1 *> \brief \b ZLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix.
3 * =========== DOCUMENTATION ===========
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
9 *> Download ZLANHS + dependencies
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21 * DOUBLE PRECISION FUNCTION ZLANHS( NORM, N, A, LDA, WORK )
23 * .. Scalar Arguments ..
27 * .. Array Arguments ..
28 * DOUBLE PRECISION WORK( * )
29 * COMPLEX*16 A( LDA, * )
38 *> ZLANHS returns the value of the one norm, or the Frobenius norm, or
39 *> the infinity norm, or the element of largest absolute value of a
40 *> Hessenberg matrix A.
46 *> ZLANHS = ( max(abs(A(i,j))), NORM = 'M' or 'm'
48 *> ( norm1(A), NORM = '1', 'O' or 'o'
50 *> ( normI(A), NORM = 'I' or 'i'
52 *> ( normF(A), NORM = 'F', 'f', 'E' or 'e'
54 *> where norm1 denotes the one norm of a matrix (maximum column sum),
55 *> normI denotes the infinity norm of a matrix (maximum row sum) and
56 *> normF denotes the Frobenius norm of a matrix (square root of sum of
57 *> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
65 *> NORM is CHARACTER*1
66 *> Specifies the value to be returned in ZLANHS as described
73 *> The order of the matrix A. N >= 0. When N = 0, ZLANHS is
79 *> A is COMPLEX*16 array, dimension (LDA,N)
80 *> The n by n upper Hessenberg matrix A; the part of A below the
81 *> first sub-diagonal is not referenced.
87 *> The leading dimension of the array A. LDA >= max(N,1).
92 *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
93 *> where LWORK >= N when NORM = 'I'; otherwise, WORK is not
100 *> \author Univ. of Tennessee
101 *> \author Univ. of California Berkeley
102 *> \author Univ. of Colorado Denver
105 *> \date September 2012
107 *> \ingroup complex16OTHERauxiliary
109 * =====================================================================
110 DOUBLE PRECISION FUNCTION ZLANHS( NORM, N, A, LDA, WORK )
112 * -- LAPACK auxiliary routine (version 3.4.2) --
113 * -- LAPACK is a software package provided by Univ. of Tennessee, --
114 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
117 * .. Scalar Arguments ..
121 * .. Array Arguments ..
122 DOUBLE PRECISION WORK( * )
123 COMPLEX*16 A( LDA, * )
126 * =====================================================================
129 DOUBLE PRECISION ONE, ZERO
130 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
132 * .. Local Scalars ..
134 DOUBLE PRECISION SCALE, SUM, VALUE
136 * .. External Functions ..
137 LOGICAL LSAME, DISNAN
138 EXTERNAL LSAME, DISNAN
140 * .. External Subroutines ..
143 * .. Intrinsic Functions ..
144 INTRINSIC ABS, MIN, SQRT
146 * .. Executable Statements ..
150 ELSE IF( LSAME( NORM, 'M' ) ) THEN
152 * Find max(abs(A(i,j))).
156 DO 10 I = 1, MIN( N, J+1 )
157 SUM = ABS( A( I, J ) )
158 IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
161 ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
168 DO 30 I = 1, MIN( N, J+1 )
169 SUM = SUM + ABS( A( I, J ) )
171 IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
173 ELSE IF( LSAME( NORM, 'I' ) ) THEN
181 DO 60 I = 1, MIN( N, J+1 )
182 WORK( I ) = WORK( I ) + ABS( A( I, J ) )
188 IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
190 ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
197 CALL ZLASSQ( MIN( N, J+1 ), A( 1, J ), 1, SCALE, SUM )
199 VALUE = SCALE*SQRT( SUM )