Annotation of rpl/lapack/lapack/zlanhb.f, revision 1.14
1.11 bertrand 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.
1.8 bertrand 2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZLANHB + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlanhb.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlanhb.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlanhb.f">
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: *
1.11 bertrand 127: *> \date September 2012
1.8 bertrand 128: *
129: *> \ingroup complex16OTHERauxiliary
130: *
131: * =====================================================================
1.1 bertrand 132: DOUBLE PRECISION FUNCTION ZLANHB( NORM, UPLO, N, K, AB, LDAB,
133: $ WORK )
134: *
1.11 bertrand 135: * -- LAPACK auxiliary routine (version 3.4.2) --
1.1 bertrand 136: * -- LAPACK is a software package provided by Univ. of Tennessee, --
137: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.11 bertrand 138: * September 2012
1.1 bertrand 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 ..
1.11 bertrand 160: LOGICAL LSAME, DISNAN
161: EXTERNAL LSAME, DISNAN
1.1 bertrand 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
1.11 bertrand 181: SUM = ABS( AB( I, J ) )
182: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
1.1 bertrand 183: 10 CONTINUE
1.11 bertrand 184: SUM = ABS( DBLE( AB( K+1, J ) ) )
185: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
1.1 bertrand 186: 20 CONTINUE
187: ELSE
188: DO 40 J = 1, N
1.11 bertrand 189: SUM = ABS( DBLE( AB( 1, J ) ) )
190: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
1.1 bertrand 191: DO 30 I = 2, MIN( N+1-J, K+1 )
1.11 bertrand 192: SUM = ABS( AB( I, J ) )
193: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
1.1 bertrand 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
1.11 bertrand 215: SUM = WORK( I )
216: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
1.1 bertrand 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
1.11 bertrand 230: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
1.1 bertrand 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
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