 LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

◆ clansy()

 real function clansy ( character NORM, character UPLO, integer N, complex, dimension( lda, * ) A, integer LDA, real, dimension( * ) WORK )

CLANSY 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 symmetric matrix.

Purpose:
``` CLANSY  returns the value of the one norm,  or the Frobenius norm, or
the  infinity norm,  or the  element of  largest absolute value  of a
complex symmetric matrix A.```
Returns
CLANSY
```    CLANSY = ( max(abs(A(i,j))), NORM = 'M' or 'm'
(
( norm1(A),         NORM = '1', 'O' or 'o'
(
( normI(A),         NORM = 'I' or 'i'
(
( normF(A),         NORM = 'F', 'f', 'E' or 'e'

where  norm1  denotes the  one norm of a matrix (maximum column sum),
normI  denotes the  infinity norm  of a matrix  (maximum row sum) and
normF  denotes the  Frobenius norm of a matrix (square root of sum of
squares).  Note that  max(abs(A(i,j)))  is not a consistent matrix norm.```
Parameters
 [in] NORM ``` NORM is CHARACTER*1 Specifies the value to be returned in CLANSY as described above.``` [in] UPLO ``` UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the symmetric matrix A is to be referenced. = 'U': Upper triangular part of A is referenced = 'L': Lower triangular part of A is referenced``` [in] N ``` N is INTEGER The order of the matrix A. N >= 0. When N = 0, CLANSY is set to zero.``` [in] A ``` A is COMPLEX array, dimension (LDA,N) The symmetric matrix A. If UPLO = 'U', the leading n by n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading n by n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(N,1).``` [out] WORK ``` WORK is REAL array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, WORK is not referenced.```
Date
December 2016

Definition at line 125 of file clansy.f.

125 *
126 * -- LAPACK auxiliary routine (version 3.7.0) --
127 * -- LAPACK is a software package provided by Univ. of Tennessee, --
128 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
129 * December 2016
130 *
131 * .. Scalar Arguments ..
132  CHARACTER norm, uplo
133  INTEGER lda, n
134 * ..
135 * .. Array Arguments ..
136  REAL work( * )
137  COMPLEX a( lda, * )
138 * ..
139 *
140 * =====================================================================
141 *
142 * .. Parameters ..
143  REAL one, zero
144  parameter( one = 1.0e+0, zero = 0.0e+0 )
145 * ..
146 * .. Local Scalars ..
147  INTEGER i, j
148  REAL absa, scale, sum, value
149 * ..
150 * .. External Functions ..
151  LOGICAL lsame, sisnan
152  EXTERNAL lsame, sisnan
153 * ..
154 * .. External Subroutines ..
155  EXTERNAL classq
156 * ..
157 * .. Intrinsic Functions ..
158  INTRINSIC abs, sqrt
159 * ..
160 * .. Executable Statements ..
161 *
162  IF( n.EQ.0 ) THEN
163  VALUE = zero
164  ELSE IF( lsame( norm, 'M' ) ) THEN
165 *
166 * Find max(abs(A(i,j))).
167 *
168  VALUE = zero
169  IF( lsame( uplo, 'U' ) ) THEN
170  DO 20 j = 1, n
171  DO 10 i = 1, j
172  sum = abs( a( i, j ) )
173  IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
174  10 CONTINUE
175  20 CONTINUE
176  ELSE
177  DO 40 j = 1, n
178  DO 30 i = j, n
179  sum = abs( a( i, j ) )
180  IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
181  30 CONTINUE
182  40 CONTINUE
183  END IF
184  ELSE IF( ( lsame( norm, 'I' ) ) .OR. ( lsame( norm, 'O' ) ) .OR.
185  \$ ( norm.EQ.'1' ) ) THEN
186 *
187 * Find normI(A) ( = norm1(A), since A is symmetric).
188 *
189  VALUE = zero
190  IF( lsame( uplo, 'U' ) ) THEN
191  DO 60 j = 1, n
192  sum = zero
193  DO 50 i = 1, j - 1
194  absa = abs( a( i, j ) )
195  sum = sum + absa
196  work( i ) = work( i ) + absa
197  50 CONTINUE
198  work( j ) = sum + abs( a( j, j ) )
199  60 CONTINUE
200  DO 70 i = 1, n
201  sum = work( i )
202  IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
203  70 CONTINUE
204  ELSE
205  DO 80 i = 1, n
206  work( i ) = zero
207  80 CONTINUE
208  DO 100 j = 1, n
209  sum = work( j ) + abs( a( j, j ) )
210  DO 90 i = j + 1, n
211  absa = abs( a( i, j ) )
212  sum = sum + absa
213  work( i ) = work( i ) + absa
214  90 CONTINUE
215  IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
216  100 CONTINUE
217  END IF
218  ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
219 *
220 * Find normF(A).
221 *
222  scale = zero
223  sum = one
224  IF( lsame( uplo, 'U' ) ) THEN
225  DO 110 j = 2, n
226  CALL classq( j-1, a( 1, j ), 1, scale, sum )
227  110 CONTINUE
228  ELSE
229  DO 120 j = 1, n - 1
230  CALL classq( n-j, a( j+1, j ), 1, scale, sum )
231  120 CONTINUE
232  END IF
233  sum = 2*sum
234  CALL classq( n, a, lda+1, scale, sum )
235  VALUE = scale*sqrt( sum )
236  END IF
237 *
238  clansy = VALUE
239  RETURN
240 *
241 * End of CLANSY
242 *
subroutine classq(N, X, INCX, SCALE, SUMSQ)
CLASSQ updates a sum of squares represented in scaled form.
Definition: classq.f:108
logical function sisnan(SIN)
SISNAN tests input for NaN.
Definition: sisnan.f:61
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
real function clansy(NORM, UPLO, N, A, LDA, WORK)
CLANSY 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 symmetric matrix.
Definition: clansy.f:125
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