LAPACK  3.10.1
LAPACK: Linear Algebra PACKage

◆ 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.

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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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

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
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