1: *> \brief \b ZLANTB 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 ZLANTB + dependencies
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11: *> [TGZ]</a>
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13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlantb.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * DOUBLE PRECISION FUNCTION ZLANTB( 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 WORK( * )
30: * COMPLEX*16 AB( LDAB, * )
31: * ..
32: *
33: *
34: *> \par Purpose:
35: * =============
36: *>
37: *> \verbatim
38: *>
39: *> ZLANTB returns the value of the one norm, or the Frobenius norm, or
40: *> the infinity norm, or the element of largest absolute value of an
41: *> n by n triangular band matrix A, with ( k + 1 ) diagonals.
42: *> \endverbatim
43: *>
44: *> \return ZLANTB
45: *> \verbatim
46: *>
47: *> ZLANTB = ( max(abs(A(i,j))), NORM = 'M' or 'm'
48: *> (
49: *> ( norm1(A), NORM = '1', 'O' or 'o'
50: *> (
51: *> ( normI(A), NORM = 'I' or 'i'
52: *> (
53: *> ( normF(A), NORM = 'F', 'f', 'E' or 'e'
54: *>
55: *> where norm1 denotes the one norm of a matrix (maximum column sum),
56: *> normI denotes the infinity norm of a matrix (maximum row sum) and
57: *> normF denotes the Frobenius norm of a matrix (square root of sum of
58: *> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
59: *> \endverbatim
60: *
61: * Arguments:
62: * ==========
63: *
64: *> \param[in] NORM
65: *> \verbatim
66: *> NORM is CHARACTER*1
67: *> Specifies the value to be returned in ZLANTB as described
68: *> above.
69: *> \endverbatim
70: *>
71: *> \param[in] UPLO
72: *> \verbatim
73: *> UPLO is CHARACTER*1
74: *> Specifies whether the matrix A is upper or lower triangular.
75: *> = 'U': Upper triangular
76: *> = 'L': Lower triangular
77: *> \endverbatim
78: *>
79: *> \param[in] DIAG
80: *> \verbatim
81: *> DIAG is CHARACTER*1
82: *> Specifies whether or not the matrix A is unit triangular.
83: *> = 'N': Non-unit triangular
84: *> = 'U': Unit triangular
85: *> \endverbatim
86: *>
87: *> \param[in] N
88: *> \verbatim
89: *> N is INTEGER
90: *> The order of the matrix A. N >= 0. When N = 0, ZLANTB is
91: *> set to zero.
92: *> \endverbatim
93: *>
94: *> \param[in] K
95: *> \verbatim
96: *> K is INTEGER
97: *> The number of super-diagonals of the matrix A if UPLO = 'U',
98: *> or the number of sub-diagonals of the matrix A if UPLO = 'L'.
99: *> K >= 0.
100: *> \endverbatim
101: *>
102: *> \param[in] AB
103: *> \verbatim
104: *> AB is COMPLEX*16 array, dimension (LDAB,N)
105: *> The upper or lower triangular band matrix A, stored in the
106: *> first k+1 rows of AB. The j-th column of A is stored
107: *> in the j-th column of the array AB as follows:
108: *> if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j;
109: *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+k).
110: *> Note that when DIAG = 'U', the elements of the array AB
111: *> corresponding to the diagonal elements of the matrix A are
112: *> not referenced, but are assumed to be one.
113: *> \endverbatim
114: *>
115: *> \param[in] LDAB
116: *> \verbatim
117: *> LDAB is INTEGER
118: *> The leading dimension of the array AB. LDAB >= K+1.
119: *> \endverbatim
120: *>
121: *> \param[out] WORK
122: *> \verbatim
123: *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
124: *> where LWORK >= N when NORM = 'I'; otherwise, WORK is not
125: *> referenced.
126: *> \endverbatim
127: *
128: * Authors:
129: * ========
130: *
131: *> \author Univ. of Tennessee
132: *> \author Univ. of California Berkeley
133: *> \author Univ. of Colorado Denver
134: *> \author NAG Ltd.
135: *
136: *> \date September 2012
137: *
138: *> \ingroup complex16OTHERauxiliary
139: *
140: * =====================================================================
141: DOUBLE PRECISION FUNCTION ZLANTB( NORM, UPLO, DIAG, N, K, AB,
142: $ LDAB, WORK )
143: *
144: * -- LAPACK auxiliary routine (version 3.4.2) --
145: * -- LAPACK is a software package provided by Univ. of Tennessee, --
146: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
147: * September 2012
148: *
149: * .. Scalar Arguments ..
150: CHARACTER DIAG, NORM, UPLO
151: INTEGER K, LDAB, N
152: * ..
153: * .. Array Arguments ..
154: DOUBLE PRECISION WORK( * )
155: COMPLEX*16 AB( LDAB, * )
156: * ..
157: *
158: * =====================================================================
159: *
160: * .. Parameters ..
161: DOUBLE PRECISION ONE, ZERO
162: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
163: * ..
164: * .. Local Scalars ..
165: LOGICAL UDIAG
166: INTEGER I, J, L
167: DOUBLE PRECISION SCALE, SUM, VALUE
168: * ..
169: * .. External Functions ..
170: LOGICAL LSAME, DISNAN
171: EXTERNAL LSAME, DISNAN
172: * ..
173: * .. External Subroutines ..
174: EXTERNAL ZLASSQ
175: * ..
176: * .. Intrinsic Functions ..
177: INTRINSIC ABS, MAX, MIN, SQRT
178: * ..
179: * .. Executable Statements ..
180: *
181: IF( N.EQ.0 ) THEN
182: VALUE = ZERO
183: ELSE IF( LSAME( NORM, 'M' ) ) THEN
184: *
185: * Find max(abs(A(i,j))).
186: *
187: IF( LSAME( DIAG, 'U' ) ) THEN
188: VALUE = ONE
189: IF( LSAME( UPLO, 'U' ) ) THEN
190: DO 20 J = 1, N
191: DO 10 I = MAX( K+2-J, 1 ), K
192: SUM = ABS( AB( I, J ) )
193: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
194: 10 CONTINUE
195: 20 CONTINUE
196: ELSE
197: DO 40 J = 1, N
198: DO 30 I = 2, MIN( N+1-J, K+1 )
199: SUM = ABS( AB( I, J ) )
200: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
201: 30 CONTINUE
202: 40 CONTINUE
203: END IF
204: ELSE
205: VALUE = ZERO
206: IF( LSAME( UPLO, 'U' ) ) THEN
207: DO 60 J = 1, N
208: DO 50 I = MAX( K+2-J, 1 ), K + 1
209: SUM = ABS( AB( I, J ) )
210: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
211: 50 CONTINUE
212: 60 CONTINUE
213: ELSE
214: DO 80 J = 1, N
215: DO 70 I = 1, MIN( N+1-J, K+1 )
216: SUM = ABS( AB( I, J ) )
217: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
218: 70 CONTINUE
219: 80 CONTINUE
220: END IF
221: END IF
222: ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
223: *
224: * Find norm1(A).
225: *
226: VALUE = ZERO
227: UDIAG = LSAME( DIAG, 'U' )
228: IF( LSAME( UPLO, 'U' ) ) THEN
229: DO 110 J = 1, N
230: IF( UDIAG ) THEN
231: SUM = ONE
232: DO 90 I = MAX( K+2-J, 1 ), K
233: SUM = SUM + ABS( AB( I, J ) )
234: 90 CONTINUE
235: ELSE
236: SUM = ZERO
237: DO 100 I = MAX( K+2-J, 1 ), K + 1
238: SUM = SUM + ABS( AB( I, J ) )
239: 100 CONTINUE
240: END IF
241: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
242: 110 CONTINUE
243: ELSE
244: DO 140 J = 1, N
245: IF( UDIAG ) THEN
246: SUM = ONE
247: DO 120 I = 2, MIN( N+1-J, K+1 )
248: SUM = SUM + ABS( AB( I, J ) )
249: 120 CONTINUE
250: ELSE
251: SUM = ZERO
252: DO 130 I = 1, MIN( N+1-J, K+1 )
253: SUM = SUM + ABS( AB( I, J ) )
254: 130 CONTINUE
255: END IF
256: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
257: 140 CONTINUE
258: END IF
259: ELSE IF( LSAME( NORM, 'I' ) ) THEN
260: *
261: * Find normI(A).
262: *
263: VALUE = ZERO
264: IF( LSAME( UPLO, 'U' ) ) THEN
265: IF( LSAME( DIAG, 'U' ) ) THEN
266: DO 150 I = 1, N
267: WORK( I ) = ONE
268: 150 CONTINUE
269: DO 170 J = 1, N
270: L = K + 1 - J
271: DO 160 I = MAX( 1, J-K ), J - 1
272: WORK( I ) = WORK( I ) + ABS( AB( L+I, J ) )
273: 160 CONTINUE
274: 170 CONTINUE
275: ELSE
276: DO 180 I = 1, N
277: WORK( I ) = ZERO
278: 180 CONTINUE
279: DO 200 J = 1, N
280: L = K + 1 - J
281: DO 190 I = MAX( 1, J-K ), J
282: WORK( I ) = WORK( I ) + ABS( AB( L+I, J ) )
283: 190 CONTINUE
284: 200 CONTINUE
285: END IF
286: ELSE
287: IF( LSAME( DIAG, 'U' ) ) THEN
288: DO 210 I = 1, N
289: WORK( I ) = ONE
290: 210 CONTINUE
291: DO 230 J = 1, N
292: L = 1 - J
293: DO 220 I = J + 1, MIN( N, J+K )
294: WORK( I ) = WORK( I ) + ABS( AB( L+I, J ) )
295: 220 CONTINUE
296: 230 CONTINUE
297: ELSE
298: DO 240 I = 1, N
299: WORK( I ) = ZERO
300: 240 CONTINUE
301: DO 260 J = 1, N
302: L = 1 - J
303: DO 250 I = J, MIN( N, J+K )
304: WORK( I ) = WORK( I ) + ABS( AB( L+I, J ) )
305: 250 CONTINUE
306: 260 CONTINUE
307: END IF
308: END IF
309: DO 270 I = 1, N
310: SUM = WORK( I )
311: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
312: 270 CONTINUE
313: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
314: *
315: * Find normF(A).
316: *
317: IF( LSAME( UPLO, 'U' ) ) THEN
318: IF( LSAME( DIAG, 'U' ) ) THEN
319: SCALE = ONE
320: SUM = N
321: IF( K.GT.0 ) THEN
322: DO 280 J = 2, N
323: CALL ZLASSQ( MIN( J-1, K ),
324: $ AB( MAX( K+2-J, 1 ), J ), 1, SCALE,
325: $ SUM )
326: 280 CONTINUE
327: END IF
328: ELSE
329: SCALE = ZERO
330: SUM = ONE
331: DO 290 J = 1, N
332: CALL ZLASSQ( MIN( J, K+1 ), AB( MAX( K+2-J, 1 ), J ),
333: $ 1, SCALE, SUM )
334: 290 CONTINUE
335: END IF
336: ELSE
337: IF( LSAME( DIAG, 'U' ) ) THEN
338: SCALE = ONE
339: SUM = N
340: IF( K.GT.0 ) THEN
341: DO 300 J = 1, N - 1
342: CALL ZLASSQ( MIN( N-J, K ), AB( 2, J ), 1, SCALE,
343: $ SUM )
344: 300 CONTINUE
345: END IF
346: ELSE
347: SCALE = ZERO
348: SUM = ONE
349: DO 310 J = 1, N
350: CALL ZLASSQ( MIN( N-J+1, K+1 ), AB( 1, J ), 1, SCALE,
351: $ SUM )
352: 310 CONTINUE
353: END IF
354: END IF
355: VALUE = SCALE*SQRT( SUM )
356: END IF
357: *
358: ZLANTB = VALUE
359: RETURN
360: *
361: * End of ZLANTB
362: *
363: END
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