LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ 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.

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 *
subroutine slassq(n, x, incx, scl, sumsq)
SLASSQ updates a sum of squares represented in scaled form.
Definition: slassq.f90:137
logical function sisnan(SIN)
SISNAN tests input for NaN.
Definition: sisnan.f:59
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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
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