LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
clanhp.f
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1 *> \brief \b CLANHP 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 supplied in packed form.
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 *> \htmlonly
9 *> Download CLANHP + dependencies
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11 *> [TGZ]</a>
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13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clanhp.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * REAL FUNCTION CLANHP( NORM, UPLO, N, AP, WORK )
22 *
23 * .. Scalar Arguments ..
24 * CHARACTER NORM, UPLO
25 * INTEGER N
26 * ..
27 * .. Array Arguments ..
28 * REAL WORK( * )
29 * COMPLEX AP( * )
30 * ..
31 *
32 *
33 *> \par Purpose:
34 * =============
35 *>
36 *> \verbatim
37 *>
38 *> CLANHP 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, supplied in packed form.
41 *> \endverbatim
42 *>
43 *> \return CLANHP
44 *> \verbatim
45 *>
46 *> CLANHP = ( 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 CLANHP 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 supplied.
75 *> = 'U': Upper triangular part of A is supplied
76 *> = 'L': Lower triangular part of A is supplied
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, CLANHP is
83 *> set to zero.
84 *> \endverbatim
85 *>
86 *> \param[in] AP
87 *> \verbatim
88 *> AP is COMPLEX array, dimension (N*(N+1)/2)
89 *> The upper or lower triangle of the hermitian matrix A, packed
90 *> columnwise in a linear array. The j-th column of A is stored
91 *> in the array AP as follows:
92 *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
93 *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
94 *> Note that the imaginary parts of the diagonal elements need
95 *> not be set and are assumed to be zero.
96 *> \endverbatim
97 *>
98 *> \param[out] WORK
99 *> \verbatim
100 *> WORK is REAL array, dimension (MAX(1,LWORK)),
101 *> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
102 *> WORK is not referenced.
103 *> \endverbatim
104 *
105 * Authors:
106 * ========
107 *
108 *> \author Univ. of Tennessee
109 *> \author Univ. of California Berkeley
110 *> \author Univ. of Colorado Denver
111 *> \author NAG Ltd.
112 *
113 *> \ingroup complexOTHERauxiliary
114 *
115 * =====================================================================
116  REAL function clanhp( norm, uplo, n, ap, work )
117 *
118 * -- LAPACK auxiliary routine --
119 * -- LAPACK is a software package provided by Univ. of Tennessee, --
120 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
121 *
122  IMPLICIT NONE
123 * .. Scalar Arguments ..
124  CHARACTER norm, uplo
125  INTEGER n
126 * ..
127 * .. Array Arguments ..
128  REAL work( * )
129  COMPLEX ap( * )
130 * ..
131 *
132 * =====================================================================
133 *
134 * .. Parameters ..
135  REAL one, zero
136  parameter( one = 1.0e+0, zero = 0.0e+0 )
137 * ..
138 * .. Local Scalars ..
139  INTEGER i, j, k
140  REAL absa, sum, value
141 * ..
142 * .. Local Arrays ..
143  REAL ssq( 2 ), colssq( 2 )
144 * ..
145 * .. External Functions ..
146  LOGICAL lsame, sisnan
147  EXTERNAL lsame, sisnan
148 * ..
149 * .. External Subroutines ..
150  EXTERNAL classq, scombssq
151 * ..
152 * .. Intrinsic Functions ..
153  INTRINSIC abs, real, sqrt
154 * ..
155 * .. Executable Statements ..
156 *
157  IF( n.EQ.0 ) THEN
158  VALUE = zero
159  ELSE IF( lsame( norm, 'M' ) ) THEN
160 *
161 * Find max(abs(A(i,j))).
162 *
163  VALUE = zero
164  IF( lsame( uplo, 'U' ) ) THEN
165  k = 0
166  DO 20 j = 1, n
167  DO 10 i = k + 1, k + j - 1
168  sum = abs( ap( i ) )
169  IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
170  10 CONTINUE
171  k = k + j
172  sum = abs( real( ap( k ) ) )
173  IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
174  20 CONTINUE
175  ELSE
176  k = 1
177  DO 40 j = 1, n
178  sum = abs( real( ap( k ) ) )
179  IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
180  DO 30 i = k + 1, k + n - j
181  sum = abs( ap( i ) )
182  IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
183  30 CONTINUE
184  k = k + n - j + 1
185  40 CONTINUE
186  END IF
187  ELSE IF( ( lsame( norm, 'I' ) ) .OR. ( lsame( norm, 'O' ) ) .OR.
188  $ ( norm.EQ.'1' ) ) THEN
189 *
190 * Find normI(A) ( = norm1(A), since A is hermitian).
191 *
192  VALUE = zero
193  k = 1
194  IF( lsame( uplo, 'U' ) ) THEN
195  DO 60 j = 1, n
196  sum = zero
197  DO 50 i = 1, j - 1
198  absa = abs( ap( k ) )
199  sum = sum + absa
200  work( i ) = work( i ) + absa
201  k = k + 1
202  50 CONTINUE
203  work( j ) = sum + abs( real( ap( k ) ) )
204  k = k + 1
205  60 CONTINUE
206  DO 70 i = 1, n
207  sum = work( i )
208  IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
209  70 CONTINUE
210  ELSE
211  DO 80 i = 1, n
212  work( i ) = zero
213  80 CONTINUE
214  DO 100 j = 1, n
215  sum = work( j ) + abs( real( ap( k ) ) )
216  k = k + 1
217  DO 90 i = j + 1, n
218  absa = abs( ap( k ) )
219  sum = sum + absa
220  work( i ) = work( i ) + absa
221  k = k + 1
222  90 CONTINUE
223  IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
224  100 CONTINUE
225  END IF
226  ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
227 *
228 * Find normF(A).
229 * SSQ(1) is scale
230 * SSQ(2) is sum-of-squares
231 * For better accuracy, sum each column separately.
232 *
233  ssq( 1 ) = zero
234  ssq( 2 ) = one
235 *
236 * Sum off-diagonals
237 *
238  k = 2
239  IF( lsame( uplo, 'U' ) ) THEN
240  DO 110 j = 2, n
241  colssq( 1 ) = zero
242  colssq( 2 ) = one
243  CALL classq( j-1, ap( k ), 1, colssq( 1 ), colssq( 2 ) )
244  CALL scombssq( ssq, colssq )
245  k = k + j
246  110 CONTINUE
247  ELSE
248  DO 120 j = 1, n - 1
249  colssq( 1 ) = zero
250  colssq( 2 ) = one
251  CALL classq( n-j, ap( k ), 1, colssq( 1 ), colssq( 2 ) )
252  CALL scombssq( ssq, colssq )
253  k = k + n - j + 1
254  120 CONTINUE
255  END IF
256  ssq( 2 ) = 2*ssq( 2 )
257 *
258 * Sum diagonal
259 *
260  k = 1
261  colssq( 1 ) = zero
262  colssq( 2 ) = one
263  DO 130 i = 1, n
264  IF( real( ap( k ) ).NE.zero ) THEN
265  absa = abs( real( ap( k ) ) )
266  IF( colssq( 1 ).LT.absa ) THEN
267  colssq( 2 ) = one + colssq(2)*( colssq(1) / absa )**2
268  colssq( 1 ) = absa
269  ELSE
270  colssq( 2 ) = colssq( 2 ) + ( absa / colssq( 1 ) )**2
271  END IF
272  END IF
273  IF( lsame( uplo, 'U' ) ) THEN
274  k = k + i + 1
275  ELSE
276  k = k + n - i + 1
277  END IF
278  130 CONTINUE
279  CALL scombssq( ssq, colssq )
280  VALUE = ssq( 1 )*sqrt( ssq( 2 ) )
281  END IF
282 *
283  clanhp = VALUE
284  RETURN
285 *
286 * End of CLANHP
287 *
288  END
subroutine scombssq(V1, V2)
SCOMBSSQ adds two scaled sum of squares quantities
Definition: scombssq.f:60
subroutine classq(n, x, incx, scl, sumsq)
CLASSQ updates a sum of squares represented in scaled form.
Definition: classq.f90:126
logical function sisnan(SIN)
SISNAN tests input for NaN.
Definition: sisnan.f:59
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
real function clanhp(NORM, UPLO, N, AP, WORK)
CLANHP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: clanhp.f:117