LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ zlansy()

 double precision function zlansy ( character NORM, character UPLO, integer N, complex*16, dimension( lda, * ) A, integer LDA, double precision, dimension( * ) WORK )

ZLANSY 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:
``` ZLANSY  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
ZLANSY
```    ZLANSY = ( 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 ZLANSY 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, ZLANSY is set to zero.``` [in] A ``` A is COMPLEX*16 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 DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, WORK is not referenced.```

Definition at line 122 of file zlansy.f.

123 *
124 * -- LAPACK auxiliary routine --
125 * -- LAPACK is a software package provided by Univ. of Tennessee, --
126 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
127 *
128 * .. Scalar Arguments ..
129  CHARACTER NORM, UPLO
130  INTEGER LDA, N
131 * ..
132 * .. Array Arguments ..
133  DOUBLE PRECISION WORK( * )
134  COMPLEX*16 A( LDA, * )
135 * ..
136 *
137 * =====================================================================
138 *
139 * .. Parameters ..
140  DOUBLE PRECISION ONE, ZERO
141  parameter( one = 1.0d+0, zero = 0.0d+0 )
142 * ..
143 * .. Local Scalars ..
144  INTEGER I, J
145  DOUBLE PRECISION ABSA, SCALE, SUM, VALUE
146 * ..
147 * .. External Functions ..
148  LOGICAL LSAME, DISNAN
149  EXTERNAL lsame, disnan
150 * ..
151 * .. External Subroutines ..
152  EXTERNAL zlassq
153 * ..
154 * .. Intrinsic Functions ..
155  INTRINSIC abs, sqrt
156 * ..
157 * .. Executable Statements ..
158 *
159  IF( n.EQ.0 ) THEN
160  VALUE = zero
161  ELSE IF( lsame( norm, 'M' ) ) THEN
162 *
163 * Find max(abs(A(i,j))).
164 *
165  VALUE = zero
166  IF( lsame( uplo, 'U' ) ) THEN
167  DO 20 j = 1, n
168  DO 10 i = 1, j
169  sum = abs( a( i, j ) )
170  IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
171  10 CONTINUE
172  20 CONTINUE
173  ELSE
174  DO 40 j = 1, n
175  DO 30 i = j, n
176  sum = abs( a( i, j ) )
177  IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
178  30 CONTINUE
179  40 CONTINUE
180  END IF
181  ELSE IF( ( lsame( norm, 'I' ) ) .OR. ( lsame( norm, 'O' ) ) .OR.
182  \$ ( norm.EQ.'1' ) ) THEN
183 *
184 * Find normI(A) ( = norm1(A), since A is symmetric).
185 *
186  VALUE = zero
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( a( i, j ) )
192  sum = sum + absa
193  work( i ) = work( i ) + absa
194  50 CONTINUE
195  work( j ) = sum + abs( a( j, j ) )
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( a( j, j ) )
207  DO 90 i = j + 1, n
208  absa = abs( a( i, j ) )
209  sum = sum + absa
210  work( i ) = work( i ) + absa
211  90 CONTINUE
212  IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
213  100 CONTINUE
214  END IF
215  ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
216 *
217 * Find normF(A).
218 *
219  scale = zero
220  sum = one
221  IF( lsame( uplo, 'U' ) ) THEN
222  DO 110 j = 2, n
223  CALL zlassq( j-1, a( 1, j ), 1, scale, sum )
224  110 CONTINUE
225  ELSE
226  DO 120 j = 1, n - 1
227  CALL zlassq( n-j, a( j+1, j ), 1, scale, sum )
228  120 CONTINUE
229  END IF
230  sum = 2*sum
231  CALL zlassq( n, a, lda+1, scale, sum )
232  VALUE = scale*sqrt( sum )
233  END IF
234 *
235  zlansy = VALUE
236  RETURN
237 *
238 * End of ZLANSY
239 *
logical function disnan(DIN)
DISNAN tests input for NaN.
Definition: disnan.f:59
subroutine zlassq(n, x, incx, scl, sumsq)
ZLASSQ updates a sum of squares represented in scaled form.
Definition: zlassq.f90:137
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
double precision function zlansy(NORM, UPLO, N, A, LDA, WORK)
ZLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: zlansy.f:123
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