> The following program segment will transfer a lower
124: *> triangular band matrix from conventional full matrix storage
125: *> to band storage:
126: *>
127: *> DO 20, J = 1, N
128: *> M = 1 - J
129: *> DO 10, I = J, MIN( N, J + K )
130: *> A( M + I, J ) = matrix( I, J )
131: *> 10 CONTINUE
132: *> 20 CONTINUE
133: *>
134: *> Note that when DIAG = 'U' or 'u' the elements of the array A
135: *> corresponding to the diagonal elements of the matrix are not
136: *> referenced, but are assumed to be unity.
137: *> \endverbatim
138: *>
139: *> \param[in] LDA
140: *> \verbatim
141: *> LDA is INTEGER
142: *> On entry, LDA specifies the first dimension of A as declared
143: *> in the calling (sub) program. LDA must be at least
144: *> ( k + 1 ).
145: *> \endverbatim
146: *>
147: *> \param[in,out] X
148: *> \verbatim
149: *> X is COMPLEX*16 array of dimension at least
150: *> ( 1 + ( n - 1 )*abs( INCX ) ).
151: *> Before entry, the incremented array X must contain the n
152: *> element right-hand side vector b. On exit, X is overwritten
153: *> with the solution vector x.
154: *> \endverbatim
155: *>
156: *> \param[in] INCX
157: *> \verbatim
158: *> INCX is INTEGER
159: *> On entry, INCX specifies the increment for the elements of
160: *> X. INCX must not be zero.
161: *> \endverbatim
162: *
163: * Authors:
164: * ========
165: *
166: *> \author Univ. of Tennessee
167: *> \author Univ. of California Berkeley
168: *> \author Univ. of Colorado Denver
169: *> \author NAG Ltd.
170: *
171: *> \date November 2011
172: *
173: *> \ingroup complex16_blas_level2
174: *
175: *> \par Further Details:
176: * =====================
177: *>
178: *> \verbatim
179: *>
180: *> Level 2 Blas routine.
181: *>
182: *> -- Written on 22-October-1986.
183: *> Jack Dongarra, Argonne National Lab.
184: *> Jeremy Du Croz, Nag Central Office.
185: *> Sven Hammarling, Nag Central Office.
186: *> Richard Hanson, Sandia National Labs.
187: *> \endverbatim
188: *>
189: * =====================================================================
190: SUBROUTINE ZTBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
191: *
192: * -- Reference BLAS level2 routine (version 3.4.0) --
193: * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
194: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
195: * November 2011
196: *
197: * .. Scalar Arguments ..
198: INTEGER INCX,K,LDA,N
199: CHARACTER DIAG,TRANS,UPLO
200: * ..
201: * .. Array Arguments ..
202: COMPLEX*16 A(LDA,*),X(*)
203: * ..
204: *
205: * =====================================================================
206: *
207: * .. Parameters ..
208: COMPLEX*16 ZERO
209: PARAMETER (ZERO= (0.0D+0,0.0D+0))
210: * ..
211: * .. Local Scalars ..
212: COMPLEX*16 TEMP
213: INTEGER I,INFO,IX,J,JX,KPLUS1,KX,L
214: LOGICAL NOCONJ,NOUNIT
215: * ..
216: * .. External Functions ..
217: LOGICAL LSAME
218: EXTERNAL LSAME
219: * ..
220: * .. External Subroutines ..
221: EXTERNAL XERBLA
222: * ..
223: * .. Intrinsic Functions ..
224: INTRINSIC DCONJG,MAX,MIN
225: * ..
226: *
227: * Test the input parameters.
228: *
229: INFO = 0
230: IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
231: INFO = 1
232: ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
233: + .NOT.LSAME(TRANS,'C')) THEN
234: INFO = 2
235: ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
236: INFO = 3
237: ELSE IF (N.LT.0) THEN
238: INFO = 4
239: ELSE IF (K.LT.0) THEN
240: INFO = 5
241: ELSE IF (LDA.LT. (K+1)) THEN
242: INFO = 7
243: ELSE IF (INCX.EQ.0) THEN
244: INFO = 9
245: END IF
246: IF (INFO.NE.0) THEN
247: CALL XERBLA('ZTBSV ',INFO)
248: RETURN
249: END IF
250: *
251: * Quick return if possible.
252: *
253: IF (N.EQ.0) RETURN
254: *
255: NOCONJ = LSAME(TRANS,'T')
256: NOUNIT = LSAME(DIAG,'N')
257: *
258: * Set up the start point in X if the increment is not unity. This
259: * will be ( N - 1 )*INCX too small for descending loops.
260: *
261: IF (INCX.LE.0) THEN
262: KX = 1 - (N-1)*INCX
263: ELSE IF (INCX.NE.1) THEN
264: KX = 1
265: END IF
266: *
267: * Start the operations. In this version the elements of A are
268: * accessed by sequentially with one pass through A.
269: *
270: IF (LSAME(TRANS,'N')) THEN
271: *
272: * Form x := inv( A )*x.
273: *
274: IF (LSAME(UPLO,'U')) THEN
275: KPLUS1 = K + 1
276: IF (INCX.EQ.1) THEN
277: DO 20 J = N,1,-1
278: IF (X(J).NE.ZERO) THEN
279: L = KPLUS1 - J
280: IF (NOUNIT) X(J) = X(J)/A(KPLUS1,J)
281: TEMP = X(J)
282: DO 10 I = J - 1,MAX(1,J-K),-1
283: X(I) = X(I) - TEMP*A(L+I,J)
284: 10 CONTINUE
285: END IF
286: 20 CONTINUE
287: ELSE
288: KX = KX + (N-1)*INCX
289: JX = KX
290: DO 40 J = N,1,-1
291: KX = KX - INCX
292: IF (X(JX).NE.ZERO) THEN
293: IX = KX
294: L = KPLUS1 - J
295: IF (NOUNIT) X(JX) = X(JX)/A(KPLUS1,J)
296: TEMP = X(JX)
297: DO 30 I = J - 1,MAX(1,J-K),-1
298: X(IX) = X(IX) - TEMP*A(L+I,J)
299: IX = IX - INCX
300: 30 CONTINUE
301: END IF
302: JX = JX - INCX
303: 40 CONTINUE
304: END IF
305: ELSE
306: IF (INCX.EQ.1) THEN
307: DO 60 J = 1,N
308: IF (X(J).NE.ZERO) THEN
309: L = 1 - J
310: IF (NOUNIT) X(J) = X(J)/A(1,J)
311: TEMP = X(J)
312: DO 50 I = J + 1,MIN(N,J+K)
313: X(I) = X(I) - TEMP*A(L+I,J)
314: 50 CONTINUE
315: END IF
316: 60 CONTINUE
317: ELSE
318: JX = KX
319: DO 80 J = 1,N
320: KX = KX + INCX
321: IF (X(JX).NE.ZERO) THEN
322: IX = KX
323: L = 1 - J
324: IF (NOUNIT) X(JX) = X(JX)/A(1,J)
325: TEMP = X(JX)
326: DO 70 I = J + 1,MIN(N,J+K)
327: X(IX) = X(IX) - TEMP*A(L+I,J)
328: IX = IX + INCX
329: 70 CONTINUE
330: END IF
331: JX = JX + INCX
332: 80 CONTINUE
333: END IF
334: END IF
335: ELSE
336: *
337: * Form x := inv( A**T )*x or x := inv( A**H )*x.
338: *
339: IF (LSAME(UPLO,'U')) THEN
340: KPLUS1 = K + 1
341: IF (INCX.EQ.1) THEN
342: DO 110 J = 1,N
343: TEMP = X(J)
344: L = KPLUS1 - J
345: IF (NOCONJ) THEN
346: DO 90 I = MAX(1,J-K),J - 1
347: TEMP = TEMP - A(L+I,J)*X(I)
348: 90 CONTINUE
349: IF (NOUNIT) TEMP = TEMP/A(KPLUS1,J)
350: ELSE
351: DO 100 I = MAX(1,J-K),J - 1
352: TEMP = TEMP - DCONJG(A(L+I,J))*X(I)
353: 100 CONTINUE
354: IF (NOUNIT) TEMP = TEMP/DCONJG(A(KPLUS1,J))
355: END IF
356: X(J) = TEMP
357: 110 CONTINUE
358: ELSE
359: JX = KX
360: DO 140 J = 1,N
361: TEMP = X(JX)
362: IX = KX
363: L = KPLUS1 - J
364: IF (NOCONJ) THEN
365: DO 120 I = MAX(1,J-K),J - 1
366: TEMP = TEMP - A(L+I,J)*X(IX)
367: IX = IX + INCX
368: 120 CONTINUE
369: IF (NOUNIT) TEMP = TEMP/A(KPLUS1,J)
370: ELSE
371: DO 130 I = MAX(1,J-K),J - 1
372: TEMP = TEMP - DCONJG(A(L+I,J))*X(IX)
373: IX = IX + INCX
374: 130 CONTINUE
375: IF (NOUNIT) TEMP = TEMP/DCONJG(A(KPLUS1,J))
376: END IF
377: X(JX) = TEMP
378: JX = JX + INCX
379: IF (J.GT.K) KX = KX + INCX
380: 140 CONTINUE
381: END IF
382: ELSE
383: IF (INCX.EQ.1) THEN
384: DO 170 J = N,1,-1
385: TEMP = X(J)
386: L = 1 - J
387: IF (NOCONJ) THEN
388: DO 150 I = MIN(N,J+K),J + 1,-1
389: TEMP = TEMP - A(L+I,J)*X(I)
390: 150 CONTINUE
391: IF (NOUNIT) TEMP = TEMP/A(1,J)
392: ELSE
393: DO 160 I = MIN(N,J+K),J + 1,-1
394: TEMP = TEMP - DCONJG(A(L+I,J))*X(I)
395: 160 CONTINUE
396: IF (NOUNIT) TEMP = TEMP/DCONJG(A(1,J))
397: END IF
398: X(J) = TEMP
399: 170 CONTINUE
400: ELSE
401: KX = KX + (N-1)*INCX
402: JX = KX
403: DO 200 J = N,1,-1
404: TEMP = X(JX)
405: IX = KX
406: L = 1 - J
407: IF (NOCONJ) THEN
408: DO 180 I = MIN(N,J+K),J + 1,-1
409: TEMP = TEMP - A(L+I,J)*X(IX)
410: IX = IX - INCX
411: 180 CONTINUE
412: IF (NOUNIT) TEMP = TEMP/A(1,J)
413: ELSE
414: DO 190 I = MIN(N,J+K),J + 1,-1
415: TEMP = TEMP - DCONJG(A(L+I,J))*X(IX)
416: IX = IX - INCX
417: 190 CONTINUE
418: IF (NOUNIT) TEMP = TEMP/DCONJG(A(1,J))
419: END IF
420: X(JX) = TEMP
421: JX = JX - INCX
422: IF ((N-J).GE.K) KX = KX - INCX
423: 200 CONTINUE
424: END IF
425: END IF
426: END IF
427: *
428: RETURN
429: *
430: * End of ZTBSV .
431: *
432: END
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