LAPACK  3.10.1 LAPACK: Linear Algebra PACKage
clansp.f
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1 *> \brief \b CLANSP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric matrix supplied in packed form.
2 *
3 * =========== DOCUMENTATION ===========
4 *
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17 *
18 * Definition:
19 * ===========
20 *
21 * REAL FUNCTION CLANSP( 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 *> CLANSP 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 symmetric matrix A, supplied in packed form.
41 *> \endverbatim
42 *>
43 *> \return CLANSP
44 *> \verbatim
45 *>
46 *> CLANSP = ( 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 CLANSP 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 *> symmetric 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, CLANSP 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 symmetric 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 *> \endverbatim
95 *>
96 *> \param[out] WORK
97 *> \verbatim
98 *> WORK is REAL array, dimension (MAX(1,LWORK)),
99 *> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
100 *> WORK is not referenced.
101 *> \endverbatim
102 *
103 * Authors:
104 * ========
105 *
106 *> \author Univ. of Tennessee
107 *> \author Univ. of California Berkeley
108 *> \author Univ. of Colorado Denver
109 *> \author NAG Ltd.
110 *
111 *> \ingroup complexOTHERauxiliary
112 *
113 * =====================================================================
114  REAL function clansp( norm, uplo, n, ap, work )
115 *
116 * -- LAPACK auxiliary routine --
117 * -- LAPACK is a software package provided by Univ. of Tennessee, --
118 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
119 *
120 * .. Scalar Arguments ..
121  CHARACTER norm, uplo
122  INTEGER n
123 * ..
124 * .. Array Arguments ..
125  REAL work( * )
126  COMPLEX ap( * )
127 * ..
128 *
129 * =====================================================================
130 *
131 * .. Parameters ..
132  REAL one, zero
133  parameter( one = 1.0e+0, zero = 0.0e+0 )
134 * ..
135 * .. Local Scalars ..
136  INTEGER i, j, k
137  REAL absa, scale, sum, value
138 * ..
139 * .. External Functions ..
140  LOGICAL lsame, sisnan
141  EXTERNAL lsame, sisnan
142 * ..
143 * .. External Subroutines ..
144  EXTERNAL classq
145 * ..
146 * .. Intrinsic Functions ..
147  INTRINSIC abs, aimag, real, sqrt
148 * ..
149 * .. Executable Statements ..
150 *
151  IF( n.EQ.0 ) THEN
152  VALUE = zero
153  ELSE IF( lsame( norm, 'M' ) ) THEN
154 *
155 * Find max(abs(A(i,j))).
156 *
157  VALUE = zero
158  IF( lsame( uplo, 'U' ) ) THEN
159  k = 1
160  DO 20 j = 1, n
161  DO 10 i = k, k + j - 1
162  sum = abs( ap( i ) )
163  IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
164  10 CONTINUE
165  k = k + j
166  20 CONTINUE
167  ELSE
168  k = 1
169  DO 40 j = 1, n
170  DO 30 i = k, k + n - j
171  sum = abs( ap( i ) )
172  IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
173  30 CONTINUE
174  k = k + n - j + 1
175  40 CONTINUE
176  END IF
177  ELSE IF( ( lsame( norm, 'I' ) ) .OR. ( lsame( norm, 'O' ) ) .OR.
178  \$ ( norm.EQ.'1' ) ) THEN
179 *
180 * Find normI(A) ( = norm1(A), since A is symmetric).
181 *
182  VALUE = zero
183  k = 1
184  IF( lsame( uplo, 'U' ) ) THEN
185  DO 60 j = 1, n
186  sum = zero
187  DO 50 i = 1, j - 1
188  absa = abs( ap( k ) )
189  sum = sum + absa
190  work( i ) = work( i ) + absa
191  k = k + 1
192  50 CONTINUE
193  work( j ) = sum + abs( ap( k ) )
194  k = k + 1
195  60 CONTINUE
196  DO 70 i = 1, n
197  sum = work( i )
198  IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
199  70 CONTINUE
200  ELSE
201  DO 80 i = 1, n
202  work( i ) = zero
203  80 CONTINUE
204  DO 100 j = 1, n
205  sum = work( j ) + abs( ap( k ) )
206  k = k + 1
207  DO 90 i = j + 1, n
208  absa = abs( ap( k ) )
209  sum = sum + absa
210  work( i ) = work( i ) + absa
211  k = k + 1
212  90 CONTINUE
213  IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
214  100 CONTINUE
215  END IF
216  ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
217 *
218 * Find normF(A).
219 *
220  scale = zero
221  sum = one
222  k = 2
223  IF( lsame( uplo, 'U' ) ) THEN
224  DO 110 j = 2, n
225  CALL classq( j-1, ap( k ), 1, scale, sum )
226  k = k + j
227  110 CONTINUE
228  ELSE
229  DO 120 j = 1, n - 1
230  CALL classq( n-j, ap( k ), 1, scale, sum )
231  k = k + n - j + 1
232  120 CONTINUE
233  END IF
234  sum = 2*sum
235  k = 1
236  DO 130 i = 1, n
237  IF( real( ap( k ) ).NE.zero ) THEN
238  absa = abs( real( ap( k ) ) )
239  IF( scale.LT.absa ) THEN
240  sum = one + sum*( scale / absa )**2
241  scale = absa
242  ELSE
243  sum = sum + ( absa / scale )**2
244  END IF
245  END IF
246  IF( aimag( ap( k ) ).NE.zero ) THEN
247  absa = abs( aimag( ap( k ) ) )
248  IF( scale.LT.absa ) THEN
249  sum = one + sum*( scale / absa )**2
250  scale = absa
251  ELSE
252  sum = sum + ( absa / scale )**2
253  END IF
254  END IF
255  IF( lsame( uplo, 'U' ) ) THEN
256  k = k + i + 1
257  ELSE
258  k = k + n - i + 1
259  END IF
260  130 CONTINUE
261  VALUE = scale*sqrt( sum )
262  END IF
263 *
264  clansp = VALUE
265  RETURN
266 *
267 * End of CLANSP
268 *
269  END
subroutine classq(n, x, incx, scl, sumsq)
CLASSQ updates a sum of squares represented in scaled form.
Definition: classq.f90:137
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 clansp(NORM, UPLO, N, AP, WORK)
CLANSP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: clansp.f:115