1*> \brief \b ZLANHB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hermitian band matrix.
2*
3*  =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6*            http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
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15*> [TXT]</a>
16*> \endhtmlonly
17*
18*  Definition:
19*  ===========
20*
21*       DOUBLE PRECISION FUNCTION ZLANHB( NORM, UPLO, N, K, AB, LDAB,
22*                        WORK )
23*
24*       .. Scalar Arguments ..
25*       CHARACTER          NORM, UPLO
26*       INTEGER            K, 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*> ZLANHB  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 hermitian band matrix A,  with k super-diagonals.
42*> \endverbatim
43*>
44*> \return ZLANHB
45*> \verbatim
46*>
47*>    ZLANHB = ( 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 ZLANHB as described
68*>          above.
69*> \endverbatim
70*>
71*> \param[in] UPLO
72*> \verbatim
73*>          UPLO is CHARACTER*1
74*>          Specifies whether the upper or lower triangular part of the
75*>          band matrix A is supplied.
76*>          = 'U':  Upper triangular
77*>          = 'L':  Lower triangular
78*> \endverbatim
79*>
80*> \param[in] N
81*> \verbatim
82*>          N is INTEGER
83*>          The order of the matrix A.  N >= 0.  When N = 0, ZLANHB is
84*>          set to zero.
85*> \endverbatim
86*>
87*> \param[in] K
88*> \verbatim
89*>          K is INTEGER
90*>          The number of super-diagonals or sub-diagonals of the
91*>          band matrix A.  K >= 0.
92*> \endverbatim
93*>
94*> \param[in] AB
95*> \verbatim
96*>          AB is COMPLEX*16 array, dimension (LDAB,N)
97*>          The upper or lower triangle of the hermitian band matrix A,
98*>          stored in the first K+1 rows of AB.  The j-th column of A is
99*>          stored in the j-th column of the array AB as follows:
100*>          if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j;
101*>          if UPLO = 'L', AB(1+i-j,j)   = A(i,j) for j<=i<=min(n,j+k).
102*>          Note that the imaginary parts of the diagonal elements need
103*>          not be set and are assumed to be zero.
104*> \endverbatim
105*>
106*> \param[in] LDAB
107*> \verbatim
108*>          LDAB is INTEGER
109*>          The leading dimension of the array AB.  LDAB >= K+1.
110*> \endverbatim
111*>
112*> \param[out] WORK
113*> \verbatim
114*>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
115*>          where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
116*>          WORK is not referenced.
117*> \endverbatim
118*
119*  Authors:
120*  ========
121*
122*> \author Univ. of Tennessee
123*> \author Univ. of California Berkeley
124*> \author Univ. of Colorado Denver
125*> \author NAG Ltd.
126*
127*> \date September 2012
128*
129*> \ingroup complex16OTHERauxiliary
130*
131*  =====================================================================
132      DOUBLE PRECISION FUNCTION ZLANHB( NORM, UPLO, N, K, AB, LDAB,
133     $                 WORK )
134*
135*  -- LAPACK auxiliary routine (version 3.4.2) --
136*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
137*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
138*     September 2012
139*
140*     .. Scalar Arguments ..
141      CHARACTER          NORM, UPLO
142      INTEGER            K, LDAB, N
143*     ..
144*     .. Array Arguments ..
145      DOUBLE PRECISION   WORK( * )
146      COMPLEX*16         AB( LDAB, * )
147*     ..
148*
149* =====================================================================
150*
151*     .. Parameters ..
152      DOUBLE PRECISION   ONE, ZERO
153      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
154*     ..
155*     .. Local Scalars ..
156      INTEGER            I, J, L
157      DOUBLE PRECISION   ABSA, SCALE, SUM, VALUE
158*     ..
159*     .. External Functions ..
160      LOGICAL            LSAME, DISNAN
161      EXTERNAL           LSAME, DISNAN
162*     ..
163*     .. External Subroutines ..
164      EXTERNAL           ZLASSQ
165*     ..
166*     .. Intrinsic Functions ..
167      INTRINSIC          ABS, DBLE, MAX, MIN, SQRT
168*     ..
169*     .. Executable Statements ..
170*
171      IF( N.EQ.0 ) THEN
172         VALUE = ZERO
173      ELSE IF( LSAME( NORM, 'M' ) ) THEN
174*
175*        Find max(abs(A(i,j))).
176*
177         VALUE = ZERO
178         IF( LSAME( UPLO, 'U' ) ) THEN
179            DO 20 J = 1, N
180               DO 10 I = MAX( K+2-J, 1 ), K
181                  SUM = ABS( AB( I, J ) )
182                  IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
183   10          CONTINUE
184               SUM = ABS( DBLE( AB( K+1, J ) ) )
185               IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
186   20       CONTINUE
187         ELSE
188            DO 40 J = 1, N
189               SUM = ABS( DBLE( AB( 1, J ) ) )
190               IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
191               DO 30 I = 2, MIN( N+1-J, K+1 )
192                  SUM = ABS( AB( I, J ) )
193                  IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
194   30          CONTINUE
195   40       CONTINUE
196         END IF
197      ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR.
198     $         ( NORM.EQ.'1' ) ) THEN
199*
200*        Find normI(A) ( = norm1(A), since A is hermitian).
201*
202         VALUE = ZERO
203         IF( LSAME( UPLO, 'U' ) ) THEN
204            DO 60 J = 1, N
205               SUM = ZERO
206               L = K + 1 - J
207               DO 50 I = MAX( 1, J-K ), J - 1
208                  ABSA = ABS( AB( L+I, J ) )
209                  SUM = SUM + ABSA
210                  WORK( I ) = WORK( I ) + ABSA
211   50          CONTINUE
212               WORK( J ) = SUM + ABS( DBLE( AB( K+1, J ) ) )
213   60       CONTINUE
214            DO 70 I = 1, N
215               SUM = WORK( I )
216               IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
217   70       CONTINUE
218         ELSE
219            DO 80 I = 1, N
220               WORK( I ) = ZERO
221   80       CONTINUE
222            DO 100 J = 1, N
223               SUM = WORK( J ) + ABS( DBLE( AB( 1, J ) ) )
224               L = 1 - J
225               DO 90 I = J + 1, MIN( N, J+K )
226                  ABSA = ABS( AB( L+I, J ) )
227                  SUM = SUM + ABSA
228                  WORK( I ) = WORK( I ) + ABSA
229   90          CONTINUE
230               IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
231  100       CONTINUE
232         END IF
233      ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
234*
235*        Find normF(A).
236*
237         SCALE = ZERO
238         SUM = ONE
239         IF( K.GT.0 ) THEN
240            IF( LSAME( UPLO, 'U' ) ) THEN
241               DO 110 J = 2, N
242                  CALL ZLASSQ( MIN( J-1, K ), AB( MAX( K+2-J, 1 ), J ),
243     $                         1, SCALE, SUM )
244  110          CONTINUE
245               L = K + 1
246            ELSE
247               DO 120 J = 1, N - 1
248                  CALL ZLASSQ( MIN( N-J, K ), AB( 2, J ), 1, SCALE,
249     $                         SUM )
250  120          CONTINUE
251               L = 1
252            END IF
253            SUM = 2*SUM
254         ELSE
255            L = 1
256         END IF
257         DO 130 J = 1, N
258            IF( DBLE( AB( L, J ) ).NE.ZERO ) THEN
259               ABSA = ABS( DBLE( AB( L, J ) ) )
260               IF( SCALE.LT.ABSA ) THEN
261                  SUM = ONE + SUM*( SCALE / ABSA )**2
262                  SCALE = ABSA
263               ELSE
264                  SUM = SUM + ( ABSA / SCALE )**2
265               END IF
266            END IF
267  130    CONTINUE
268         VALUE = SCALE*SQRT( SUM )
269      END IF
270*
271      ZLANHB = VALUE
272      RETURN
273*
274*     End of ZLANHB
275*
276      END
277