LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 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.```
Date
September 2012

Definition at line 103 of file zlanht.f.

103 *
104 * -- LAPACK auxiliary routine (version 3.4.2) --
105 * -- LAPACK is a software package provided by Univ. of Tennessee, --
106 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
107 * September 2012
108 *
109 * .. Scalar Arguments ..
110  CHARACTER norm
111  INTEGER n
112 * ..
113 * .. Array Arguments ..
114  DOUBLE PRECISION d( * )
115  COMPLEX*16 e( * )
116 * ..
117 *
118 * =====================================================================
119 *
120 * .. Parameters ..
121  DOUBLE PRECISION one, zero
122  parameter ( one = 1.0d+0, zero = 0.0d+0 )
123 * ..
124 * .. Local Scalars ..
125  INTEGER i
126  DOUBLE PRECISION anorm, scale, sum
127 * ..
128 * .. External Functions ..
129  LOGICAL lsame, disnan
130  EXTERNAL lsame, disnan
131 * ..
132 * .. External Subroutines ..
133  EXTERNAL dlassq, zlassq
134 * ..
135 * .. Intrinsic Functions ..
136  INTRINSIC abs, max, sqrt
137 * ..
138 * .. Executable Statements ..
139 *
140  IF( n.LE.0 ) THEN
141  anorm = zero
142  ELSE IF( lsame( norm, 'M' ) ) THEN
143 *
144 * Find max(abs(A(i,j))).
145 *
146  anorm = abs( d( n ) )
147  DO 10 i = 1, n - 1
148  sum = abs( d( i ) )
149  IF( anorm .LT. sum .OR. disnan( sum ) ) anorm = sum
150  sum = abs( e( i ) )
151  IF( anorm .LT. sum .OR. disnan( sum ) ) anorm = sum
152  10 CONTINUE
153  ELSE IF( lsame( norm, 'O' ) .OR. norm.EQ.'1' .OR.
154  \$ lsame( norm, 'I' ) ) THEN
155 *
156 * Find norm1(A).
157 *
158  IF( n.EQ.1 ) THEN
159  anorm = abs( d( 1 ) )
160  ELSE
161  anorm = abs( d( 1 ) )+abs( e( 1 ) )
162  sum = abs( e( n-1 ) )+abs( d( n ) )
163  IF( anorm .LT. sum .OR. disnan( sum ) ) anorm = sum
164  DO 20 i = 2, n - 1
165  sum = abs( d( i ) )+abs( e( i ) )+abs( e( i-1 ) )
166  IF( anorm .LT. sum .OR. disnan( sum ) ) anorm = sum
167  20 CONTINUE
168  END IF
169  ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
170 *
171 * Find normF(A).
172 *
173  scale = zero
174  sum = one
175  IF( n.GT.1 ) THEN
176  CALL zlassq( n-1, e, 1, scale, sum )
177  sum = 2*sum
178  END IF
179  CALL dlassq( n, d, 1, scale, sum )
180  anorm = scale*sqrt( sum )
181  END IF
182 *
183  zlanht = anorm
184  RETURN
185 *
186 * End of ZLANHT
187 *
logical function disnan(DIN)
DISNAN tests input for NaN.
Definition: disnan.f:61
subroutine zlassq(N, X, INCX, SCALE, SUMSQ)
ZLASSQ updates a sum of squares represented in scaled form.
Definition: zlassq.f:108
double precision function zlanht(NORM, N, D, 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.
Definition: zlanht.f:103
subroutine dlassq(N, X, INCX, SCALE, SUMSQ)
DLASSQ updates a sum of squares represented in scaled form.
Definition: dlassq.f:105
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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