LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
clanhe.f
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1 *> \brief \b CLANHE returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix.
2 *
3 * =========== DOCUMENTATION ===========
4 *
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17 *
18 * Definition:
19 * ===========
20 *
21 * REAL FUNCTION CLANHE( NORM, UPLO, N, A, LDA, WORK )
22 *
23 * .. Scalar Arguments ..
24 * CHARACTER NORM, UPLO
25 * INTEGER LDA, N
26 * ..
27 * .. Array Arguments ..
28 * REAL WORK( * )
29 * COMPLEX A( LDA, * )
30 * ..
31 *
32 *
33 *> \par Purpose:
34 * =============
35 *>
36 *> \verbatim
37 *>
38 *> CLANHE 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 CLANHE
44 *> \verbatim
45 *>
46 *> CLANHE = ( 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 CLANHE 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, CLANHE is
83 *> set to zero.
84 *> \endverbatim
85 *>
86 *> \param[in] A
87 *> \verbatim
88 *> A is COMPLEX 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 REAL 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 September 2012
121 *
122 *> \ingroup complexHEauxiliary
123 *
124 * =====================================================================
125  REAL FUNCTION clanhe( NORM, UPLO, N, A, LDA, WORK )
126 *
127 * -- LAPACK auxiliary routine (version 3.4.2) --
128 * -- LAPACK is a software package provided by Univ. of Tennessee, --
129 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
130 * September 2012
131 *
132 * .. Scalar Arguments ..
133  CHARACTER NORM, UPLO
134  INTEGER LDA, N
135 * ..
136 * .. Array Arguments ..
137  REAL WORK( * )
138  COMPLEX A( lda, * )
139 * ..
140 *
141 * =====================================================================
142 *
143 * .. Parameters ..
144  REAL ONE, ZERO
145  parameter ( one = 1.0e+0, zero = 0.0e+0 )
146 * ..
147 * .. Local Scalars ..
148  INTEGER I, J
149  REAL ABSA, SCALE, SUM, VALUE
150 * ..
151 * .. External Functions ..
152  LOGICAL LSAME, SISNAN
153  EXTERNAL lsame, sisnan
154 * ..
155 * .. External Subroutines ..
156  EXTERNAL classq
157 * ..
158 * .. Intrinsic Functions ..
159  INTRINSIC abs, REAL, 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  sum = abs( a( i, j ) )
174  IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
175  10 CONTINUE
176  sum = abs( REAL( A( J, J ) ) )
177  IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
178  20 CONTINUE
179  ELSE
180  DO 40 j = 1, n
181  sum = abs( REAL( A( J, J ) ) )
182  IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
183  DO 30 i = j + 1, n
184  sum = abs( a( i, j ) )
185  IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
186  30 CONTINUE
187  40 CONTINUE
188  END IF
189  ELSE IF( ( lsame( norm, 'I' ) ) .OR. ( lsame( norm, 'O' ) ) .OR.
190  \$ ( norm.EQ.'1' ) ) THEN
191 *
192 * Find normI(A) ( = norm1(A), since A is hermitian).
193 *
194  VALUE = zero
195  IF( lsame( uplo, 'U' ) ) THEN
196  DO 60 j = 1, n
197  sum = zero
198  DO 50 i = 1, j - 1
199  absa = abs( a( i, j ) )
200  sum = sum + absa
201  work( i ) = work( i ) + absa
202  50 CONTINUE
203  work( j ) = sum + abs( REAL( A( J, J ) ) )
204  60 CONTINUE
205  DO 70 i = 1, n
206  sum = work( i )
207  IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
208  70 CONTINUE
209  ELSE
210  DO 80 i = 1, n
211  work( i ) = zero
212  80 CONTINUE
213  DO 100 j = 1, n
214  sum = work( j ) + abs( REAL( A( J, J ) ) )
215  DO 90 i = j + 1, n
216  absa = abs( a( i, j ) )
217  sum = sum + absa
218  work( i ) = work( i ) + absa
219  90 CONTINUE
220  IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
221  100 CONTINUE
222  END IF
223  ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
224 *
225 * Find normF(A).
226 *
227  scale = zero
228  sum = one
229  IF( lsame( uplo, 'U' ) ) THEN
230  DO 110 j = 2, n
231  CALL classq( j-1, a( 1, j ), 1, scale, sum )
232  110 CONTINUE
233  ELSE
234  DO 120 j = 1, n - 1
235  CALL classq( n-j, a( j+1, j ), 1, scale, sum )
236  120 CONTINUE
237  END IF
238  sum = 2*sum
239  DO 130 i = 1, n
240  IF( REAL( A( I, I ) ).NE.zero ) then
241  absa = abs( REAL( A( I, I ) ) )
242  IF( scale.LT.absa ) THEN
243  sum = one + sum*( scale / absa )**2
244  scale = absa
245  ELSE
246  sum = sum + ( absa / scale )**2
247  END IF
248  END IF
249  130 CONTINUE
250  VALUE = scale*sqrt( sum )
251  END IF
252 *
253  clanhe = VALUE
254  RETURN
255 *
256 * End of CLANHE
257 *
258  END
subroutine classq(N, X, INCX, SCALE, SUMSQ)
CLASSQ updates a sum of squares represented in scaled form.
Definition: classq.f:108
real function clanhe(NORM, UPLO, N, A, LDA, WORK)
CLANHE returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix.
Definition: clanhe.f:126