LAPACK  3.8.0 LAPACK: Linear Algebra PACKage
dlansp.f
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1 *> \brief \b DLANSP 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 DLANSP( NORM, UPLO, N, AP, WORK )
22 *
23 * .. Scalar Arguments ..
24 * CHARACTER NORM, UPLO
25 * INTEGER N
26 * ..
27 * .. Array Arguments ..
28 * DOUBLE PRECISION AP( * ), WORK( * )
29 * ..
30 *
31 *
32 *> \par Purpose:
33 * =============
34 *>
35 *> \verbatim
36 *>
37 *> DLANSP returns the value of the one norm, or the Frobenius norm, or
38 *> the infinity norm, or the element of largest absolute value of a
39 *> real symmetric matrix A, supplied in packed form.
40 *> \endverbatim
41 *>
42 *> \return DLANSP
43 *> \verbatim
44 *>
45 *> DLANSP = ( max(abs(A(i,j))), NORM = 'M' or 'm'
46 *> (
47 *> ( norm1(A), NORM = '1', 'O' or 'o'
48 *> (
49 *> ( normI(A), NORM = 'I' or 'i'
50 *> (
51 *> ( normF(A), NORM = 'F', 'f', 'E' or 'e'
52 *>
53 *> where norm1 denotes the one norm of a matrix (maximum column sum),
54 *> normI denotes the infinity norm of a matrix (maximum row sum) and
55 *> normF denotes the Frobenius norm of a matrix (square root of sum of
56 *> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
57 *> \endverbatim
58 *
59 * Arguments:
60 * ==========
61 *
62 *> \param[in] NORM
63 *> \verbatim
64 *> NORM is CHARACTER*1
65 *> Specifies the value to be returned in DLANSP as described
66 *> above.
67 *> \endverbatim
68 *>
69 *> \param[in] UPLO
70 *> \verbatim
71 *> UPLO is CHARACTER*1
72 *> Specifies whether the upper or lower triangular part of the
73 *> symmetric matrix A is supplied.
74 *> = 'U': Upper triangular part of A is supplied
75 *> = 'L': Lower triangular part of A is supplied
76 *> \endverbatim
77 *>
78 *> \param[in] N
79 *> \verbatim
80 *> N is INTEGER
81 *> The order of the matrix A. N >= 0. When N = 0, DLANSP is
82 *> set to zero.
83 *> \endverbatim
84 *>
85 *> \param[in] AP
86 *> \verbatim
87 *> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
88 *> The upper or lower triangle of the symmetric matrix A, packed
89 *> columnwise in a linear array. The j-th column of A is stored
90 *> in the array AP as follows:
91 *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
92 *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
93 *> \endverbatim
94 *>
95 *> \param[out] WORK
96 *> \verbatim
97 *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
98 *> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
99 *> WORK is not referenced.
100 *> \endverbatim
101 *
102 * Authors:
103 * ========
104 *
105 *> \author Univ. of Tennessee
106 *> \author Univ. of California Berkeley
107 *> \author Univ. of Colorado Denver
108 *> \author NAG Ltd.
109 *
110 *> \date December 2016
111 *
112 *> \ingroup doubleOTHERauxiliary
113 *
114 * =====================================================================
115  DOUBLE PRECISION FUNCTION dlansp( NORM, UPLO, N, AP, WORK )
116 *
117 * -- LAPACK auxiliary routine (version 3.7.0) --
118 * -- LAPACK is a software package provided by Univ. of Tennessee, --
119 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
120 * December 2016
121 *
122 * .. Scalar Arguments ..
123  CHARACTER NORM, UPLO
124  INTEGER N
125 * ..
126 * .. Array Arguments ..
127  DOUBLE PRECISION AP( * ), WORK( * )
128 * ..
129 *
130 * =====================================================================
131 *
132 * .. Parameters ..
133  DOUBLE PRECISION ONE, ZERO
134  parameter( one = 1.0d+0, zero = 0.0d+0 )
135 * ..
136 * .. Local Scalars ..
137  INTEGER I, J, K
138  DOUBLE PRECISION ABSA, SCALE, SUM, VALUE
139 * ..
140 * .. External Subroutines ..
141  EXTERNAL dlassq
142 * ..
143 * .. External Functions ..
144  LOGICAL LSAME, DISNAN
145  EXTERNAL lsame, disnan
146 * ..
147 * .. Intrinsic Functions ..
148  INTRINSIC abs, sqrt
149 * ..
150 * .. Executable Statements ..
151 *
152  IF( n.EQ.0 ) THEN
153  VALUE = zero
154  ELSE IF( lsame( norm, 'M' ) ) THEN
155 *
156 * Find max(abs(A(i,j))).
157 *
158  VALUE = zero
159  IF( lsame( uplo, 'U' ) ) THEN
160  k = 1
161  DO 20 j = 1, n
162  DO 10 i = k, k + j - 1
163  sum = abs( ap( i ) )
164  IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
165  10 CONTINUE
166  k = k + j
167  20 CONTINUE
168  ELSE
169  k = 1
170  DO 40 j = 1, n
171  DO 30 i = k, k + n - j
172  sum = abs( ap( i ) )
173  IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
174  30 CONTINUE
175  k = k + n - j + 1
176  40 CONTINUE
177  END IF
178  ELSE IF( ( lsame( norm, 'I' ) ) .OR. ( lsame( norm, 'O' ) ) .OR.
179  \$ ( norm.EQ.'1' ) ) THEN
180 *
181 * Find normI(A) ( = norm1(A), since A is symmetric).
182 *
183  VALUE = zero
184  k = 1
185  IF( lsame( uplo, 'U' ) ) THEN
186  DO 60 j = 1, n
187  sum = zero
188  DO 50 i = 1, j - 1
189  absa = abs( ap( k ) )
190  sum = sum + absa
191  work( i ) = work( i ) + absa
192  k = k + 1
193  50 CONTINUE
194  work( j ) = sum + abs( ap( k ) )
195  k = k + 1
196  60 CONTINUE
197  DO 70 i = 1, n
198  sum = work( i )
199  IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
200  70 CONTINUE
201  ELSE
202  DO 80 i = 1, n
203  work( i ) = zero
204  80 CONTINUE
205  DO 100 j = 1, n
206  sum = work( j ) + abs( ap( k ) )
207  k = k + 1
208  DO 90 i = j + 1, n
209  absa = abs( ap( k ) )
210  sum = sum + absa
211  work( i ) = work( i ) + absa
212  k = k + 1
213  90 CONTINUE
214  IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
215  100 CONTINUE
216  END IF
217  ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
218 *
219 * Find normF(A).
220 *
221  scale = zero
222  sum = one
223  k = 2
224  IF( lsame( uplo, 'U' ) ) THEN
225  DO 110 j = 2, n
226  CALL dlassq( j-1, ap( k ), 1, scale, sum )
227  k = k + j
228  110 CONTINUE
229  ELSE
230  DO 120 j = 1, n - 1
231  CALL dlassq( n-j, ap( k ), 1, scale, sum )
232  k = k + n - j + 1
233  120 CONTINUE
234  END IF
235  sum = 2*sum
236  k = 1
237  DO 130 i = 1, n
238  IF( ap( k ).NE.zero ) THEN
239  absa = abs( ap( k ) )
240  IF( scale.LT.absa ) THEN
241  sum = one + sum*( scale / absa )**2
242  scale = absa
243  ELSE
244  sum = sum + ( absa / scale )**2
245  END IF
246  END IF
247  IF( lsame( uplo, 'U' ) ) THEN
248  k = k + i + 1
249  ELSE
250  k = k + n - i + 1
251  END IF
252  130 CONTINUE
253  VALUE = scale*sqrt( sum )
254  END IF
255 *
256  dlansp = VALUE
257  RETURN
258 *
259 * End of DLANSP
260 *
261  END
double precision function dlansp(NORM, UPLO, N, AP, WORK)
DLANSP 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: dlansp.f:116
subroutine dlassq(N, X, INCX, SCALE, SUMSQ)
DLASSQ updates a sum of squares represented in scaled form.
Definition: dlassq.f:105