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1: *> \brief \b ZLANSB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric 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 ZLANSB + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlansb.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlansb.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlansb.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * DOUBLE PRECISION FUNCTION ZLANSB( NORM, UPLO, N, K, AB, LDAB,
22: * WORK )
23: *
24: * .. Scalar Arguments ..
25: * CHARACTER 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: *> ZLANSB 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 symmetric band matrix A, with k super-diagonals.
42: *> \endverbatim
43: *>
44: *> \return ZLANSB
45: *> \verbatim
46: *>
47: *> ZLANSB = ( 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 ZLANSB as described
68: *> above.
69: *> \endverbatim
70: *>
71: *> \param[in] UPLO
72: *> \verbatim
73: *> UPLO is CHARACTER*1
74: *> Specifies whether the upper or lower triangular part of the
75: *> band matrix A is supplied.
76: *> = 'U': Upper triangular part is supplied
77: *> = 'L': Lower triangular part is supplied
78: *> \endverbatim
79: *>
80: *> \param[in] N
81: *> \verbatim
82: *> N is INTEGER
83: *> The order of the matrix A. N >= 0. When N = 0, ZLANSB is
84: *> set to zero.
85: *> \endverbatim
86: *>
87: *> \param[in] K
88: *> \verbatim
89: *> K is INTEGER
90: *> The number of super-diagonals or sub-diagonals of the
91: *> band matrix A. K >= 0.
92: *> \endverbatim
93: *>
94: *> \param[in] AB
95: *> \verbatim
96: *> AB is COMPLEX*16 array, dimension (LDAB,N)
97: *> The upper or lower triangle of the symmetric band matrix A,
98: *> stored in the first K+1 rows of AB. The j-th column of A is
99: *> stored in the j-th column of the array AB as follows:
100: *> if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j;
101: *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+k).
102: *> \endverbatim
103: *>
104: *> \param[in] LDAB
105: *> \verbatim
106: *> LDAB is INTEGER
107: *> The leading dimension of the array AB. LDAB >= K+1.
108: *> \endverbatim
109: *>
110: *> \param[out] WORK
111: *> \verbatim
112: *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
113: *> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
114: *> WORK is not referenced.
115: *> \endverbatim
116: *
117: * Authors:
118: * ========
119: *
120: *> \author Univ. of Tennessee
121: *> \author Univ. of California Berkeley
122: *> \author Univ. of Colorado Denver
123: *> \author NAG Ltd.
124: *
125: *> \date September 2012
126: *
127: *> \ingroup complex16OTHERauxiliary
128: *
129: * =====================================================================
130: DOUBLE PRECISION FUNCTION ZLANSB( NORM, UPLO, N, K, AB, LDAB,
131: $ WORK )
132: *
133: * -- LAPACK auxiliary routine (version 3.4.2) --
134: * -- LAPACK is a software package provided by Univ. of Tennessee, --
135: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
136: * September 2012
137: *
138: * .. Scalar Arguments ..
139: CHARACTER NORM, UPLO
140: INTEGER K, LDAB, N
141: * ..
142: * .. Array Arguments ..
143: DOUBLE PRECISION WORK( * )
144: COMPLEX*16 AB( LDAB, * )
145: * ..
146: *
147: * =====================================================================
148: *
149: * .. Parameters ..
150: DOUBLE PRECISION ONE, ZERO
151: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
152: * ..
153: * .. Local Scalars ..
154: INTEGER I, J, L
155: DOUBLE PRECISION ABSA, SCALE, SUM, VALUE
156: * ..
157: * .. External Functions ..
158: LOGICAL LSAME, DISNAN
159: EXTERNAL LSAME, DISNAN
160: * ..
161: * .. External Subroutines ..
162: EXTERNAL ZLASSQ
163: * ..
164: * .. Intrinsic Functions ..
165: INTRINSIC ABS, MAX, MIN, SQRT
166: * ..
167: * .. Executable Statements ..
168: *
169: IF( N.EQ.0 ) THEN
170: VALUE = ZERO
171: ELSE IF( LSAME( NORM, 'M' ) ) THEN
172: *
173: * Find max(abs(A(i,j))).
174: *
175: VALUE = ZERO
176: IF( LSAME( UPLO, 'U' ) ) THEN
177: DO 20 J = 1, N
178: DO 10 I = MAX( K+2-J, 1 ), K + 1
179: SUM = ABS( AB( I, J ) )
180: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
181: 10 CONTINUE
182: 20 CONTINUE
183: ELSE
184: DO 40 J = 1, N
185: DO 30 I = 1, MIN( N+1-J, K+1 )
186: SUM = ABS( AB( I, J ) )
187: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
188: 30 CONTINUE
189: 40 CONTINUE
190: END IF
191: ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR.
192: $ ( NORM.EQ.'1' ) ) THEN
193: *
194: * Find normI(A) ( = norm1(A), since A is symmetric).
195: *
196: VALUE = ZERO
197: IF( LSAME( UPLO, 'U' ) ) THEN
198: DO 60 J = 1, N
199: SUM = ZERO
200: L = K + 1 - J
201: DO 50 I = MAX( 1, J-K ), J - 1
202: ABSA = ABS( AB( L+I, J ) )
203: SUM = SUM + ABSA
204: WORK( I ) = WORK( I ) + ABSA
205: 50 CONTINUE
206: WORK( J ) = SUM + ABS( AB( K+1, J ) )
207: 60 CONTINUE
208: DO 70 I = 1, N
209: SUM = WORK( I )
210: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
211: 70 CONTINUE
212: ELSE
213: DO 80 I = 1, N
214: WORK( I ) = ZERO
215: 80 CONTINUE
216: DO 100 J = 1, N
217: SUM = WORK( J ) + ABS( AB( 1, J ) )
218: L = 1 - J
219: DO 90 I = J + 1, MIN( N, J+K )
220: ABSA = ABS( AB( L+I, J ) )
221: SUM = SUM + ABSA
222: WORK( I ) = WORK( I ) + ABSA
223: 90 CONTINUE
224: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
225: 100 CONTINUE
226: END IF
227: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
228: *
229: * Find normF(A).
230: *
231: SCALE = ZERO
232: SUM = ONE
233: IF( K.GT.0 ) THEN
234: IF( LSAME( UPLO, 'U' ) ) THEN
235: DO 110 J = 2, N
236: CALL ZLASSQ( MIN( J-1, K ), AB( MAX( K+2-J, 1 ), J ),
237: $ 1, SCALE, SUM )
238: 110 CONTINUE
239: L = K + 1
240: ELSE
241: DO 120 J = 1, N - 1
242: CALL ZLASSQ( MIN( N-J, K ), AB( 2, J ), 1, SCALE,
243: $ SUM )
244: 120 CONTINUE
245: L = 1
246: END IF
247: SUM = 2*SUM
248: ELSE
249: L = 1
250: END IF
251: CALL ZLASSQ( N, AB( L, 1 ), LDAB, SCALE, SUM )
252: VALUE = SCALE*SQRT( SUM )
253: END IF
254: *
255: ZLANSB = VALUE
256: RETURN
257: *
258: * End of ZLANSB
259: *
260: END
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