1: *> \brief \b ZLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of general 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 ZLANGB + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlangb.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlangb.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlangb.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * DOUBLE PRECISION FUNCTION ZLANGB( NORM, N, KL, KU, AB, LDAB,
22: * WORK )
23: *
24: * .. Scalar Arguments ..
25: * CHARACTER NORM
26: * INTEGER KL, KU, 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: *> ZLANGB 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 band matrix A, with kl sub-diagonals and ku super-diagonals.
42: *> \endverbatim
43: *>
44: *> \return ZLANGB
45: *> \verbatim
46: *>
47: *> ZLANGB = ( 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 ZLANGB as described
68: *> above.
69: *> \endverbatim
70: *>
71: *> \param[in] N
72: *> \verbatim
73: *> N is INTEGER
74: *> The order of the matrix A. N >= 0. When N = 0, ZLANGB is
75: *> set to zero.
76: *> \endverbatim
77: *>
78: *> \param[in] KL
79: *> \verbatim
80: *> KL is INTEGER
81: *> The number of sub-diagonals of the matrix A. KL >= 0.
82: *> \endverbatim
83: *>
84: *> \param[in] KU
85: *> \verbatim
86: *> KU is INTEGER
87: *> The number of super-diagonals of the matrix A. KU >= 0.
88: *> \endverbatim
89: *>
90: *> \param[in] AB
91: *> \verbatim
92: *> AB is COMPLEX*16 array, dimension (LDAB,N)
93: *> The band matrix A, stored in rows 1 to KL+KU+1. The j-th
94: *> column of A is stored in the j-th column of the array AB as
95: *> follows:
96: *> AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).
97: *> \endverbatim
98: *>
99: *> \param[in] LDAB
100: *> \verbatim
101: *> LDAB is INTEGER
102: *> The leading dimension of the array AB. LDAB >= KL+KU+1.
103: *> \endverbatim
104: *>
105: *> \param[out] WORK
106: *> \verbatim
107: *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
108: *> where LWORK >= N when NORM = 'I'; otherwise, WORK is not
109: *> referenced.
110: *> \endverbatim
111: *
112: * Authors:
113: * ========
114: *
115: *> \author Univ. of Tennessee
116: *> \author Univ. of California Berkeley
117: *> \author Univ. of Colorado Denver
118: *> \author NAG Ltd.
119: *
120: *> \date September 2012
121: *
122: *> \ingroup complex16GBauxiliary
123: *
124: * =====================================================================
125: DOUBLE PRECISION FUNCTION ZLANGB( NORM, N, KL, KU, AB, LDAB,
126: $ WORK )
127: *
128: * -- LAPACK auxiliary routine (version 3.4.2) --
129: * -- LAPACK is a software package provided by Univ. of Tennessee, --
130: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
131: * September 2012
132: *
133: * .. Scalar Arguments ..
134: CHARACTER NORM
135: INTEGER KL, KU, LDAB, N
136: * ..
137: * .. Array Arguments ..
138: DOUBLE PRECISION WORK( * )
139: COMPLEX*16 AB( LDAB, * )
140: * ..
141: *
142: * =====================================================================
143: *
144: * .. Parameters ..
145: DOUBLE PRECISION ONE, ZERO
146: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
147: * ..
148: * .. Local Scalars ..
149: INTEGER I, J, K, L
150: DOUBLE PRECISION SCALE, SUM, VALUE, TEMP
151: * ..
152: * .. External Functions ..
153: LOGICAL LSAME, DISNAN
154: EXTERNAL LSAME, DISNAN
155: * ..
156: * .. External Subroutines ..
157: EXTERNAL ZLASSQ
158: * ..
159: * .. Intrinsic Functions ..
160: INTRINSIC ABS, MAX, MIN, SQRT
161: * ..
162: * .. Executable Statements ..
163: *
164: IF( N.EQ.0 ) THEN
165: VALUE = ZERO
166: ELSE IF( LSAME( NORM, 'M' ) ) THEN
167: *
168: * Find max(abs(A(i,j))).
169: *
170: VALUE = ZERO
171: DO 20 J = 1, N
172: DO 10 I = MAX( KU+2-J, 1 ), MIN( N+KU+1-J, KL+KU+1 )
173: TEMP = ABS( AB( I, J ) )
174: IF( VALUE.LT.TEMP .OR. DISNAN( TEMP ) ) VALUE = TEMP
175: 10 CONTINUE
176: 20 CONTINUE
177: ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
178: *
179: * Find norm1(A).
180: *
181: VALUE = ZERO
182: DO 40 J = 1, N
183: SUM = ZERO
184: DO 30 I = MAX( KU+2-J, 1 ), MIN( N+KU+1-J, KL+KU+1 )
185: SUM = SUM + ABS( AB( I, J ) )
186: 30 CONTINUE
187: IF( VALUE.LT.SUM .OR. DISNAN( SUM ) ) VALUE = SUM
188: 40 CONTINUE
189: ELSE IF( LSAME( NORM, 'I' ) ) THEN
190: *
191: * Find normI(A).
192: *
193: DO 50 I = 1, N
194: WORK( I ) = ZERO
195: 50 CONTINUE
196: DO 70 J = 1, N
197: K = KU + 1 - J
198: DO 60 I = MAX( 1, J-KU ), MIN( N, J+KL )
199: WORK( I ) = WORK( I ) + ABS( AB( K+I, J ) )
200: 60 CONTINUE
201: 70 CONTINUE
202: VALUE = ZERO
203: DO 80 I = 1, N
204: TEMP = WORK( I )
205: IF( VALUE.LT.TEMP .OR. DISNAN( TEMP ) ) VALUE = TEMP
206: 80 CONTINUE
207: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
208: *
209: * Find normF(A).
210: *
211: SCALE = ZERO
212: SUM = ONE
213: DO 90 J = 1, N
214: L = MAX( 1, J-KU )
215: K = KU + 1 - J + L
216: CALL ZLASSQ( MIN( N, J+KL )-L+1, AB( K, J ), 1, SCALE, SUM )
217: 90 CONTINUE
218: VALUE = SCALE*SQRT( SUM )
219: END IF
220: *
221: ZLANGB = VALUE
222: RETURN
223: *
224: * End of ZLANGB
225: *
226: END
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