1: *> \brief \b DLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular band matrix.
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DLANTB + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlantb.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlantb.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlantb.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * DOUBLE PRECISION FUNCTION DLANTB( NORM, UPLO, DIAG, N, K, AB,
22: * LDAB, WORK )
23: *
24: * .. Scalar Arguments ..
25: * CHARACTER DIAG, NORM, UPLO
26: * INTEGER K, LDAB, N
27: * ..
28: * .. Array Arguments ..
29: * DOUBLE PRECISION AB( LDAB, * ), WORK( * )
30: * ..
31: *
32: *
33: *> \par Purpose:
34: * =============
35: *>
36: *> \verbatim
37: *>
38: *> DLANTB returns the value of the one norm, or the Frobenius norm, or
39: *> the infinity norm, or the element of largest absolute value of an
40: *> n by n triangular band matrix A, with ( k + 1 ) diagonals.
41: *> \endverbatim
42: *>
43: *> \return DLANTB
44: *> \verbatim
45: *>
46: *> DLANTB = ( max(abs(A(i,j))), NORM = 'M' or 'm'
47: *> (
48: *> ( norm1(A), NORM = '1', 'O' or 'o'
49: *> (
50: *> ( normI(A), NORM = 'I' or 'i'
51: *> (
52: *> ( normF(A), NORM = 'F', 'f', 'E' or 'e'
53: *>
54: *> where norm1 denotes the one norm of a matrix (maximum column sum),
55: *> normI denotes the infinity norm of a matrix (maximum row sum) and
56: *> normF denotes the Frobenius norm of a matrix (square root of sum of
57: *> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
58: *> \endverbatim
59: *
60: * Arguments:
61: * ==========
62: *
63: *> \param[in] NORM
64: *> \verbatim
65: *> NORM is CHARACTER*1
66: *> Specifies the value to be returned in DLANTB as described
67: *> above.
68: *> \endverbatim
69: *>
70: *> \param[in] UPLO
71: *> \verbatim
72: *> UPLO is CHARACTER*1
73: *> Specifies whether the matrix A is upper or lower triangular.
74: *> = 'U': Upper triangular
75: *> = 'L': Lower triangular
76: *> \endverbatim
77: *>
78: *> \param[in] DIAG
79: *> \verbatim
80: *> DIAG is CHARACTER*1
81: *> Specifies whether or not the matrix A is unit triangular.
82: *> = 'N': Non-unit triangular
83: *> = 'U': Unit triangular
84: *> \endverbatim
85: *>
86: *> \param[in] N
87: *> \verbatim
88: *> N is INTEGER
89: *> The order of the matrix A. N >= 0. When N = 0, DLANTB is
90: *> set to zero.
91: *> \endverbatim
92: *>
93: *> \param[in] K
94: *> \verbatim
95: *> K is INTEGER
96: *> The number of super-diagonals of the matrix A if UPLO = 'U',
97: *> or the number of sub-diagonals of the matrix A if UPLO = 'L'.
98: *> K >= 0.
99: *> \endverbatim
100: *>
101: *> \param[in] AB
102: *> \verbatim
103: *> AB is DOUBLE PRECISION array, dimension (LDAB,N)
104: *> The upper or lower triangular band matrix A, stored in the
105: *> first k+1 rows of AB. The j-th column of A is stored
106: *> in the j-th column of the array AB as follows:
107: *> if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j;
108: *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+k).
109: *> Note that when DIAG = 'U', the elements of the array AB
110: *> corresponding to the diagonal elements of the matrix A are
111: *> not referenced, but are assumed to be one.
112: *> \endverbatim
113: *>
114: *> \param[in] LDAB
115: *> \verbatim
116: *> LDAB is INTEGER
117: *> The leading dimension of the array AB. LDAB >= K+1.
118: *> \endverbatim
119: *>
120: *> \param[out] WORK
121: *> \verbatim
122: *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
123: *> where LWORK >= N when NORM = 'I'; otherwise, WORK is not
124: *> referenced.
125: *> \endverbatim
126: *
127: * Authors:
128: * ========
129: *
130: *> \author Univ. of Tennessee
131: *> \author Univ. of California Berkeley
132: *> \author Univ. of Colorado Denver
133: *> \author NAG Ltd.
134: *
135: *> \ingroup doubleOTHERauxiliary
136: *
137: * =====================================================================
138: DOUBLE PRECISION FUNCTION DLANTB( NORM, UPLO, DIAG, N, K, AB,
139: $ LDAB, WORK )
140: *
141: * -- LAPACK auxiliary routine --
142: * -- LAPACK is a software package provided by Univ. of Tennessee, --
143: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
144: *
145: * .. Scalar Arguments ..
146: CHARACTER DIAG, NORM, UPLO
147: INTEGER K, LDAB, N
148: * ..
149: * .. Array Arguments ..
150: DOUBLE PRECISION AB( LDAB, * ), WORK( * )
151: * ..
152: *
153: * =====================================================================
154: *
155: * .. Parameters ..
156: DOUBLE PRECISION ONE, ZERO
157: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
158: * ..
159: * .. Local Scalars ..
160: LOGICAL UDIAG
161: INTEGER I, J, L
162: DOUBLE PRECISION SCALE, SUM, VALUE
163: * ..
164: * .. External Subroutines ..
165: EXTERNAL DLASSQ
166: * ..
167: * .. External Functions ..
168: LOGICAL LSAME, DISNAN
169: EXTERNAL LSAME, DISNAN
170: * ..
171: * .. Intrinsic Functions ..
172: INTRINSIC ABS, MAX, MIN, SQRT
173: * ..
174: * .. Executable Statements ..
175: *
176: IF( N.EQ.0 ) THEN
177: VALUE = ZERO
178: ELSE IF( LSAME( NORM, 'M' ) ) THEN
179: *
180: * Find max(abs(A(i,j))).
181: *
182: IF( LSAME( DIAG, 'U' ) ) THEN
183: VALUE = ONE
184: IF( LSAME( UPLO, 'U' ) ) THEN
185: DO 20 J = 1, N
186: DO 10 I = MAX( K+2-J, 1 ), K
187: SUM = ABS( AB( I, J ) )
188: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
189: 10 CONTINUE
190: 20 CONTINUE
191: ELSE
192: DO 40 J = 1, N
193: DO 30 I = 2, MIN( N+1-J, K+1 )
194: SUM = ABS( AB( I, J ) )
195: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
196: 30 CONTINUE
197: 40 CONTINUE
198: END IF
199: ELSE
200: VALUE = ZERO
201: IF( LSAME( UPLO, 'U' ) ) THEN
202: DO 60 J = 1, N
203: DO 50 I = MAX( K+2-J, 1 ), K + 1
204: SUM = ABS( AB( I, J ) )
205: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
206: 50 CONTINUE
207: 60 CONTINUE
208: ELSE
209: DO 80 J = 1, N
210: DO 70 I = 1, MIN( N+1-J, K+1 )
211: SUM = ABS( AB( I, J ) )
212: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
213: 70 CONTINUE
214: 80 CONTINUE
215: END IF
216: END IF
217: ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
218: *
219: * Find norm1(A).
220: *
221: VALUE = ZERO
222: UDIAG = LSAME( DIAG, 'U' )
223: IF( LSAME( UPLO, 'U' ) ) THEN
224: DO 110 J = 1, N
225: IF( UDIAG ) THEN
226: SUM = ONE
227: DO 90 I = MAX( K+2-J, 1 ), K
228: SUM = SUM + ABS( AB( I, J ) )
229: 90 CONTINUE
230: ELSE
231: SUM = ZERO
232: DO 100 I = MAX( K+2-J, 1 ), K + 1
233: SUM = SUM + ABS( AB( I, J ) )
234: 100 CONTINUE
235: END IF
236: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
237: 110 CONTINUE
238: ELSE
239: DO 140 J = 1, N
240: IF( UDIAG ) THEN
241: SUM = ONE
242: DO 120 I = 2, MIN( N+1-J, K+1 )
243: SUM = SUM + ABS( AB( I, J ) )
244: 120 CONTINUE
245: ELSE
246: SUM = ZERO
247: DO 130 I = 1, MIN( N+1-J, K+1 )
248: SUM = SUM + ABS( AB( I, J ) )
249: 130 CONTINUE
250: END IF
251: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
252: 140 CONTINUE
253: END IF
254: ELSE IF( LSAME( NORM, 'I' ) ) THEN
255: *
256: * Find normI(A).
257: *
258: VALUE = ZERO
259: IF( LSAME( UPLO, 'U' ) ) THEN
260: IF( LSAME( DIAG, 'U' ) ) THEN
261: DO 150 I = 1, N
262: WORK( I ) = ONE
263: 150 CONTINUE
264: DO 170 J = 1, N
265: L = K + 1 - J
266: DO 160 I = MAX( 1, J-K ), J - 1
267: WORK( I ) = WORK( I ) + ABS( AB( L+I, J ) )
268: 160 CONTINUE
269: 170 CONTINUE
270: ELSE
271: DO 180 I = 1, N
272: WORK( I ) = ZERO
273: 180 CONTINUE
274: DO 200 J = 1, N
275: L = K + 1 - J
276: DO 190 I = MAX( 1, J-K ), J
277: WORK( I ) = WORK( I ) + ABS( AB( L+I, J ) )
278: 190 CONTINUE
279: 200 CONTINUE
280: END IF
281: ELSE
282: IF( LSAME( DIAG, 'U' ) ) THEN
283: DO 210 I = 1, N
284: WORK( I ) = ONE
285: 210 CONTINUE
286: DO 230 J = 1, N
287: L = 1 - J
288: DO 220 I = J + 1, MIN( N, J+K )
289: WORK( I ) = WORK( I ) + ABS( AB( L+I, J ) )
290: 220 CONTINUE
291: 230 CONTINUE
292: ELSE
293: DO 240 I = 1, N
294: WORK( I ) = ZERO
295: 240 CONTINUE
296: DO 260 J = 1, N
297: L = 1 - J
298: DO 250 I = J, MIN( N, J+K )
299: WORK( I ) = WORK( I ) + ABS( AB( L+I, J ) )
300: 250 CONTINUE
301: 260 CONTINUE
302: END IF
303: END IF
304: DO 270 I = 1, N
305: SUM = WORK( I )
306: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
307: 270 CONTINUE
308: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
309: *
310: * Find normF(A).
311: *
312: IF( LSAME( UPLO, 'U' ) ) THEN
313: IF( LSAME( DIAG, 'U' ) ) THEN
314: SCALE = ONE
315: SUM = N
316: IF( K.GT.0 ) THEN
317: DO 280 J = 2, N
318: CALL DLASSQ( MIN( J-1, K ),
319: $ AB( MAX( K+2-J, 1 ), J ), 1, SCALE,
320: $ SUM )
321: 280 CONTINUE
322: END IF
323: ELSE
324: SCALE = ZERO
325: SUM = ONE
326: DO 290 J = 1, N
327: CALL DLASSQ( MIN( J, K+1 ), AB( MAX( K+2-J, 1 ), J ),
328: $ 1, SCALE, SUM )
329: 290 CONTINUE
330: END IF
331: ELSE
332: IF( LSAME( DIAG, 'U' ) ) THEN
333: SCALE = ONE
334: SUM = N
335: IF( K.GT.0 ) THEN
336: DO 300 J = 1, N - 1
337: CALL DLASSQ( MIN( N-J, K ), AB( 2, J ), 1, SCALE,
338: $ SUM )
339: 300 CONTINUE
340: END IF
341: ELSE
342: SCALE = ZERO
343: SUM = ONE
344: DO 310 J = 1, N
345: CALL DLASSQ( MIN( N-J+1, K+1 ), AB( 1, J ), 1, SCALE,
346: $ SUM )
347: 310 CONTINUE
348: END IF
349: END IF
350: VALUE = SCALE*SQRT( SUM )
351: END IF
352: *
353: DLANTB = VALUE
354: RETURN
355: *
356: * End of DLANTB
357: *
358: END
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