 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ zlanhp()

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

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

Purpose:
``` ZLANHP  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 hermitian matrix A,  supplied in packed form.```
Returns
ZLANHP
```    ZLANHP = ( 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 ZLANHP as described above.``` [in] UPLO ``` UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the hermitian 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, ZLANHP is set to zero.``` [in] AP ``` AP is COMPLEX*16 array, dimension (N*(N+1)/2) The upper or lower triangle of the hermitian 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. Note that the imaginary parts of the diagonal elements need not be set and are assumed to be zero.``` [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 116 of file zlanhp.f.

117 *
118 * -- LAPACK auxiliary routine --
119 * -- LAPACK is a software package provided by Univ. of Tennessee, --
120 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
121 *
122 * .. Scalar Arguments ..
123  CHARACTER NORM, UPLO
124  INTEGER N
125 * ..
126 * .. Array Arguments ..
127  DOUBLE PRECISION WORK( * )
128  COMPLEX*16 AP( * )
129 * ..
130 *
131 * =====================================================================
132 *
133 * .. Parameters ..
134  DOUBLE PRECISION ONE, ZERO
135  parameter( one = 1.0d+0, zero = 0.0d+0 )
136 * ..
137 * .. Local Scalars ..
138  INTEGER I, J, K
139  DOUBLE PRECISION ABSA, SCALE, SUM, VALUE
140 * ..
141 * .. External Functions ..
142  LOGICAL LSAME, DISNAN
143  EXTERNAL lsame, disnan
144 * ..
145 * .. External Subroutines ..
146  EXTERNAL zlassq
147 * ..
148 * .. Intrinsic Functions ..
149  INTRINSIC abs, dble, sqrt
150 * ..
151 * .. Executable Statements ..
152 *
153  IF( n.EQ.0 ) THEN
154  VALUE = zero
155  ELSE IF( lsame( norm, 'M' ) ) THEN
156 *
157 * Find max(abs(A(i,j))).
158 *
159  VALUE = zero
160  IF( lsame( uplo, 'U' ) ) THEN
161  k = 0
162  DO 20 j = 1, n
163  DO 10 i = k + 1, k + j - 1
164  sum = abs( ap( i ) )
165  IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
166  10 CONTINUE
167  k = k + j
168  sum = abs( dble( ap( k ) ) )
169  IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
170  20 CONTINUE
171  ELSE
172  k = 1
173  DO 40 j = 1, n
174  sum = abs( dble( ap( k ) ) )
175  IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
176  DO 30 i = k + 1, k + n - j
177  sum = abs( ap( i ) )
178  IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
179  30 CONTINUE
180  k = k + n - j + 1
181  40 CONTINUE
182  END IF
183  ELSE IF( ( lsame( norm, 'I' ) ) .OR. ( lsame( norm, 'O' ) ) .OR.
184  \$ ( norm.EQ.'1' ) ) THEN
185 *
186 * Find normI(A) ( = norm1(A), since A is hermitian).
187 *
188  VALUE = zero
189  k = 1
190  IF( lsame( uplo, 'U' ) ) THEN
191  DO 60 j = 1, n
192  sum = zero
193  DO 50 i = 1, j - 1
194  absa = abs( ap( k ) )
195  sum = sum + absa
196  work( i ) = work( i ) + absa
197  k = k + 1
198  50 CONTINUE
199  work( j ) = sum + abs( dble( ap( k ) ) )
200  k = k + 1
201  60 CONTINUE
202  DO 70 i = 1, n
203  sum = work( i )
204  IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
205  70 CONTINUE
206  ELSE
207  DO 80 i = 1, n
208  work( i ) = zero
209  80 CONTINUE
210  DO 100 j = 1, n
211  sum = work( j ) + abs( dble( ap( k ) ) )
212  k = k + 1
213  DO 90 i = j + 1, n
214  absa = abs( ap( k ) )
215  sum = sum + absa
216  work( i ) = work( i ) + absa
217  k = k + 1
218  90 CONTINUE
219  IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
220  100 CONTINUE
221  END IF
222  ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
223 *
224 * Find normF(A).
225 *
226  scale = zero
227  sum = one
228  k = 2
229  IF( lsame( uplo, 'U' ) ) THEN
230  DO 110 j = 2, n
231  CALL zlassq( j-1, ap( k ), 1, scale, sum )
232  k = k + j
233  110 CONTINUE
234  ELSE
235  DO 120 j = 1, n - 1
236  CALL zlassq( n-j, ap( k ), 1, scale, sum )
237  k = k + n - j + 1
238  120 CONTINUE
239  END IF
240  sum = 2*sum
241  k = 1
242  DO 130 i = 1, n
243  IF( dble( ap( k ) ).NE.zero ) THEN
244  absa = abs( dble( ap( k ) ) )
245  IF( scale.LT.absa ) THEN
246  sum = one + sum*( scale / absa )**2
247  scale = absa
248  ELSE
249  sum = sum + ( absa / scale )**2
250  END IF
251  END IF
252  IF( lsame( uplo, 'U' ) ) THEN
253  k = k + i + 1
254  ELSE
255  k = k + n - i + 1
256  END IF
257  130 CONTINUE
258  VALUE = scale*sqrt( sum )
259  END IF
260 *
261  zlanhp = VALUE
262  RETURN
263 *
264 * End of ZLANHP
265 *
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 zlanhp(NORM, UPLO, N, AP, WORK)
ZLANHP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: zlanhp.f:117
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