LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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zlangb.f
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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*> \ingroup langb
121*
122* =====================================================================
123 DOUBLE PRECISION FUNCTION zlangb( NORM, N, KL, KU, AB, LDAB,
124 $ WORK )
125*
126* -- LAPACK auxiliary routine --
127* -- LAPACK is a software package provided by Univ. of Tennessee, --
128* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
129*
130* .. Scalar Arguments ..
131 CHARACTER norm
132 INTEGER kl, ku, ldab, n
133* ..
134* .. Array Arguments ..
135 DOUBLE PRECISION work( * )
136 COMPLEX*16 ab( ldab, * )
137* ..
138*
139* =====================================================================
140*
141* .. Parameters ..
142 DOUBLE PRECISION one, zero
143 parameter( one = 1.0d+0, zero = 0.0d+0 )
144* ..
145* .. Local Scalars ..
146 INTEGER i, j, k, l
147 DOUBLE PRECISION scale, sum, VALUE, temp
148* ..
149* .. External Functions ..
150 LOGICAL lsame, disnan
151 EXTERNAL lsame, disnan
152* ..
153* .. External Subroutines ..
154 EXTERNAL zlassq
155* ..
156* .. Intrinsic Functions ..
157 INTRINSIC abs, max, min, sqrt
158* ..
159* .. Executable Statements ..
160*
161 IF( n.EQ.0 ) THEN
162 VALUE = zero
163 ELSE IF( lsame( norm, 'M' ) ) THEN
164*
165* Find max(abs(A(i,j))).
166*
167 VALUE = zero
168 DO 20 j = 1, n
169 DO 10 i = max( ku+2-j, 1 ), min( n+ku+1-j, kl+ku+1 )
170 temp = abs( ab( i, j ) )
171 IF( VALUE.LT.temp .OR. disnan( temp ) ) VALUE = temp
172 10 CONTINUE
173 20 CONTINUE
174 ELSE IF( ( lsame( norm, 'O' ) ) .OR. ( norm.EQ.'1' ) ) THEN
175*
176* Find norm1(A).
177*
178 VALUE = zero
179 DO 40 j = 1, n
180 sum = zero
181 DO 30 i = max( ku+2-j, 1 ), min( n+ku+1-j, kl+ku+1 )
182 sum = sum + abs( ab( i, j ) )
183 30 CONTINUE
184 IF( VALUE.LT.sum .OR. disnan( sum ) ) VALUE = sum
185 40 CONTINUE
186 ELSE IF( lsame( norm, 'I' ) ) THEN
187*
188* Find normI(A).
189*
190 DO 50 i = 1, n
191 work( i ) = zero
192 50 CONTINUE
193 DO 70 j = 1, n
194 k = ku + 1 - j
195 DO 60 i = max( 1, j-ku ), min( n, j+kl )
196 work( i ) = work( i ) + abs( ab( k+i, j ) )
197 60 CONTINUE
198 70 CONTINUE
199 VALUE = zero
200 DO 80 i = 1, n
201 temp = work( i )
202 IF( VALUE.LT.temp .OR. disnan( temp ) ) VALUE = temp
203 80 CONTINUE
204 ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
205*
206* Find normF(A).
207*
208 scale = zero
209 sum = one
210 DO 90 j = 1, n
211 l = max( 1, j-ku )
212 k = ku + 1 - j + l
213 CALL zlassq( min( n, j+kl )-l+1, ab( k, j ), 1, scale, sum )
214 90 CONTINUE
215 VALUE = scale*sqrt( sum )
216 END IF
217*
218 zlangb = VALUE
219 RETURN
220*
221* End of ZLANGB
222*
223 END
logical function disnan(din)
DISNAN tests input for NaN.
Definition disnan.f:59
double precision function zlangb(norm, n, kl, ku, ab, ldab, work)
ZLANGB returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value ...
Definition zlangb.f:125
subroutine zlassq(n, x, incx, scale, sumsq)
ZLASSQ updates a sum of squares represented in scaled form.
Definition zlassq.f90:124
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48