LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
zlansp.f
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1 *> \brief \b ZLANSP 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 * DOUBLE PRECISION FUNCTION ZLANSP( NORM, UPLO, N, AP, WORK )
22 *
23 * .. Scalar Arguments ..
24 * CHARACTER NORM, UPLO
25 * INTEGER N
26 * ..
27 * .. Array Arguments ..
28 * DOUBLE PRECISION WORK( * )
29 * COMPLEX*16 AP( * )
30 * ..
31 *
32 *
33 *> \par Purpose:
34 * =============
35 *>
36 *> \verbatim
37 *>
38 *> ZLANSP 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 ZLANSP
44 *> \verbatim
45 *>
46 *> ZLANSP = ( 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 ZLANSP 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, ZLANSP is
83 *> set to zero.
84 *> \endverbatim
85 *>
86 *> \param[in] AP
87 *> \verbatim
88 *> AP is COMPLEX*16 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 DOUBLE PRECISION 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 *> \date September 2012
112 *
113 *> \ingroup complex16OTHERauxiliary
114 *
115 * =====================================================================
116  DOUBLE PRECISION FUNCTION zlansp( NORM, UPLO, N, AP, WORK )
117 *
118 * -- LAPACK auxiliary routine (version 3.4.2) --
119 * -- LAPACK is a software package provided by Univ. of Tennessee, --
120 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
121 * September 2012
122 *
123 * .. Scalar Arguments ..
124  CHARACTER NORM, UPLO
125  INTEGER N
126 * ..
127 * .. Array Arguments ..
128  DOUBLE PRECISION WORK( * )
129  COMPLEX*16 AP( * )
130 * ..
131 *
132 * =====================================================================
133 *
134 * .. Parameters ..
135  DOUBLE PRECISION ONE, ZERO
136  parameter ( one = 1.0d+0, zero = 0.0d+0 )
137 * ..
138 * .. Local Scalars ..
139  INTEGER I, J, K
140  DOUBLE PRECISION ABSA, SCALE, SUM, VALUE
141 * ..
142 * .. External Functions ..
143  LOGICAL LSAME, DISNAN
144  EXTERNAL lsame, disnan
145 * ..
146 * .. External Subroutines ..
147  EXTERNAL zlassq
148 * ..
149 * .. Intrinsic Functions ..
150  INTRINSIC abs, dble, dimag, sqrt
151 * ..
152 * .. Executable Statements ..
153 *
154  IF( n.EQ.0 ) THEN
155  VALUE = zero
156  ELSE IF( lsame( norm, 'M' ) ) THEN
157 *
158 * Find max(abs(A(i,j))).
159 *
160  VALUE = zero
161  IF( lsame( uplo, 'U' ) ) THEN
162  k = 1
163  DO 20 j = 1, n
164  DO 10 i = k, k + j - 1
165  sum = abs( ap( i ) )
166  IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
167  10 CONTINUE
168  k = k + j
169  20 CONTINUE
170  ELSE
171  k = 1
172  DO 40 j = 1, n
173  DO 30 i = k, k + n - j
174  sum = abs( ap( i ) )
175  IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
176  30 CONTINUE
177  k = k + n - j + 1
178  40 CONTINUE
179  END IF
180  ELSE IF( ( lsame( norm, 'I' ) ) .OR. ( lsame( norm, 'O' ) ) .OR.
181  \$ ( norm.EQ.'1' ) ) THEN
182 *
183 * Find normI(A) ( = norm1(A), since A is symmetric).
184 *
185  VALUE = zero
186  k = 1
187  IF( lsame( uplo, 'U' ) ) THEN
188  DO 60 j = 1, n
189  sum = zero
190  DO 50 i = 1, j - 1
191  absa = abs( ap( k ) )
192  sum = sum + absa
193  work( i ) = work( i ) + absa
194  k = k + 1
195  50 CONTINUE
196  work( j ) = sum + abs( ap( k ) )
197  k = k + 1
198  60 CONTINUE
199  DO 70 i = 1, n
200  sum = work( i )
201  IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
202  70 CONTINUE
203  ELSE
204  DO 80 i = 1, n
205  work( i ) = zero
206  80 CONTINUE
207  DO 100 j = 1, n
208  sum = work( j ) + abs( ap( k ) )
209  k = k + 1
210  DO 90 i = j + 1, n
211  absa = abs( ap( k ) )
212  sum = sum + absa
213  work( i ) = work( i ) + absa
214  k = k + 1
215  90 CONTINUE
216  IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
217  100 CONTINUE
218  END IF
219  ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
220 *
221 * Find normF(A).
222 *
223  scale = zero
224  sum = one
225  k = 2
226  IF( lsame( uplo, 'U' ) ) THEN
227  DO 110 j = 2, n
228  CALL zlassq( j-1, ap( k ), 1, scale, sum )
229  k = k + j
230  110 CONTINUE
231  ELSE
232  DO 120 j = 1, n - 1
233  CALL zlassq( n-j, ap( k ), 1, scale, sum )
234  k = k + n - j + 1
235  120 CONTINUE
236  END IF
237  sum = 2*sum
238  k = 1
239  DO 130 i = 1, n
240  IF( dble( ap( k ) ).NE.zero ) THEN
241  absa = abs( dble( ap( k ) ) )
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  IF( dimag( ap( k ) ).NE.zero ) THEN
250  absa = abs( dimag( ap( k ) ) )
251  IF( scale.LT.absa ) THEN
252  sum = one + sum*( scale / absa )**2
253  scale = absa
254  ELSE
255  sum = sum + ( absa / scale )**2
256  END IF
257  END IF
258  IF( lsame( uplo, 'U' ) ) THEN
259  k = k + i + 1
260  ELSE
261  k = k + n - i + 1
262  END IF
263  130 CONTINUE
264  VALUE = scale*sqrt( sum )
265  END IF
266 *
267  zlansp = VALUE
268  RETURN
269 *
270 * End of ZLANSP
271 *
272  END
subroutine zlassq(N, X, INCX, SCALE, SUMSQ)
ZLASSQ updates a sum of squares represented in scaled form.
Definition: zlassq.f:108
double precision function zlansp(NORM, UPLO, N, AP, WORK)
ZLANSP 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.
Definition: zlansp.f:117