1 DOUBLE PRECISION FUNCTION ZLANHT( NORM, N, D, E )
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 N
11 * ..
12 * .. Array Arguments ..
13 DOUBLE PRECISION D( * )
14 COMPLEX*16 E( * )
15 * ..
16 *
17 * Purpose
18 * =======
19 *
20 * ZLANHT 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 * complex Hermitian tridiagonal matrix A.
23 *
24 * Description
25 * ===========
26 *
27 * ZLANHT returns the value
28 *
29 * ZLANHT = ( 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 ZLANHT as described
47 * above.
48 *
49 * N (input) INTEGER
50 * The order of the matrix A. N >= 0. When N = 0, ZLANHT is
51 * set to zero.
52 *
53 * D (input) DOUBLE PRECISION array, dimension (N)
54 * The diagonal elements of A.
55 *
56 * E (input) COMPLEX*16 array, dimension (N-1)
57 * The (n-1) sub-diagonal or super-diagonal elements of A.
58 *
59 * =====================================================================
60 *
61 * .. Parameters ..
62 DOUBLE PRECISION ONE, ZERO
63 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
64 * ..
65 * .. Local Scalars ..
66 INTEGER I
67 DOUBLE PRECISION ANORM, SCALE, SUM
68 * ..
69 * .. External Functions ..
70 LOGICAL LSAME
71 EXTERNAL LSAME
72 * ..
73 * .. External Subroutines ..
74 EXTERNAL DLASSQ, ZLASSQ
75 * ..
76 * .. Intrinsic Functions ..
77 INTRINSIC ABS, MAX, SQRT
78 * ..
79 * .. Executable Statements ..
80 *
81 IF( N.LE.0 ) THEN
82 ANORM = ZERO
83 ELSE IF( LSAME( NORM, 'M' ) ) THEN
84 *
85 * Find max(abs(A(i,j))).
86 *
87 ANORM = ABS( D( N ) )
88 DO 10 I = 1, N - 1
89 ANORM = MAX( ANORM, ABS( D( I ) ) )
90 ANORM = MAX( ANORM, ABS( E( I ) ) )
91 10 CONTINUE
92 ELSE IF( LSAME( NORM, 'O' ) .OR. NORM.EQ.'1' .OR.
93 $ LSAME( NORM, 'I' ) ) THEN
94 *
95 * Find norm1(A).
96 *
97 IF( N.EQ.1 ) THEN
98 ANORM = ABS( D( 1 ) )
99 ELSE
100 ANORM = MAX( ABS( D( 1 ) )+ABS( E( 1 ) ),
101 $ ABS( E( N-1 ) )+ABS( D( N ) ) )
102 DO 20 I = 2, N - 1
103 ANORM = MAX( ANORM, ABS( D( I ) )+ABS( E( I ) )+
104 $ ABS( E( I-1 ) ) )
105 20 CONTINUE
106 END IF
107 ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
108 *
109 * Find normF(A).
110 *
111 SCALE = ZERO
112 SUM = ONE
113 IF( N.GT.1 ) THEN
114 CALL ZLASSQ( N-1, E, 1, SCALE, SUM )
115 SUM = 2*SUM
116 END IF
117 CALL DLASSQ( N, D, 1, SCALE, SUM )
118 ANORM = SCALE*SQRT( SUM )
119 END IF
120 *
121 ZLANHT = ANORM
122 RETURN
123 *
124 * End of ZLANHT
125 *
126 END
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 N
11 * ..
12 * .. Array Arguments ..
13 DOUBLE PRECISION D( * )
14 COMPLEX*16 E( * )
15 * ..
16 *
17 * Purpose
18 * =======
19 *
20 * ZLANHT 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 * complex Hermitian tridiagonal matrix A.
23 *
24 * Description
25 * ===========
26 *
27 * ZLANHT returns the value
28 *
29 * ZLANHT = ( 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 ZLANHT as described
47 * above.
48 *
49 * N (input) INTEGER
50 * The order of the matrix A. N >= 0. When N = 0, ZLANHT is
51 * set to zero.
52 *
53 * D (input) DOUBLE PRECISION array, dimension (N)
54 * The diagonal elements of A.
55 *
56 * E (input) COMPLEX*16 array, dimension (N-1)
57 * The (n-1) sub-diagonal or super-diagonal elements of A.
58 *
59 * =====================================================================
60 *
61 * .. Parameters ..
62 DOUBLE PRECISION ONE, ZERO
63 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
64 * ..
65 * .. Local Scalars ..
66 INTEGER I
67 DOUBLE PRECISION ANORM, SCALE, SUM
68 * ..
69 * .. External Functions ..
70 LOGICAL LSAME
71 EXTERNAL LSAME
72 * ..
73 * .. External Subroutines ..
74 EXTERNAL DLASSQ, ZLASSQ
75 * ..
76 * .. Intrinsic Functions ..
77 INTRINSIC ABS, MAX, SQRT
78 * ..
79 * .. Executable Statements ..
80 *
81 IF( N.LE.0 ) THEN
82 ANORM = ZERO
83 ELSE IF( LSAME( NORM, 'M' ) ) THEN
84 *
85 * Find max(abs(A(i,j))).
86 *
87 ANORM = ABS( D( N ) )
88 DO 10 I = 1, N - 1
89 ANORM = MAX( ANORM, ABS( D( I ) ) )
90 ANORM = MAX( ANORM, ABS( E( I ) ) )
91 10 CONTINUE
92 ELSE IF( LSAME( NORM, 'O' ) .OR. NORM.EQ.'1' .OR.
93 $ LSAME( NORM, 'I' ) ) THEN
94 *
95 * Find norm1(A).
96 *
97 IF( N.EQ.1 ) THEN
98 ANORM = ABS( D( 1 ) )
99 ELSE
100 ANORM = MAX( ABS( D( 1 ) )+ABS( E( 1 ) ),
101 $ ABS( E( N-1 ) )+ABS( D( N ) ) )
102 DO 20 I = 2, N - 1
103 ANORM = MAX( ANORM, ABS( D( I ) )+ABS( E( I ) )+
104 $ ABS( E( I-1 ) ) )
105 20 CONTINUE
106 END IF
107 ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
108 *
109 * Find normF(A).
110 *
111 SCALE = ZERO
112 SUM = ONE
113 IF( N.GT.1 ) THEN
114 CALL ZLASSQ( N-1, E, 1, SCALE, SUM )
115 SUM = 2*SUM
116 END IF
117 CALL DLASSQ( N, D, 1, SCALE, SUM )
118 ANORM = SCALE*SQRT( SUM )
119 END IF
120 *
121 ZLANHT = ANORM
122 RETURN
123 *
124 * End of ZLANHT
125 *
126 END