 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
Searching...
No Matches

## ◆ zlansp()

 double precision function zlansp ( character NORM, character UPLO, integer N, complex*16, dimension( * ) AP, double precision, dimension( * ) WORK )

ZLANSP 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.

Purpose:
``` ZLANSP  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
ZLANSP
```    ZLANSP = ( 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 ZLANSP 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, ZLANSP is set to zero.``` [in] AP ``` AP is COMPLEX*16 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 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 114 of file zlansp.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 DOUBLE PRECISION WORK( * )
126 COMPLEX*16 AP( * )
127* ..
128*
129* =====================================================================
130*
131* .. Parameters ..
132 DOUBLE PRECISION ONE, ZERO
133 parameter( one = 1.0d+0, zero = 0.0d+0 )
134* ..
135* .. Local Scalars ..
136 INTEGER I, J, K
137 DOUBLE PRECISION ABSA, SCALE, SUM, VALUE
138* ..
139* .. External Functions ..
140 LOGICAL LSAME, DISNAN
141 EXTERNAL lsame, disnan
142* ..
143* .. External Subroutines ..
144 EXTERNAL zlassq
145* ..
146* .. Intrinsic Functions ..
147 INTRINSIC abs, dble, dimag, 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. disnan( 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. disnan( 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. disnan( 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. disnan( 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 zlassq( 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 zlassq( 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( dble( ap( k ) ).NE.zero ) THEN
238 absa = abs( dble( 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( dimag( ap( k ) ).NE.zero ) THEN
247 absa = abs( dimag( 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 zlansp = VALUE
265 RETURN
266*
267* End of ZLANSP
268*
logical function disnan(DIN)
DISNAN tests input for NaN.
Definition: disnan.f:59
subroutine zlassq(n, x, incx, scl, sumsq)
ZLASSQ updates a sum of squares represented in scaled form.
Definition: zlassq.f90:137
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
double precision function zlansp(NORM, UPLO, N, AP, WORK)
ZLANSP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: zlansp.f:115
Here is the call graph for this function:
Here is the caller graph for this function: