LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ dlanst()

double precision function dlanst ( character  NORM,
integer  N,
double precision, dimension( * )  D,
double precision, dimension( * )  E 
)

DLANST returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric tridiagonal matrix.

Download DLANST + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 DLANST  returns the value of the one norm,  or the Frobenius norm, or
 the  infinity norm,  or the  element of  largest absolute value  of a
 real symmetric tridiagonal matrix A.
Returns
DLANST
    DLANST = ( 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 DLANST as described
          above.
[in]N
          N is INTEGER
          The order of the matrix A.  N >= 0.  When N = 0, DLANST is
          set to zero.
[in]D
          D is DOUBLE PRECISION array, dimension (N)
          The diagonal elements of A.
[in]E
          E is DOUBLE PRECISION array, dimension (N-1)
          The (n-1) sub-diagonal or super-diagonal elements of A.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 99 of file dlanst.f.

100 *
101 * -- LAPACK auxiliary routine --
102 * -- LAPACK is a software package provided by Univ. of Tennessee, --
103 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
104 *
105 * .. Scalar Arguments ..
106  CHARACTER NORM
107  INTEGER N
108 * ..
109 * .. Array Arguments ..
110  DOUBLE PRECISION D( * ), E( * )
111 * ..
112 *
113 * =====================================================================
114 *
115 * .. Parameters ..
116  DOUBLE PRECISION ONE, ZERO
117  parameter( one = 1.0d+0, zero = 0.0d+0 )
118 * ..
119 * .. Local Scalars ..
120  INTEGER I
121  DOUBLE PRECISION ANORM, SCALE, SUM
122 * ..
123 * .. External Functions ..
124  LOGICAL LSAME, DISNAN
125  EXTERNAL lsame, disnan
126 * ..
127 * .. External Subroutines ..
128  EXTERNAL dlassq
129 * ..
130 * .. Intrinsic Functions ..
131  INTRINSIC abs, sqrt
132 * ..
133 * .. Executable Statements ..
134 *
135  IF( n.LE.0 ) THEN
136  anorm = zero
137  ELSE IF( lsame( norm, 'M' ) ) THEN
138 *
139 * Find max(abs(A(i,j))).
140 *
141  anorm = abs( d( n ) )
142  DO 10 i = 1, n - 1
143  sum = abs( d( i ) )
144  IF( anorm .LT. sum .OR. disnan( sum ) ) anorm = sum
145  sum = abs( e( i ) )
146  IF( anorm .LT. sum .OR. disnan( sum ) ) anorm = sum
147  10 CONTINUE
148  ELSE IF( lsame( norm, 'O' ) .OR. norm.EQ.'1' .OR.
149  $ lsame( norm, 'I' ) ) THEN
150 *
151 * Find norm1(A).
152 *
153  IF( n.EQ.1 ) THEN
154  anorm = abs( d( 1 ) )
155  ELSE
156  anorm = abs( d( 1 ) )+abs( e( 1 ) )
157  sum = abs( e( n-1 ) )+abs( d( n ) )
158  IF( anorm .LT. sum .OR. disnan( sum ) ) anorm = sum
159  DO 20 i = 2, n - 1
160  sum = abs( d( i ) )+abs( e( i ) )+abs( e( i-1 ) )
161  IF( anorm .LT. sum .OR. disnan( sum ) ) anorm = sum
162  20 CONTINUE
163  END IF
164  ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
165 *
166 * Find normF(A).
167 *
168  scale = zero
169  sum = one
170  IF( n.GT.1 ) THEN
171  CALL dlassq( n-1, e, 1, scale, sum )
172  sum = 2*sum
173  END IF
174  CALL dlassq( n, d, 1, scale, sum )
175  anorm = scale*sqrt( sum )
176  END IF
177 *
178  dlanst = anorm
179  RETURN
180 *
181 * End of DLANST
182 *
logical function disnan(DIN)
DISNAN tests input for NaN.
Definition: disnan.f:59
double precision function dlanst(NORM, N, D, E)
DLANST returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: dlanst.f:100
subroutine dlassq(n, x, incx, scl, sumsq)
DLASSQ updates a sum of squares represented in scaled form.
Definition: dlassq.f90:126
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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