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1.1 bertrand 1: DOUBLE PRECISION FUNCTION ZLANHS( NORM, N, A, LDA, WORK )
2: *
3: * -- LAPACK auxiliary routine (version 3.2) --
4: * -- LAPACK is a software package provided by Univ. of Tennessee, --
5: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
6: * November 2006
7: *
8: * .. Scalar Arguments ..
9: CHARACTER NORM
10: INTEGER LDA, N
11: * ..
12: * .. Array Arguments ..
13: DOUBLE PRECISION WORK( * )
14: COMPLEX*16 A( LDA, * )
15: * ..
16: *
17: * Purpose
18: * =======
19: *
20: * ZLANHS returns the value of the one norm, or the Frobenius norm, or
21: * the infinity norm, or the element of largest absolute value of a
22: * Hessenberg matrix A.
23: *
24: * Description
25: * ===========
26: *
27: * ZLANHS returns the value
28: *
29: * ZLANHS = ( max(abs(A(i,j))), NORM = 'M' or 'm'
30: * (
31: * ( norm1(A), NORM = '1', 'O' or 'o'
32: * (
33: * ( normI(A), NORM = 'I' or 'i'
34: * (
35: * ( normF(A), NORM = 'F', 'f', 'E' or 'e'
36: *
37: * where norm1 denotes the one norm of a matrix (maximum column sum),
38: * normI denotes the infinity norm of a matrix (maximum row sum) and
39: * normF denotes the Frobenius norm of a matrix (square root of sum of
40: * squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
41: *
42: * Arguments
43: * =========
44: *
45: * NORM (input) CHARACTER*1
46: * Specifies the value to be returned in ZLANHS as described
47: * above.
48: *
49: * N (input) INTEGER
50: * The order of the matrix A. N >= 0. When N = 0, ZLANHS is
51: * set to zero.
52: *
53: * A (input) COMPLEX*16 array, dimension (LDA,N)
54: * The n by n upper Hessenberg matrix A; the part of A below the
55: * first sub-diagonal is not referenced.
56: *
57: * LDA (input) INTEGER
58: * The leading dimension of the array A. LDA >= max(N,1).
59: *
60: * WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
61: * where LWORK >= N when NORM = 'I'; otherwise, WORK is not
62: * referenced.
63: *
64: * =====================================================================
65: *
66: * .. Parameters ..
67: DOUBLE PRECISION ONE, ZERO
68: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
69: * ..
70: * .. Local Scalars ..
71: INTEGER I, J
72: DOUBLE PRECISION SCALE, SUM, VALUE
73: * ..
74: * .. External Functions ..
75: LOGICAL LSAME
76: EXTERNAL LSAME
77: * ..
78: * .. External Subroutines ..
79: EXTERNAL ZLASSQ
80: * ..
81: * .. Intrinsic Functions ..
82: INTRINSIC ABS, MAX, MIN, SQRT
83: * ..
84: * .. Executable Statements ..
85: *
86: IF( N.EQ.0 ) THEN
87: VALUE = ZERO
88: ELSE IF( LSAME( NORM, 'M' ) ) THEN
89: *
90: * Find max(abs(A(i,j))).
91: *
92: VALUE = ZERO
93: DO 20 J = 1, N
94: DO 10 I = 1, MIN( N, J+1 )
95: VALUE = MAX( VALUE, ABS( A( I, J ) ) )
96: 10 CONTINUE
97: 20 CONTINUE
98: ELSE IF( ( LSAME( NORM, 'O' ) ) .OR. ( NORM.EQ.'1' ) ) THEN
99: *
100: * Find norm1(A).
101: *
102: VALUE = ZERO
103: DO 40 J = 1, N
104: SUM = ZERO
105: DO 30 I = 1, MIN( N, J+1 )
106: SUM = SUM + ABS( A( I, J ) )
107: 30 CONTINUE
108: VALUE = MAX( VALUE, SUM )
109: 40 CONTINUE
110: ELSE IF( LSAME( NORM, 'I' ) ) THEN
111: *
112: * Find normI(A).
113: *
114: DO 50 I = 1, N
115: WORK( I ) = ZERO
116: 50 CONTINUE
117: DO 70 J = 1, N
118: DO 60 I = 1, MIN( N, J+1 )
119: WORK( I ) = WORK( I ) + ABS( A( I, J ) )
120: 60 CONTINUE
121: 70 CONTINUE
122: VALUE = ZERO
123: DO 80 I = 1, N
124: VALUE = MAX( VALUE, WORK( I ) )
125: 80 CONTINUE
126: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
127: *
128: * Find normF(A).
129: *
130: SCALE = ZERO
131: SUM = ONE
132: DO 90 J = 1, N
133: CALL ZLASSQ( MIN( N, J+1 ), A( 1, J ), 1, SCALE, SUM )
134: 90 CONTINUE
135: VALUE = SCALE*SQRT( SUM )
136: END IF
137: *
138: ZLANHS = VALUE
139: RETURN
140: *
141: * End of ZLANHS
142: *
143: END