1: *> \brief \b DLANGB 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 DLANGB + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlangb.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlangb.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlangb.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * DOUBLE PRECISION FUNCTION DLANGB( 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 AB( LDAB, * ), WORK( * )
30: * ..
31: *
32: *
33: *> \par Purpose:
34: * =============
35: *>
36: *> \verbatim
37: *>
38: *> DLANGB 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 band matrix A, with kl sub-diagonals and ku super-diagonals.
41: *> \endverbatim
42: *>
43: *> \return DLANGB
44: *> \verbatim
45: *>
46: *> DLANGB = ( 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 DLANGB as described
67: *> above.
68: *> \endverbatim
69: *>
70: *> \param[in] N
71: *> \verbatim
72: *> N is INTEGER
73: *> The order of the matrix A. N >= 0. When N = 0, DLANGB is
74: *> set to zero.
75: *> \endverbatim
76: *>
77: *> \param[in] KL
78: *> \verbatim
79: *> KL is INTEGER
80: *> The number of sub-diagonals of the matrix A. KL >= 0.
81: *> \endverbatim
82: *>
83: *> \param[in] KU
84: *> \verbatim
85: *> KU is INTEGER
86: *> The number of super-diagonals of the matrix A. KU >= 0.
87: *> \endverbatim
88: *>
89: *> \param[in] AB
90: *> \verbatim
91: *> AB is DOUBLE PRECISION array, dimension (LDAB,N)
92: *> The band matrix A, stored in rows 1 to KL+KU+1. The j-th
93: *> column of A is stored in the j-th column of the array AB as
94: *> follows:
95: *> AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku)<=i<=min(n,j+kl).
96: *> \endverbatim
97: *>
98: *> \param[in] LDAB
99: *> \verbatim
100: *> LDAB is INTEGER
101: *> The leading dimension of the array AB. LDAB >= KL+KU+1.
102: *> \endverbatim
103: *>
104: *> \param[out] WORK
105: *> \verbatim
106: *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
107: *> where LWORK >= N when NORM = 'I'; otherwise, WORK is not
108: *> referenced.
109: *> \endverbatim
110: *
111: * Authors:
112: * ========
113: *
114: *> \author Univ. of Tennessee
115: *> \author Univ. of California Berkeley
116: *> \author Univ. of Colorado Denver
117: *> \author NAG Ltd.
118: *
119: *> \ingroup doubleGBauxiliary
120: *
121: * =====================================================================
122: DOUBLE PRECISION FUNCTION DLANGB( NORM, N, KL, KU, AB, LDAB,
123: $ WORK )
124: *
125: * -- LAPACK auxiliary routine --
126: * -- LAPACK is a software package provided by Univ. of Tennessee, --
127: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
128: *
129: * .. Scalar Arguments ..
130: CHARACTER NORM
131: INTEGER KL, KU, LDAB, N
132: * ..
133: * .. Array Arguments ..
134: DOUBLE PRECISION AB( LDAB, * ), WORK( * )
135: * ..
136: *
137: * =====================================================================
138: *
139: *
140: * .. Parameters ..
141: DOUBLE PRECISION ONE, ZERO
142: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
143: * ..
144: * .. Local Scalars ..
145: INTEGER I, J, K, L
146: DOUBLE PRECISION SCALE, SUM, VALUE, TEMP
147: * ..
148: * .. External Subroutines ..
149: EXTERNAL DLASSQ
150: * ..
151: * .. External Functions ..
152: LOGICAL LSAME, DISNAN
153: EXTERNAL LSAME, DISNAN
154: * ..
155: * .. Intrinsic Functions ..
156: INTRINSIC ABS, MAX, MIN, SQRT
157: * ..
158: * .. Executable Statements ..
159: *
160: IF( N.EQ.0 ) THEN
161: VALUE = ZERO
162: ELSE IF( LSAME( NORM, 'M' ) ) THEN
163: *
164: * Find max(abs(A(i,j))).
165: *
166: VALUE = ZERO
167: DO 20 J = 1, N
168: DO 10 I = MAX( KU+2-J, 1 ), MIN( N+KU+1-J, KL+KU+1 )
169: TEMP = ABS( AB( I, J ) )
170: IF( VALUE.LT.TEMP .OR. DISNAN( TEMP ) ) VALUE = TEMP
171: 10 CONTINUE
172: 20 CONTINUE
173: ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
174: *
175: * Find norm1(A).
176: *
177: VALUE = ZERO
178: DO 40 J = 1, N
179: SUM = ZERO
180: DO 30 I = MAX( KU+2-J, 1 ), MIN( N+KU+1-J, KL+KU+1 )
181: SUM = SUM + ABS( AB( I, J ) )
182: 30 CONTINUE
183: IF( VALUE.LT.SUM .OR. DISNAN( SUM ) ) VALUE = SUM
184: 40 CONTINUE
185: ELSE IF( LSAME( NORM, 'I' ) ) THEN
186: *
187: * Find normI(A).
188: *
189: DO 50 I = 1, N
190: WORK( I ) = ZERO
191: 50 CONTINUE
192: DO 70 J = 1, N
193: K = KU + 1 - J
194: DO 60 I = MAX( 1, J-KU ), MIN( N, J+KL )
195: WORK( I ) = WORK( I ) + ABS( AB( K+I, J ) )
196: 60 CONTINUE
197: 70 CONTINUE
198: VALUE = ZERO
199: DO 80 I = 1, N
200: TEMP = WORK( I )
201: IF( VALUE.LT.TEMP .OR. DISNAN( TEMP ) ) VALUE = TEMP
202: 80 CONTINUE
203: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
204: *
205: * Find normF(A).
206: *
207: SCALE = ZERO
208: SUM = ONE
209: DO 90 J = 1, N
210: L = MAX( 1, J-KU )
211: K = KU + 1 - J + L
212: CALL DLASSQ( MIN( N, J+KL )-L+1, AB( K, J ), 1, SCALE, SUM )
213: 90 CONTINUE
214: VALUE = SCALE*SQRT( SUM )
215: END IF
216: *
217: DLANGB = VALUE
218: RETURN
219: *
220: * End of DLANGB
221: *
222: END
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