LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ slansy()

 real function slansy ( character norm, character uplo, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) work )

SLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix.

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Purpose:
``` SLANSY  returns the value of the one norm,  or the Frobenius norm, or
the  infinity norm,  or the  element of  largest absolute value  of a
real symmetric matrix A.```
Returns
SLANSY
```    SLANSY = ( 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 SLANSY 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, SLANSY is set to zero.``` [in] A ``` A is REAL 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.```

Definition at line 121 of file slansy.f.

122*
123* -- LAPACK auxiliary routine --
124* -- LAPACK is a software package provided by Univ. of Tennessee, --
125* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
126*
127* .. Scalar Arguments ..
128 CHARACTER NORM, UPLO
129 INTEGER LDA, N
130* ..
131* .. Array Arguments ..
132 REAL A( LDA, * ), WORK( * )
133* ..
134*
135* =====================================================================
136*
137* .. Parameters ..
138 REAL ONE, ZERO
139 parameter( one = 1.0e+0, zero = 0.0e+0 )
140* ..
141* .. Local Scalars ..
142 INTEGER I, J
143 REAL ABSA, SCALE, SUM, VALUE
144* ..
145* .. External Subroutines ..
146 EXTERNAL slassq
147* ..
148* .. External Functions ..
149 LOGICAL LSAME, SISNAN
150 EXTERNAL lsame, sisnan
151* ..
152* .. Intrinsic Functions ..
153 INTRINSIC abs, sqrt
154* ..
155* .. Executable Statements ..
156*
157 IF( n.EQ.0 ) THEN
158 VALUE = zero
159 ELSE IF( lsame( norm, 'M' ) ) THEN
160*
161* Find max(abs(A(i,j))).
162*
163 VALUE = zero
164 IF( lsame( uplo, 'U' ) ) THEN
165 DO 20 j = 1, n
166 DO 10 i = 1, j
167 sum = abs( a( i, j ) )
168 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
169 10 CONTINUE
170 20 CONTINUE
171 ELSE
172 DO 40 j = 1, n
173 DO 30 i = j, n
174 sum = abs( a( i, j ) )
175 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
176 30 CONTINUE
177 40 CONTINUE
178 END IF
179 ELSE IF( ( lsame( norm, 'I' ) ) .OR. ( lsame( norm, 'O' ) ) .OR.
180 \$ ( norm.EQ.'1' ) ) THEN
181*
182* Find normI(A) ( = norm1(A), since A is symmetric).
183*
184 VALUE = zero
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( a( i, j ) )
190 sum = sum + absa
191 work( i ) = work( i ) + absa
192 50 CONTINUE
193 work( j ) = sum + abs( a( j, j ) )
194 60 CONTINUE
195 DO 70 i = 1, n
196 sum = work( i )
197 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
198 70 CONTINUE
199 ELSE
200 DO 80 i = 1, n
201 work( i ) = zero
202 80 CONTINUE
203 DO 100 j = 1, n
204 sum = work( j ) + abs( a( j, j ) )
205 DO 90 i = j + 1, n
206 absa = abs( a( i, j ) )
207 sum = sum + absa
208 work( i ) = work( i ) + absa
209 90 CONTINUE
210 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
211 100 CONTINUE
212 END IF
213 ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
214*
215* Find normF(A).
216*
217 scale = zero
218 sum = one
219 IF( lsame( uplo, 'U' ) ) THEN
220 DO 110 j = 2, n
221 CALL slassq( j-1, a( 1, j ), 1, scale, sum )
222 110 CONTINUE
223 ELSE
224 DO 120 j = 1, n - 1
225 CALL slassq( n-j, a( j+1, j ), 1, scale, sum )
226 120 CONTINUE
227 END IF
228 sum = 2*sum
229 CALL slassq( n, a, lda+1, scale, sum )
230 VALUE = scale*sqrt( sum )
231 END IF
232*
233 slansy = VALUE
234 RETURN
235*
236* End of SLANSY
237*
logical function sisnan(sin)
SISNAN tests input for NaN.
Definition sisnan.f:59
real function slansy(norm, uplo, n, a, lda, work)
SLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition slansy.f:122
subroutine slassq(n, x, incx, scale, sumsq)
SLASSQ updates a sum of squares represented in scaled form.
Definition slassq.f90:124
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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