LAPACK
3.4.2
LAPACK: Linear Algebra PACKage

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Functions/Subroutines  
REAL function  clanhf (NORM, TRANSR, UPLO, N, A, WORK) 
CLANHF returns the value of the 1norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hermitian matrix in RFP format. 
REAL function clanhf  (  character  NORM, 
character  TRANSR,  
character  UPLO,  
integer  N,  
complex, dimension( 0: * )  A,  
real, dimension( 0: * )  WORK  
) 
CLANHF returns the value of the 1norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hermitian matrix in RFP format.
Download CLANHF + dependencies [TGZ] [ZIP] [TXT]CLANHF returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix A in RFP format.
CLANHF = ( max(abs(A(i,j))), NORM = 'M' or 'm' ( ( norm1(A), NORM = '1', 'O' or 'o' ( ( normI(A), NORM = 'I' or 'i' ( ( normF(A), NORM = 'F', 'f', 'E' or 'e' where norm1 denotes the one norm of a matrix (maximum column sum), normI denotes the infinity norm of a matrix (maximum row sum) and normF denotes the Frobenius norm of a matrix (square root of sum of squares). Note that max(abs(A(i,j))) is not a matrix norm.
[in]  NORM  NORM is CHARACTER Specifies the value to be returned in CLANHF as described above. 
[in]  TRANSR  TRANSR is CHARACTER Specifies whether the RFP format of A is normal or conjugatetransposed format. = 'N': RFP format is Normal = 'C': RFP format is Conjugatetransposed 
[in]  UPLO  UPLO is CHARACTER On entry, UPLO specifies whether the RFP matrix A came from an upper or lower triangular matrix as follows: UPLO = 'U' or 'u' RFP A came from an upper triangular matrix UPLO = 'L' or 'l' RFP A came from a lower triangular matrix 
[in]  N  N is INTEGER The order of the matrix A. N >= 0. When N = 0, CLANHF is set to zero. 
[in]  A  A is COMPLEX array, dimension ( N*(N+1)/2 ); On entry, the matrix A in RFP Format. RFP Format is described by TRANSR, UPLO and N as follows: If TRANSR='N' then RFP A is (0:N,0:K1) when N is even; K=N/2. RFP A is (0:N1,0:K) when N is odd; K=N/2. If TRANSR = 'C' then RFP is the Conjugatetranspose of RFP A as defined when TRANSR = 'N'. The contents of RFP A are defined by UPLO as follows: If UPLO = 'U' the RFP A contains the ( N*(N+1)/2 ) elements of upper packed A either in normal or conjugatetranspose Format. If UPLO = 'L' the RFP A contains the ( N*(N+1) /2 ) elements of lower packed A either in normal or conjugatetranspose Format. The LDA of RFP A is (N+1)/2 when TRANSR = 'C'. When TRANSR is 'N' the LDA is N+1 when N is even and is N when is odd. See the Note below for more details. Unchanged on exit. 
[out]  WORK  WORK is REAL array, dimension (LWORK), where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, WORK is not referenced. 
We first consider Standard Packed Format when N is even. We give an example where N = 6. AP is Upper AP is Lower 00 01 02 03 04 05 00 11 12 13 14 15 10 11 22 23 24 25 20 21 22 33 34 35 30 31 32 33 44 45 40 41 42 43 44 55 50 51 52 53 54 55 Let TRANSR = 'N'. RFP holds AP as follows: For UPLO = 'U' the upper trapezoid A(0:5,0:2) consists of the last three columns of AP upper. The lower triangle A(4:6,0:2) consists of conjugatetranspose of the first three columns of AP upper. For UPLO = 'L' the lower trapezoid A(1:6,0:2) consists of the first three columns of AP lower. The upper triangle A(0:2,0:2) consists of conjugatetranspose of the last three columns of AP lower. To denote conjugate we place  above the element. This covers the case N even and TRANSR = 'N'. RFP A RFP A    03 04 05 33 43 53   13 14 15 00 44 54  23 24 25 10 11 55 33 34 35 20 21 22  00 44 45 30 31 32   01 11 55 40 41 42    02 12 22 50 51 52 Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate transpose of RFP A above. One therefore gets: RFP A RFP A           03 13 23 33 00 01 02 33 00 10 20 30 40 50           04 14 24 34 44 11 12 43 44 11 21 31 41 51           05 15 25 35 45 55 22 53 54 55 22 32 42 52 We next consider Standard Packed Format when N is odd. We give an example where N = 5. AP is Upper AP is Lower 00 01 02 03 04 00 11 12 13 14 10 11 22 23 24 20 21 22 33 34 30 31 32 33 44 40 41 42 43 44 Let TRANSR = 'N'. RFP holds AP as follows: For UPLO = 'U' the upper trapezoid A(0:4,0:2) consists of the last three columns of AP upper. The lower triangle A(3:4,0:1) consists of conjugatetranspose of the first two columns of AP upper. For UPLO = 'L' the lower trapezoid A(0:4,0:2) consists of the first three columns of AP lower. The upper triangle A(0:1,1:2) consists of conjugatetranspose of the last two columns of AP lower. To denote conjugate we place  above the element. This covers the case N odd and TRANSR = 'N'. RFP A RFP A   02 03 04 00 33 43  12 13 14 10 11 44 22 23 24 20 21 22  00 33 34 30 31 32   01 11 44 40 41 42 Now let TRANSR = 'C'. RFP A in both UPLO cases is just the conjugate transpose of RFP A above. One therefore gets: RFP A RFP A          02 12 22 00 01 00 10 20 30 40 50          03 13 23 33 11 33 11 21 31 41 51          04 14 24 34 44 43 44 22 32 42 52
Definition at line 247 of file clanhf.f.