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: *> \ingroup complex16OTHERauxiliary
126: *
127: * =====================================================================
128: DOUBLE PRECISION FUNCTION ZLANSB( NORM, UPLO, N, K, AB, LDAB,
129: $ WORK )
130: *
131: * -- LAPACK auxiliary routine --
132: * -- LAPACK is a software package provided by Univ. of Tennessee, --
133: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
134: *
135: * .. Scalar Arguments ..
136: CHARACTER NORM, UPLO
137: INTEGER K, LDAB, N
138: * ..
139: * .. Array Arguments ..
140: DOUBLE PRECISION WORK( * )
141: COMPLEX*16 AB( LDAB, * )
142: * ..
143: *
144: * =====================================================================
145: *
146: * .. Parameters ..
147: DOUBLE PRECISION ONE, ZERO
148: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
149: * ..
150: * .. Local Scalars ..
151: INTEGER I, J, L
152: DOUBLE PRECISION ABSA, SCALE, SUM, VALUE
153: * ..
154: * .. External Functions ..
155: LOGICAL LSAME, DISNAN
156: EXTERNAL LSAME, DISNAN
157: * ..
158: * .. External Subroutines ..
159: EXTERNAL ZLASSQ
160: * ..
161: * .. Intrinsic Functions ..
162: INTRINSIC ABS, MAX, MIN, SQRT
163: * ..
164: * .. Executable Statements ..
165: *
166: IF( N.EQ.0 ) THEN
167: VALUE = ZERO
168: ELSE IF( LSAME( NORM, 'M' ) ) THEN
169: *
170: * Find max(abs(A(i,j))).
171: *
172: VALUE = ZERO
173: IF( LSAME( UPLO, 'U' ) ) THEN
174: DO 20 J = 1, N
175: DO 10 I = MAX( K+2-J, 1 ), K + 1
176: SUM = ABS( AB( I, J ) )
177: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
178: 10 CONTINUE
179: 20 CONTINUE
180: ELSE
181: DO 40 J = 1, N
182: DO 30 I = 1, MIN( N+1-J, K+1 )
183: SUM = ABS( AB( I, J ) )
184: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
185: 30 CONTINUE
186: 40 CONTINUE
187: END IF
188: ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR.
189: $ ( NORM.EQ.'1' ) ) THEN
190: *
191: * Find normI(A) ( = norm1(A), since A is symmetric).
192: *
193: VALUE = ZERO
194: IF( LSAME( UPLO, 'U' ) ) THEN
195: DO 60 J = 1, N
196: SUM = ZERO
197: L = K + 1 - J
198: DO 50 I = MAX( 1, J-K ), J - 1
199: ABSA = ABS( AB( L+I, J ) )
200: SUM = SUM + ABSA
201: WORK( I ) = WORK( I ) + ABSA
202: 50 CONTINUE
203: WORK( J ) = SUM + ABS( AB( K+1, J ) )
204: 60 CONTINUE
205: DO 70 I = 1, N
206: SUM = WORK( I )
207: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
208: 70 CONTINUE
209: ELSE
210: DO 80 I = 1, N
211: WORK( I ) = ZERO
212: 80 CONTINUE
213: DO 100 J = 1, N
214: SUM = WORK( J ) + ABS( AB( 1, J ) )
215: L = 1 - J
216: DO 90 I = J + 1, MIN( N, J+K )
217: ABSA = ABS( AB( L+I, J ) )
218: SUM = SUM + ABSA
219: WORK( I ) = WORK( I ) + ABSA
220: 90 CONTINUE
221: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
222: 100 CONTINUE
223: END IF
224: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
225: *
226: * Find normF(A).
227: *
228: SCALE = ZERO
229: SUM = ONE
230: IF( K.GT.0 ) THEN
231: IF( LSAME( UPLO, 'U' ) ) THEN
232: DO 110 J = 2, N
233: CALL ZLASSQ( MIN( J-1, K ), AB( MAX( K+2-J, 1 ), J ),
234: $ 1, SCALE, SUM )
235: 110 CONTINUE
236: L = K + 1
237: ELSE
238: DO 120 J = 1, N - 1
239: CALL ZLASSQ( MIN( N-J, K ), AB( 2, J ), 1, SCALE,
240: $ SUM )
241: 120 CONTINUE
242: L = 1
243: END IF
244: SUM = 2*SUM
245: ELSE
246: L = 1
247: END IF
248: CALL ZLASSQ( N, AB( L, 1 ), LDAB, SCALE, SUM )
249: VALUE = SCALE*SQRT( SUM )
250: END IF
251: *
252: ZLANSB = VALUE
253: RETURN
254: *
255: * End of ZLANSB
256: *
257: END
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