1*> \brief \b SLANGB 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 SLANGB( 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               AB( LDAB, * ), WORK( * )
30*       ..
31*
32*
33*> \par Purpose:
34*  =============
35*>
36*> \verbatim
37*>
38*> SLANGB  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 SLANGB
44*> \verbatim
45*>
46*>    SLANGB = ( 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 SLANGB 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, SLANGB 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 REAL 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 REAL 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 realGBauxiliary
120*
121*  =====================================================================
122      REAL             FUNCTION SLANGB( 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      IMPLICIT NONE
130*     .. Scalar Arguments ..
131      CHARACTER          NORM
132      INTEGER            KL, KU, LDAB, N
133*     ..
134*     .. Array Arguments ..
135      REAL               AB( LDAB, * ), WORK( * )
136*     ..
137*
138* =====================================================================
139*
140*     .. Parameters ..
141      REAL               ONE, ZERO
142      PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
143*     ..
144*     .. Local Scalars ..
145      INTEGER            I, J, K, L
146      REAL               SUM, VALUE, TEMP
147*     ..
148*     .. Local Arrays ..
149      REAL               SSQ( 2 ), COLSSQ( 2 )
150*     ..
151*     .. External Functions ..
152      LOGICAL            LSAME, SISNAN
153      EXTERNAL           LSAME, SISNAN
154*     ..
155*     .. External Subroutines ..
156      EXTERNAL           SLASSQ, SCOMBSSQ
157*     ..
158*     .. Intrinsic Functions ..
159      INTRINSIC          ABS, MAX, MIN, SQRT
160*     ..
161*     .. Executable Statements ..
162*
163      IF( N.EQ.0 ) THEN
164         VALUE = ZERO
165      ELSE IF( LSAME( NORM, 'M' ) ) THEN
166*
167*        Find max(abs(A(i,j))).
168*
169         VALUE = ZERO
170         DO 20 J = 1, N
171            DO 10 I = MAX( KU+2-J, 1 ), MIN( N+KU+1-J, KL+KU+1 )
172               TEMP = ABS( AB( I, J ) )
173               IF( VALUE.LT.TEMP .OR. SISNAN( TEMP ) ) VALUE = TEMP
174   10       CONTINUE
175   20    CONTINUE
176      ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
177*
178*        Find norm1(A).
179*
180         VALUE = ZERO
181         DO 40 J = 1, N
182            SUM = ZERO
183            DO 30 I = MAX( KU+2-J, 1 ), MIN( N+KU+1-J, KL+KU+1 )
184               SUM = SUM + ABS( AB( I, J ) )
185   30       CONTINUE
186            IF( VALUE.LT.SUM .OR. SISNAN( SUM ) ) VALUE = SUM
187   40    CONTINUE
188      ELSE IF( LSAME( NORM, 'I' ) ) THEN
189*
190*        Find normI(A).
191*
192         DO 50 I = 1, N
193            WORK( I ) = ZERO
194   50    CONTINUE
195         DO 70 J = 1, N
196            K = KU + 1 - J
197            DO 60 I = MAX( 1, J-KU ), MIN( N, J+KL )
198               WORK( I ) = WORK( I ) + ABS( AB( K+I, J ) )
199   60       CONTINUE
200   70    CONTINUE
201         VALUE = ZERO
202         DO 80 I = 1, N
203            TEMP = WORK( I )
204            IF( VALUE.LT.TEMP .OR. SISNAN( TEMP ) ) VALUE = TEMP
205   80    CONTINUE
206      ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
207*
208*        Find normF(A).
209*        SSQ(1) is scale
210*        SSQ(2) is sum-of-squares
211*        For better accuracy, sum each column separately.
212*
213         SSQ( 1 ) = ZERO
214         SSQ( 2 ) = ONE
215         DO 90 J = 1, N
216            L = MAX( 1, J-KU )
217            K = KU + 1 - J + L
218            COLSSQ( 1 ) = ZERO
219            COLSSQ( 2 ) = ONE
220            CALL SLASSQ( MIN( N, J+KL )-L+1, AB( K, J ), 1,
221     $                   COLSSQ( 1 ), COLSSQ( 2 ) )
222            CALL SCOMBSSQ( SSQ, COLSSQ )
223   90    CONTINUE
224         VALUE = SSQ( 1 )*SQRT( SSQ( 2 ) )
225      END IF
226*
227      SLANGB = VALUE
228      RETURN
229*
230*     End of SLANGB
231*
232      END
233