1*> \brief \b CLANGB 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*
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16*> \endhtmlonly
17*
18*  Definition:
19*  ===========
20*
21*       REAL             FUNCTION CLANGB( 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*       REAL               WORK( * )
30*       COMPLEX            AB( LDAB, * )
31*       ..
32*
33*
34*> \par Purpose:
35*  =============
36*>
37*> \verbatim
38*>
39*> CLANGB  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 CLANGB
45*> \verbatim
46*>
47*>    CLANGB = ( 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 CLANGB 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, CLANGB 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 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 REAL 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 complexGBauxiliary
121*
122*  =====================================================================
123      REAL             FUNCTION CLANGB( 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      IMPLICIT NONE
131*     .. Scalar Arguments ..
132      CHARACTER          NORM
133      INTEGER            KL, KU, LDAB, N
134*     ..
135*     .. Array Arguments ..
136      REAL               WORK( * )
137      COMPLEX            AB( LDAB, * )
138*     ..
139*
140* =====================================================================
141*
142*     .. Parameters ..
143      REAL               ONE, ZERO
144      PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
145*     ..
146*     .. Local Scalars ..
147      INTEGER            I, J, K, L
148      REAL               SUM, VALUE, TEMP
149*     ..
150*     .. Local Arrays ..
151      REAL               SSQ( 2 ), COLSSQ( 2 )
152*     ..
153*     .. External Functions ..
154      LOGICAL            LSAME, SISNAN
155      EXTERNAL           LSAME, SISNAN
156*     ..
157*     .. External Subroutines ..
158      EXTERNAL           CLASSQ, SCOMBSSQ
159*     ..
160*     .. Intrinsic Functions ..
161      INTRINSIC          ABS, MAX, MIN, SQRT
162*     ..
163*     .. Executable Statements ..
164*
165      IF( N.EQ.0 ) THEN
166         VALUE = ZERO
167      ELSE IF( LSAME( NORM, 'M' ) ) THEN
168*
169*        Find max(abs(A(i,j))).
170*
171         VALUE = ZERO
172         DO 20 J = 1, N
173            DO 10 I = MAX( KU+2-J, 1 ), MIN( N+KU+1-J, KL+KU+1 )
174               TEMP = ABS( AB( I, J ) )
175               IF( VALUE.LT.TEMP .OR. SISNAN( TEMP ) ) VALUE = TEMP
176   10       CONTINUE
177   20    CONTINUE
178      ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
179*
180*        Find norm1(A).
181*
182         VALUE = ZERO
183         DO 40 J = 1, N
184            SUM = ZERO
185            DO 30 I = MAX( KU+2-J, 1 ), MIN( N+KU+1-J, KL+KU+1 )
186               SUM = SUM + ABS( AB( I, J ) )
187   30       CONTINUE
188            IF( VALUE.LT.SUM .OR. SISNAN( SUM ) ) VALUE = SUM
189   40    CONTINUE
190      ELSE IF( LSAME( NORM, 'I' ) ) THEN
191*
192*        Find normI(A).
193*
194         DO 50 I = 1, N
195            WORK( I ) = ZERO
196   50    CONTINUE
197         DO 70 J = 1, N
198            K = KU + 1 - J
199            DO 60 I = MAX( 1, J-KU ), MIN( N, J+KL )
200               WORK( I ) = WORK( I ) + ABS( AB( K+I, J ) )
201   60       CONTINUE
202   70    CONTINUE
203         VALUE = ZERO
204         DO 80 I = 1, N
205            TEMP = WORK( I )
206            IF( VALUE.LT.TEMP .OR. SISNAN( TEMP ) ) VALUE = TEMP
207   80    CONTINUE
208      ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
209*
210*        Find normF(A).
211*        SSQ(1) is scale
212*        SSQ(2) is sum-of-squares
213*        For better accuracy, sum each column separately.
214*
215         SSQ( 1 ) = ZERO
216         SSQ( 2 ) = ONE
217         DO 90 J = 1, N
218            L = MAX( 1, J-KU )
219            K = KU + 1 - J + L
220            COLSSQ( 1 ) = ZERO
221            COLSSQ( 2 ) = ONE
222            CALL CLASSQ( MIN( N, J+KL )-L+1, AB( K, J ), 1,
223     $                   COLSSQ( 1 ), COLSSQ( 2 ) )
224            CALL SCOMBSSQ( SSQ, COLSSQ )
225   90    CONTINUE
226         VALUE = SSQ( 1 )*SQRT( SSQ( 2 ) )
227      END IF
228*
229      CLANGB = VALUE
230      RETURN
231*
232*     End of CLANGB
233*
234      END
235