LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ clansp()

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

CLANSP 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:
``` CLANSP  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,  supplied in packed form.```
Returns
CLANSP
```    CLANSP = ( 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 CLANSP 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, CLANSP is set to zero.``` [in] AP ``` AP is COMPLEX 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.```

Definition at line 114 of file clansp.f.

115 *
116 * -- LAPACK auxiliary routine --
117 * -- LAPACK is a software package provided by Univ. of Tennessee, --
118 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
119 *
120 * .. Scalar Arguments ..
121  CHARACTER NORM, UPLO
122  INTEGER N
123 * ..
124 * .. Array Arguments ..
125  REAL WORK( * )
126  COMPLEX AP( * )
127 * ..
128 *
129 * =====================================================================
130 *
131 * .. Parameters ..
132  REAL ONE, ZERO
133  parameter( one = 1.0e+0, zero = 0.0e+0 )
134 * ..
135 * .. Local Scalars ..
136  INTEGER I, J, K
137  REAL ABSA, SCALE, SUM, VALUE
138 * ..
139 * .. External Functions ..
140  LOGICAL LSAME, SISNAN
141  EXTERNAL lsame, sisnan
142 * ..
143 * .. External Subroutines ..
144  EXTERNAL classq
145 * ..
146 * .. Intrinsic Functions ..
147  INTRINSIC abs, aimag, real, sqrt
148 * ..
149 * .. Executable Statements ..
150 *
151  IF( n.EQ.0 ) THEN
152  VALUE = zero
153  ELSE IF( lsame( norm, 'M' ) ) THEN
154 *
155 * Find max(abs(A(i,j))).
156 *
157  VALUE = zero
158  IF( lsame( uplo, 'U' ) ) THEN
159  k = 1
160  DO 20 j = 1, n
161  DO 10 i = k, k + j - 1
162  sum = abs( ap( i ) )
163  IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
164  10 CONTINUE
165  k = k + j
166  20 CONTINUE
167  ELSE
168  k = 1
169  DO 40 j = 1, n
170  DO 30 i = k, k + n - j
171  sum = abs( ap( i ) )
172  IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
173  30 CONTINUE
174  k = k + n - j + 1
175  40 CONTINUE
176  END IF
177  ELSE IF( ( lsame( norm, 'I' ) ) .OR. ( lsame( norm, 'O' ) ) .OR.
178  \$ ( norm.EQ.'1' ) ) THEN
179 *
180 * Find normI(A) ( = norm1(A), since A is symmetric).
181 *
182  VALUE = zero
183  k = 1
184  IF( lsame( uplo, 'U' ) ) THEN
185  DO 60 j = 1, n
186  sum = zero
187  DO 50 i = 1, j - 1
188  absa = abs( ap( k ) )
189  sum = sum + absa
190  work( i ) = work( i ) + absa
191  k = k + 1
192  50 CONTINUE
193  work( j ) = sum + abs( ap( k ) )
194  k = k + 1
195  60 CONTINUE
196  DO 70 i = 1, n
197  sum = work( i )
198  IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
199  70 CONTINUE
200  ELSE
201  DO 80 i = 1, n
202  work( i ) = zero
203  80 CONTINUE
204  DO 100 j = 1, n
205  sum = work( j ) + abs( ap( k ) )
206  k = k + 1
207  DO 90 i = j + 1, n
208  absa = abs( ap( k ) )
209  sum = sum + absa
210  work( i ) = work( i ) + absa
211  k = k + 1
212  90 CONTINUE
213  IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
214  100 CONTINUE
215  END IF
216  ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
217 *
218 * Find normF(A).
219 *
220  scale = zero
221  sum = one
222  k = 2
223  IF( lsame( uplo, 'U' ) ) THEN
224  DO 110 j = 2, n
225  CALL classq( j-1, ap( k ), 1, scale, sum )
226  k = k + j
227  110 CONTINUE
228  ELSE
229  DO 120 j = 1, n - 1
230  CALL classq( n-j, ap( k ), 1, scale, sum )
231  k = k + n - j + 1
232  120 CONTINUE
233  END IF
234  sum = 2*sum
235  k = 1
236  DO 130 i = 1, n
237  IF( real( ap( k ) ).NE.zero ) THEN
238  absa = abs( real( ap( k ) ) )
239  IF( scale.LT.absa ) THEN
240  sum = one + sum*( scale / absa )**2
241  scale = absa
242  ELSE
243  sum = sum + ( absa / scale )**2
244  END IF
245  END IF
246  IF( aimag( ap( k ) ).NE.zero ) THEN
247  absa = abs( aimag( ap( k ) ) )
248  IF( scale.LT.absa ) THEN
249  sum = one + sum*( scale / absa )**2
250  scale = absa
251  ELSE
252  sum = sum + ( absa / scale )**2
253  END IF
254  END IF
255  IF( lsame( uplo, 'U' ) ) THEN
256  k = k + i + 1
257  ELSE
258  k = k + n - i + 1
259  END IF
260  130 CONTINUE
261  VALUE = scale*sqrt( sum )
262  END IF
263 *
264  clansp = VALUE
265  RETURN
266 *
267 * End of CLANSP
268 *
subroutine classq(n, x, incx, scl, sumsq)
CLASSQ updates a sum of squares represented in scaled form.
Definition: classq.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 clansp(NORM, UPLO, N, AP, WORK)
CLANSP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: clansp.f:115
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