 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ zlanht()

 double precision function zlanht ( character NORM, integer N, double precision, dimension( * ) D, complex*16, dimension( * ) E )

ZLANHT 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 tridiagonal matrix.

Purpose:
``` ZLANHT  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 tridiagonal matrix A.```
Returns
ZLANHT
```    ZLANHT = ( 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 ZLANHT as described above.``` [in] N ``` N is INTEGER The order of the matrix A. N >= 0. When N = 0, ZLANHT is set to zero.``` [in] D ``` D is DOUBLE PRECISION array, dimension (N) The diagonal elements of A.``` [in] E ``` E is COMPLEX*16 array, dimension (N-1) The (n-1) sub-diagonal or super-diagonal elements of A.```

Definition at line 100 of file zlanht.f.

101*
102* -- LAPACK auxiliary routine --
103* -- LAPACK is a software package provided by Univ. of Tennessee, --
104* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
105*
106* .. Scalar Arguments ..
107 CHARACTER NORM
108 INTEGER N
109* ..
110* .. Array Arguments ..
111 DOUBLE PRECISION D( * )
112 COMPLEX*16 E( * )
113* ..
114*
115* =====================================================================
116*
117* .. Parameters ..
118 DOUBLE PRECISION ONE, ZERO
119 parameter( one = 1.0d+0, zero = 0.0d+0 )
120* ..
121* .. Local Scalars ..
122 INTEGER I
123 DOUBLE PRECISION ANORM, SCALE, SUM
124* ..
125* .. External Functions ..
126 LOGICAL LSAME, DISNAN
127 EXTERNAL lsame, disnan
128* ..
129* .. External Subroutines ..
130 EXTERNAL dlassq, zlassq
131* ..
132* .. Intrinsic Functions ..
133 INTRINSIC abs, max, sqrt
134* ..
135* .. Executable Statements ..
136*
137 IF( n.LE.0 ) THEN
138 anorm = zero
139 ELSE IF( lsame( norm, 'M' ) ) THEN
140*
141* Find max(abs(A(i,j))).
142*
143 anorm = abs( d( n ) )
144 DO 10 i = 1, n - 1
145 sum = abs( d( i ) )
146 IF( anorm .LT. sum .OR. disnan( sum ) ) anorm = sum
147 sum = abs( e( i ) )
148 IF( anorm .LT. sum .OR. disnan( sum ) ) anorm = sum
149 10 CONTINUE
150 ELSE IF( lsame( norm, 'O' ) .OR. norm.EQ.'1' .OR.
151 \$ lsame( norm, 'I' ) ) THEN
152*
153* Find norm1(A).
154*
155 IF( n.EQ.1 ) THEN
156 anorm = abs( d( 1 ) )
157 ELSE
158 anorm = abs( d( 1 ) )+abs( e( 1 ) )
159 sum = abs( e( n-1 ) )+abs( d( n ) )
160 IF( anorm .LT. sum .OR. disnan( sum ) ) anorm = sum
161 DO 20 i = 2, n - 1
162 sum = abs( d( i ) )+abs( e( i ) )+abs( e( i-1 ) )
163 IF( anorm .LT. sum .OR. disnan( sum ) ) anorm = sum
164 20 CONTINUE
165 END IF
166 ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
167*
168* Find normF(A).
169*
170 scale = zero
171 sum = one
172 IF( n.GT.1 ) THEN
173 CALL zlassq( n-1, e, 1, scale, sum )
174 sum = 2*sum
175 END IF
176 CALL dlassq( n, d, 1, scale, sum )
177 anorm = scale*sqrt( sum )
178 END IF
179*
180 zlanht = anorm
181 RETURN
182*
183* End of ZLANHT
184*
logical function disnan(DIN)
DISNAN tests input for NaN.
Definition: disnan.f:59
subroutine dlassq(n, x, incx, scl, sumsq)
DLASSQ updates a sum of squares represented in scaled form.
Definition: dlassq.f90:137
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 zlanht(NORM, N, D, E)
ZLANHT returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: zlanht.f:101
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