LAPACK  3.10.0 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  IMPLICIT NONE
129 * .. Scalar Arguments ..
130  CHARACTER NORM, UPLO
131  INTEGER LDA, N
132 * ..
133 * .. Array Arguments ..
134  DOUBLE PRECISION WORK( * )
135  COMPLEX*16 A( LDA, * )
136 * ..
137 *
138 * =====================================================================
139 *
140 * .. Parameters ..
141  DOUBLE PRECISION ONE, ZERO
142  parameter( one = 1.0d+0, zero = 0.0d+0 )
143 * ..
144 * .. Local Scalars ..
145  INTEGER I, J
146  DOUBLE PRECISION ABSA, SUM, VALUE
147 * ..
148 * .. Local Arrays ..
149  DOUBLE PRECISION SSQ( 2 ), COLSSQ( 2 )
150 * ..
151 * .. External Functions ..
152  LOGICAL LSAME, DISNAN
153  EXTERNAL lsame, disnan
154 * ..
155 * .. External Subroutines ..
156  EXTERNAL zlassq, dcombssq
157 * ..
158 * .. Intrinsic Functions ..
159  INTRINSIC abs, sqrt
160 * ..
161 * .. Executable Statements ..
162 *
163  IF( n.EQ.0 ) THEN
164  VALUE = zero
165  ELSE IF( lsame( norm, 'M' ) ) THEN
166 *
167 * Find max(abs(A(i,j))).
168 *
169  VALUE = zero
170  IF( lsame( uplo, 'U' ) ) THEN
171  DO 20 j = 1, n
172  DO 10 i = 1, j
173  sum = abs( a( i, j ) )
174  IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
175  10 CONTINUE
176  20 CONTINUE
177  ELSE
178  DO 40 j = 1, n
179  DO 30 i = j, n
180  sum = abs( a( i, j ) )
181  IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
182  30 CONTINUE
183  40 CONTINUE
184  END IF
185  ELSE IF( ( lsame( norm, 'I' ) ) .OR. ( lsame( norm, 'O' ) ) .OR.
186  \$ ( norm.EQ.'1' ) ) THEN
187 *
188 * Find normI(A) ( = norm1(A), since A is symmetric).
189 *
190  VALUE = zero
191  IF( lsame( uplo, 'U' ) ) THEN
192  DO 60 j = 1, n
193  sum = zero
194  DO 50 i = 1, j - 1
195  absa = abs( a( i, j ) )
196  sum = sum + absa
197  work( i ) = work( i ) + absa
198  50 CONTINUE
199  work( j ) = sum + abs( a( j, j ) )
200  60 CONTINUE
201  DO 70 i = 1, n
202  sum = work( i )
203  IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
204  70 CONTINUE
205  ELSE
206  DO 80 i = 1, n
207  work( i ) = zero
208  80 CONTINUE
209  DO 100 j = 1, n
210  sum = work( j ) + abs( a( j, j ) )
211  DO 90 i = j + 1, n
212  absa = abs( a( i, j ) )
213  sum = sum + absa
214  work( i ) = work( i ) + absa
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 * SSQ(1) is scale
223 * SSQ(2) is sum-of-squares
224 * For better accuracy, sum each column separately.
225 *
226  ssq( 1 ) = zero
227  ssq( 2 ) = one
228 *
229 * Sum off-diagonals
230 *
231  IF( lsame( uplo, 'U' ) ) THEN
232  DO 110 j = 2, n
233  colssq( 1 ) = zero
234  colssq( 2 ) = one
235  CALL zlassq( j-1, a( 1, j ), 1, colssq(1), colssq(2) )
236  CALL dcombssq( ssq, colssq )
237  110 CONTINUE
238  ELSE
239  DO 120 j = 1, n - 1
240  colssq( 1 ) = zero
241  colssq( 2 ) = one
242  CALL zlassq( n-j, a( j+1, j ), 1, colssq(1), colssq(2) )
243  CALL dcombssq( ssq, colssq )
244  120 CONTINUE
245  END IF
246  ssq( 2 ) = 2*ssq( 2 )
247 *
248 * Sum diagonal
249 *
250  colssq( 1 ) = zero
251  colssq( 2 ) = one
252  CALL zlassq( n, a, lda+1, colssq( 1 ), colssq( 2 ) )
253  CALL dcombssq( ssq, colssq )
254  VALUE = ssq( 1 )*sqrt( ssq( 2 ) )
255  END IF
256 *
257  zlansy = VALUE
258  RETURN
259 *
260 * End of ZLANSY
261 *
logical function disnan(DIN)
DISNAN tests input for NaN.
Definition: disnan.f:59
subroutine dcombssq(V1, V2)
DCOMBSSQ adds two scaled sum of squares quantities.
Definition: dcombssq.f:60
subroutine zlassq(n, x, incx, scl, sumsq)
ZLASSQ updates a sum of squares represented in scaled form.
Definition: zlassq.f90:126
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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