1: *> \brief \b ZLANHE
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZLANHE + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlanhe.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlanhe.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlanhe.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * DOUBLE PRECISION FUNCTION ZLANHE( NORM, UPLO, N, A, LDA, WORK )
22: *
23: * .. Scalar Arguments ..
24: * CHARACTER NORM, UPLO
25: * INTEGER LDA, N
26: * ..
27: * .. Array Arguments ..
28: * DOUBLE PRECISION WORK( * )
29: * COMPLEX*16 A( LDA, * )
30: * ..
31: *
32: *
33: *> \par Purpose:
34: * =============
35: *>
36: *> \verbatim
37: *>
38: *> ZLANHE returns the value of the one norm, or the Frobenius norm, or
39: *> the infinity norm, or the element of largest absolute value of a
40: *> complex hermitian matrix A.
41: *> \endverbatim
42: *>
43: *> \return ZLANHE
44: *> \verbatim
45: *>
46: *> ZLANHE = ( 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 ZLANHE as described
67: *> above.
68: *> \endverbatim
69: *>
70: *> \param[in] UPLO
71: *> \verbatim
72: *> UPLO is CHARACTER*1
73: *> Specifies whether the upper or lower triangular part of the
74: *> hermitian matrix A is to be referenced.
75: *> = 'U': Upper triangular part of A is referenced
76: *> = 'L': Lower triangular part of A is referenced
77: *> \endverbatim
78: *>
79: *> \param[in] N
80: *> \verbatim
81: *> N is INTEGER
82: *> The order of the matrix A. N >= 0. When N = 0, ZLANHE is
83: *> set to zero.
84: *> \endverbatim
85: *>
86: *> \param[in] A
87: *> \verbatim
88: *> A is COMPLEX*16 array, dimension (LDA,N)
89: *> The hermitian matrix A. If UPLO = 'U', the leading n by n
90: *> upper triangular part of A contains the upper triangular part
91: *> of the matrix A, and the strictly lower triangular part of A
92: *> is not referenced. If UPLO = 'L', the leading n by n lower
93: *> triangular part of A contains the lower triangular part of
94: *> the matrix A, and the strictly upper triangular part of A is
95: *> not referenced. Note that the imaginary parts of the diagonal
96: *> elements need not be set and are assumed to be zero.
97: *> \endverbatim
98: *>
99: *> \param[in] LDA
100: *> \verbatim
101: *> LDA is INTEGER
102: *> The leading dimension of the array A. LDA >= max(N,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' or '1' or 'O'; otherwise,
109: *> WORK is not 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: *> \date November 2011
121: *
122: *> \ingroup complex16HEauxiliary
123: *
124: * =====================================================================
125: DOUBLE PRECISION FUNCTION ZLANHE( NORM, UPLO, N, A, LDA, WORK )
126: *
127: * -- LAPACK auxiliary routine (version 3.4.0) --
128: * -- LAPACK is a software package provided by Univ. of Tennessee, --
129: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
130: * November 2011
131: *
132: * .. Scalar Arguments ..
133: CHARACTER NORM, UPLO
134: INTEGER LDA, N
135: * ..
136: * .. Array Arguments ..
137: DOUBLE PRECISION WORK( * )
138: COMPLEX*16 A( LDA, * )
139: * ..
140: *
141: * =====================================================================
142: *
143: * .. Parameters ..
144: DOUBLE PRECISION ONE, ZERO
145: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
146: * ..
147: * .. Local Scalars ..
148: INTEGER I, J
149: DOUBLE PRECISION ABSA, SCALE, SUM, VALUE
150: * ..
151: * .. External Functions ..
152: LOGICAL LSAME
153: EXTERNAL LSAME
154: * ..
155: * .. External Subroutines ..
156: EXTERNAL ZLASSQ
157: * ..
158: * .. Intrinsic Functions ..
159: INTRINSIC ABS, DBLE, MAX, 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: IF( LSAME( UPLO, 'U' ) ) THEN
171: DO 20 J = 1, N
172: DO 10 I = 1, J - 1
173: VALUE = MAX( VALUE, ABS( A( I, J ) ) )
174: 10 CONTINUE
175: VALUE = MAX( VALUE, ABS( DBLE( A( J, J ) ) ) )
176: 20 CONTINUE
177: ELSE
178: DO 40 J = 1, N
179: VALUE = MAX( VALUE, ABS( DBLE( A( J, J ) ) ) )
180: DO 30 I = J + 1, N
181: VALUE = MAX( VALUE, ABS( A( I, J ) ) )
182: 30 CONTINUE
183: 40 CONTINUE
184: END IF
185: ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR.
186: $ ( NORM.EQ.'1' ) ) THEN
187: *
188: * Find normI(A) ( = norm1(A), since A is hermitian).
189: *
190: VALUE = ZERO
191: IF( LSAME( UPLO, 'U' ) ) THEN
192: DO 60 J = 1, N
193: SUM = ZERO
194: DO 50 I = 1, J - 1
195: ABSA = ABS( A( I, J ) )
196: SUM = SUM + ABSA
197: WORK( I ) = WORK( I ) + ABSA
198: 50 CONTINUE
199: WORK( J ) = SUM + ABS( DBLE( A( J, J ) ) )
200: 60 CONTINUE
201: DO 70 I = 1, N
202: VALUE = MAX( VALUE, WORK( I ) )
203: 70 CONTINUE
204: ELSE
205: DO 80 I = 1, N
206: WORK( I ) = ZERO
207: 80 CONTINUE
208: DO 100 J = 1, N
209: SUM = WORK( J ) + ABS( DBLE( A( J, J ) ) )
210: DO 90 I = J + 1, N
211: ABSA = ABS( A( I, J ) )
212: SUM = SUM + ABSA
213: WORK( I ) = WORK( I ) + ABSA
214: 90 CONTINUE
215: VALUE = MAX( VALUE, SUM )
216: 100 CONTINUE
217: END IF
218: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
219: *
220: * Find normF(A).
221: *
222: SCALE = ZERO
223: SUM = ONE
224: IF( LSAME( UPLO, 'U' ) ) THEN
225: DO 110 J = 2, N
226: CALL ZLASSQ( J-1, A( 1, J ), 1, SCALE, SUM )
227: 110 CONTINUE
228: ELSE
229: DO 120 J = 1, N - 1
230: CALL ZLASSQ( N-J, A( J+1, J ), 1, SCALE, SUM )
231: 120 CONTINUE
232: END IF
233: SUM = 2*SUM
234: DO 130 I = 1, N
235: IF( DBLE( A( I, I ) ).NE.ZERO ) THEN
236: ABSA = ABS( DBLE( A( I, I ) ) )
237: IF( SCALE.LT.ABSA ) THEN
238: SUM = ONE + SUM*( SCALE / ABSA )**2
239: SCALE = ABSA
240: ELSE
241: SUM = SUM + ( ABSA / SCALE )**2
242: END IF
243: END IF
244: 130 CONTINUE
245: VALUE = SCALE*SQRT( SUM )
246: END IF
247: *
248: ZLANHE = VALUE
249: RETURN
250: *
251: * End of ZLANHE
252: *
253: END
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