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
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