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1.1 bertrand 1: SUBROUTINE ZTBMV(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 COMPLEX A(LDA,*),X(*)
8: * ..
9: *
10: * Purpose
11: * =======
12: *
13: * ZTBMV performs one of the matrix-vector operations
14: *
1.7 ! bertrand 15: * x := A*x, or x := A**T*x, or x := A**H*x,
1.1 bertrand 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: *
1.7 ! bertrand 39: * TRANS = 'T' or 't' x := A**T*x.
1.1 bertrand 40: *
1.7 ! bertrand 41: * TRANS = 'C' or 'c' x := A**H*x.
1.1 bertrand 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 - COMPLEX*16 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 - COMPLEX*16 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.
1.7 ! bertrand 132: * The vector and matrix arguments are not referenced when N = 0, or M = 0
1.1 bertrand 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: DOUBLE COMPLEX ZERO
144: PARAMETER (ZERO= (0.0D+0,0.0D+0))
145: * ..
146: * .. Local Scalars ..
147: DOUBLE COMPLEX TEMP
148: INTEGER I,INFO,IX,J,JX,KPLUS1,KX,L
149: LOGICAL NOCONJ,NOUNIT
150: * ..
151: * .. External Functions ..
152: LOGICAL LSAME
153: EXTERNAL LSAME
154: * ..
155: * .. External Subroutines ..
156: EXTERNAL XERBLA
157: * ..
158: * .. Intrinsic Functions ..
159: INTRINSIC DCONJG,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('ZTBMV ',INFO)
183: RETURN
184: END IF
185: *
186: * Quick return if possible.
187: *
188: IF (N.EQ.0) RETURN
189: *
190: NOCONJ = LSAME(TRANS,'T')
191: NOUNIT = LSAME(DIAG,'N')
192: *
193: * Set up the start point in X if the increment is not unity. This
194: * will be ( N - 1 )*INCX too small for descending loops.
195: *
196: IF (INCX.LE.0) THEN
197: KX = 1 - (N-1)*INCX
198: ELSE IF (INCX.NE.1) THEN
199: KX = 1
200: END IF
201: *
202: * Start the operations. In this version the elements of A are
203: * accessed sequentially with one pass through A.
204: *
205: IF (LSAME(TRANS,'N')) THEN
206: *
207: * Form x := A*x.
208: *
209: IF (LSAME(UPLO,'U')) THEN
210: KPLUS1 = K + 1
211: IF (INCX.EQ.1) THEN
212: DO 20 J = 1,N
213: IF (X(J).NE.ZERO) THEN
214: TEMP = X(J)
215: L = KPLUS1 - J
216: DO 10 I = MAX(1,J-K),J - 1
217: X(I) = X(I) + TEMP*A(L+I,J)
218: 10 CONTINUE
219: IF (NOUNIT) X(J) = X(J)*A(KPLUS1,J)
220: END IF
221: 20 CONTINUE
222: ELSE
223: JX = KX
224: DO 40 J = 1,N
225: IF (X(JX).NE.ZERO) THEN
226: TEMP = X(JX)
227: IX = KX
228: L = KPLUS1 - J
229: DO 30 I = MAX(1,J-K),J - 1
230: X(IX) = X(IX) + TEMP*A(L+I,J)
231: IX = IX + INCX
232: 30 CONTINUE
233: IF (NOUNIT) X(JX) = X(JX)*A(KPLUS1,J)
234: END IF
235: JX = JX + INCX
236: IF (J.GT.K) KX = KX + INCX
237: 40 CONTINUE
238: END IF
239: ELSE
240: IF (INCX.EQ.1) THEN
241: DO 60 J = N,1,-1
242: IF (X(J).NE.ZERO) THEN
243: TEMP = X(J)
244: L = 1 - J
245: DO 50 I = MIN(N,J+K),J + 1,-1
246: X(I) = X(I) + TEMP*A(L+I,J)
247: 50 CONTINUE
248: IF (NOUNIT) X(J) = X(J)*A(1,J)
249: END IF
250: 60 CONTINUE
251: ELSE
252: KX = KX + (N-1)*INCX
253: JX = KX
254: DO 80 J = N,1,-1
255: IF (X(JX).NE.ZERO) THEN
256: TEMP = X(JX)
257: IX = KX
258: L = 1 - J
259: DO 70 I = MIN(N,J+K),J + 1,-1
260: X(IX) = X(IX) + TEMP*A(L+I,J)
261: IX = IX - INCX
262: 70 CONTINUE
263: IF (NOUNIT) X(JX) = X(JX)*A(1,J)
264: END IF
265: JX = JX - INCX
266: IF ((N-J).GE.K) KX = KX - INCX
267: 80 CONTINUE
268: END IF
269: END IF
270: ELSE
271: *
1.7 ! bertrand 272: * Form x := A**T*x or x := A**H*x.
1.1 bertrand 273: *
274: IF (LSAME(UPLO,'U')) THEN
275: KPLUS1 = K + 1
276: IF (INCX.EQ.1) THEN
277: DO 110 J = N,1,-1
278: TEMP = X(J)
279: L = KPLUS1 - J
280: IF (NOCONJ) THEN
281: IF (NOUNIT) TEMP = TEMP*A(KPLUS1,J)
282: DO 90 I = J - 1,MAX(1,J-K),-1
283: TEMP = TEMP + A(L+I,J)*X(I)
284: 90 CONTINUE
285: ELSE
286: IF (NOUNIT) TEMP = TEMP*DCONJG(A(KPLUS1,J))
287: DO 100 I = J - 1,MAX(1,J-K),-1
288: TEMP = TEMP + DCONJG(A(L+I,J))*X(I)
289: 100 CONTINUE
290: END IF
291: X(J) = TEMP
292: 110 CONTINUE
293: ELSE
294: KX = KX + (N-1)*INCX
295: JX = KX
296: DO 140 J = N,1,-1
297: TEMP = X(JX)
298: KX = KX - INCX
299: IX = KX
300: L = KPLUS1 - J
301: IF (NOCONJ) THEN
302: IF (NOUNIT) TEMP = TEMP*A(KPLUS1,J)
303: DO 120 I = J - 1,MAX(1,J-K),-1
304: TEMP = TEMP + A(L+I,J)*X(IX)
305: IX = IX - INCX
306: 120 CONTINUE
307: ELSE
308: IF (NOUNIT) TEMP = TEMP*DCONJG(A(KPLUS1,J))
309: DO 130 I = J - 1,MAX(1,J-K),-1
310: TEMP = TEMP + DCONJG(A(L+I,J))*X(IX)
311: IX = IX - INCX
312: 130 CONTINUE
313: END IF
314: X(JX) = TEMP
315: JX = JX - INCX
316: 140 CONTINUE
317: END IF
318: ELSE
319: IF (INCX.EQ.1) THEN
320: DO 170 J = 1,N
321: TEMP = X(J)
322: L = 1 - J
323: IF (NOCONJ) THEN
324: IF (NOUNIT) TEMP = TEMP*A(1,J)
325: DO 150 I = J + 1,MIN(N,J+K)
326: TEMP = TEMP + A(L+I,J)*X(I)
327: 150 CONTINUE
328: ELSE
329: IF (NOUNIT) TEMP = TEMP*DCONJG(A(1,J))
330: DO 160 I = J + 1,MIN(N,J+K)
331: TEMP = TEMP + DCONJG(A(L+I,J))*X(I)
332: 160 CONTINUE
333: END IF
334: X(J) = TEMP
335: 170 CONTINUE
336: ELSE
337: JX = KX
338: DO 200 J = 1,N
339: TEMP = X(JX)
340: KX = KX + INCX
341: IX = KX
342: L = 1 - J
343: IF (NOCONJ) THEN
344: IF (NOUNIT) TEMP = TEMP*A(1,J)
345: DO 180 I = J + 1,MIN(N,J+K)
346: TEMP = TEMP + A(L+I,J)*X(IX)
347: IX = IX + INCX
348: 180 CONTINUE
349: ELSE
350: IF (NOUNIT) TEMP = TEMP*DCONJG(A(1,J))
351: DO 190 I = J + 1,MIN(N,J+K)
352: TEMP = TEMP + DCONJG(A(L+I,J))*X(IX)
353: IX = IX + INCX
354: 190 CONTINUE
355: END IF
356: X(JX) = TEMP
357: JX = JX + INCX
358: 200 CONTINUE
359: END IF
360: END IF
361: END IF
362: *
363: RETURN
364: *
365: * End of ZTBMV .
366: *
367: END