LAPACK  3.10.1
LAPACK: Linear Algebra PACKage

◆ slansp()

real function slansp ( character  NORM,
character  UPLO,
integer  N,
real, dimension( * )  AP,
real, dimension( * )  WORK 
)

SLANSP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric matrix supplied in packed form.

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Purpose:
 SLANSP  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,  supplied in packed form.
Returns
SLANSP
    SLANSP = ( 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 SLANSP as described
          above.
[in]UPLO
          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          symmetric matrix A is supplied.
          = 'U':  Upper triangular part of A is supplied
          = 'L':  Lower triangular part of A is supplied
[in]N
          N is INTEGER
          The order of the matrix A.  N >= 0.  When N = 0, SLANSP is
          set to zero.
[in]AP
          AP is REAL array, dimension (N*(N+1)/2)
          The upper or lower triangle of the symmetric matrix A, packed
          columnwise in a linear array.  The j-th column of A is stored
          in the array AP as follows:
          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
[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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 113 of file slansp.f.

114 *
115 * -- LAPACK auxiliary routine --
116 * -- LAPACK is a software package provided by Univ. of Tennessee, --
117 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
118 *
119 * .. Scalar Arguments ..
120  CHARACTER NORM, UPLO
121  INTEGER N
122 * ..
123 * .. Array Arguments ..
124  REAL AP( * ), WORK( * )
125 * ..
126 *
127 * =====================================================================
128 *
129 * .. Parameters ..
130  REAL ONE, ZERO
131  parameter( one = 1.0e+0, zero = 0.0e+0 )
132 * ..
133 * .. Local Scalars ..
134  INTEGER I, J, K
135  REAL ABSA, SCALE, SUM, VALUE
136 * ..
137 * .. External Subroutines ..
138  EXTERNAL slassq
139 * ..
140 * .. External Functions ..
141  LOGICAL LSAME, SISNAN
142  EXTERNAL lsame, sisnan
143 * ..
144 * .. Intrinsic Functions ..
145  INTRINSIC abs, sqrt
146 * ..
147 * .. Executable Statements ..
148 *
149  IF( n.EQ.0 ) THEN
150  VALUE = zero
151  ELSE IF( lsame( norm, 'M' ) ) THEN
152 *
153 * Find max(abs(A(i,j))).
154 *
155  VALUE = zero
156  IF( lsame( uplo, 'U' ) ) THEN
157  k = 1
158  DO 20 j = 1, n
159  DO 10 i = k, k + j - 1
160  sum = abs( ap( i ) )
161  IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
162  10 CONTINUE
163  k = k + j
164  20 CONTINUE
165  ELSE
166  k = 1
167  DO 40 j = 1, n
168  DO 30 i = k, k + n - j
169  sum = abs( ap( i ) )
170  IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
171  30 CONTINUE
172  k = k + n - j + 1
173  40 CONTINUE
174  END IF
175  ELSE IF( ( lsame( norm, 'I' ) ) .OR. ( lsame( norm, 'O' ) ) .OR.
176  $ ( norm.EQ.'1' ) ) THEN
177 *
178 * Find normI(A) ( = norm1(A), since A is symmetric).
179 *
180  VALUE = zero
181  k = 1
182  IF( lsame( uplo, 'U' ) ) THEN
183  DO 60 j = 1, n
184  sum = zero
185  DO 50 i = 1, j - 1
186  absa = abs( ap( k ) )
187  sum = sum + absa
188  work( i ) = work( i ) + absa
189  k = k + 1
190  50 CONTINUE
191  work( j ) = sum + abs( ap( k ) )
192  k = k + 1
193  60 CONTINUE
194  DO 70 i = 1, n
195  sum = work( i )
196  IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
197  70 CONTINUE
198  ELSE
199  DO 80 i = 1, n
200  work( i ) = zero
201  80 CONTINUE
202  DO 100 j = 1, n
203  sum = work( j ) + abs( ap( k ) )
204  k = k + 1
205  DO 90 i = j + 1, n
206  absa = abs( ap( k ) )
207  sum = sum + absa
208  work( i ) = work( i ) + absa
209  k = k + 1
210  90 CONTINUE
211  IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
212  100 CONTINUE
213  END IF
214  ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
215 *
216 * Find normF(A).
217 *
218  scale = zero
219  sum = one
220  k = 2
221  IF( lsame( uplo, 'U' ) ) THEN
222  DO 110 j = 2, n
223  CALL slassq( j-1, ap( k ), 1, scale, sum )
224  k = k + j
225  110 CONTINUE
226  ELSE
227  DO 120 j = 1, n - 1
228  CALL slassq( n-j, ap( k ), 1, scale, sum )
229  k = k + n - j + 1
230  120 CONTINUE
231  END IF
232  sum = 2*sum
233  k = 1
234  DO 130 i = 1, n
235  IF( ap( k ).NE.zero ) THEN
236  absa = abs( ap( k ) )
237  IF( scale.LT.absa ) THEN
238  sum = one + sum*( scale / absa )**2
239  scale = absa
240  ELSE
241  sum = sum + ( absa / scale )**2
242  END IF
243  END IF
244  IF( lsame( uplo, 'U' ) ) THEN
245  k = k + i + 1
246  ELSE
247  k = k + n - i + 1
248  END IF
249  130 CONTINUE
250  VALUE = scale*sqrt( sum )
251  END IF
252 *
253  slansp = VALUE
254  RETURN
255 *
256 * End of SLANSP
257 *
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 slansp(NORM, UPLO, N, AP, WORK)
SLANSP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: slansp.f:114
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