1SLANTR(1) LAPACK auxiliary routine (version 3.2) SLANTR(1)
2
6 SLANTR - returns the value of the one norm, or the Frobenius norm, or
7 the infinity norm, or the element of largest absolute value of a trape‐
8 zoidal or triangular matrix A
9
11 REAL FUNCTION SLANTR( NORM, UPLO, DIAG, M, N, A, LDA, WORK )
12 CHARACTER DIAG, NORM, UPLO
14 INTEGER LDA, M, N
16 REAL A( LDA, * ), WORK( * )
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20 SLANTR 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 trapezoidal or triangular matrix A.
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25 SLANTR returns the value
26 SLANTR = ( max(abs(A(i,j))), NORM = 'M' or 'm'
27 (
28 ( norm1(A), NORM = '1', 'O' or 'o'
29 (
30 ( normI(A), NORM = 'I' or 'i'
31 (
32 ( normF(A), NORM = 'F', 'f', 'E' or 'e' where
33 norm1 denotes the one norm of a matrix (maximum column sum), normI
34 denotes the infinity norm of a matrix (maximum row sum) and normF
35 denotes the Frobenius norm of a matrix (square root of sum of
36 squares). Note that max(abs(A(i,j))) is not a consistent matrix
37 norm.
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40 NORM (input) CHARACTER*1
41 Specifies the value to be returned in SLANTR as described
42 above.
43 UPLO (input) CHARACTER*1
45 Specifies whether the matrix A is upper or lower trapezoidal.
46 = 'U': Upper trapezoidal
47 = 'L': Lower trapezoidal Note that A is triangular instead of
48 trapezoidal if M = N.
49 DIAG (input) CHARACTER*1
51 Specifies whether or not the matrix A has unit diagonal. =
52 'N': Non-unit diagonal
53 = 'U': Unit diagonal
54 M (input) INTEGER
56 The number of rows of the matrix A. M >= 0, and if UPLO = 'U',
57 M <= N. When M = 0, SLANTR is set to zero.
58 N (input) INTEGER
60 The number of columns of the matrix A. N >= 0, and if UPLO =
61 'L', N <= M. When N = 0, SLANTR is set to zero.
62 A (input) REAL array, dimension (LDA,N)
64 The trapezoidal matrix A (A is triangular if M = N). If UPLO =
65 'U', the leading m by n upper trapezoidal part of the array A
66 contains the upper trapezoidal matrix, and the strictly lower
67 triangular part of A is not referenced. If UPLO = 'L', the
68 leading m by n lower trapezoidal part of the array A contains
69 the lower trapezoidal matrix, and the strictly upper triangular
70 part of A is not referenced. Note that when DIAG = 'U', the
71 diagonal elements of A are not referenced and are assumed to be
72 one.
73 LDA (input) INTEGER
75 The leading dimension of the array A. LDA >= max(M,1).
76 WORK (workspace) REAL array, dimension (MAX(1,LWORK)),
78 where LWORK >= M when NORM = 'I'; otherwise, WORK is not refer‐
79 enced.
80 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008 SLANTR(1)