zlanhf - norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hermitian matrix in RFP format
DOUBLE PRECISION FUNCTION ZLANHF(NORM, TRANSR, UPLO, N, A, WORK) CHARACTER*1 NORM, TRANSR, UPLO INTEGER N DOUBLE PRECISION WORK(0: *) DOUBLE COMPLEX A(0: *) DOUBLE PRECISION FUNCTION ZLANHF_64(NORM, TRANSR, UPLO, N, A, WORK) CHARACTER*1 NORM, TRANSR, UPLO INTEGER*8 N DOUBLE PRECISION WORK(0: *) DOUBLE COMPLEX A(0: *) F95 INTERFACE REAL(8) FUNCTION LANHF(NORM, TRANSR, UPLO, N, A, WORK) INTEGER :: N CHARACTER(LEN=1) :: NORM, TRANSR, UPLO COMPLEX(8), DIMENSION(:) :: A REAL(8), DIMENSION(:) :: WORK REAL(8) FUNCTION LANHF_64(NORM, TRANSR, UPLO, N, A, WORK) INTEGER(8) :: N CHARACTER(LEN=1) :: NORM, TRANSR, UPLO COMPLEX(8), DIMENSION(:) :: A REAL(8), DIMENSION(:) :: WORK C INTERFACE #include <sunperf.h> double zlanhf (char norm, char transr, char uplo, int n, doublecomplex *a); double zlanhf_64 (char norm, char transr, char uplo, long n, doublecom- plex *a);
Oracle Solaris Studio Performance Library zlanhf(3P)
NAME
zlanhf - return the value of the 1-norm, or the Frobenius norm, or the
infinity norm, or the element of largest absolute value of a Hermitian
matrix in RFP format
SYNOPSIS
DOUBLE PRECISION FUNCTION ZLANHF(NORM, TRANSR, UPLO, N, A, WORK)
CHARACTER*1 NORM, TRANSR, UPLO
INTEGER N
DOUBLE PRECISION WORK(0: *)
DOUBLE COMPLEX A(0: *)
DOUBLE PRECISION FUNCTION ZLANHF_64(NORM, TRANSR, UPLO, N, A, WORK)
CHARACTER*1 NORM, TRANSR, UPLO
INTEGER*8 N
DOUBLE PRECISION WORK(0: *)
DOUBLE COMPLEX A(0: *)
F95 INTERFACE
REAL(8) FUNCTION LANHF(NORM, TRANSR, UPLO, N, A, WORK)
INTEGER :: N
CHARACTER(LEN=1) :: NORM, TRANSR, UPLO
COMPLEX(8), DIMENSION(:) :: A
REAL(8), DIMENSION(:) :: WORK
REAL(8) FUNCTION LANHF_64(NORM, TRANSR, UPLO, N, A, WORK)
INTEGER(8) :: N
CHARACTER(LEN=1) :: NORM, TRANSR, UPLO
COMPLEX(8), DIMENSION(:) :: A
REAL(8), DIMENSION(:) :: WORK
C INTERFACE
#include <sunperf.h>
double zlanhf (char norm, char transr, char uplo, int n, doublecomplex
*a);
double zlanhf_64 (char norm, char transr, char uplo, long n, doublecom-
plex *a);
PURPOSE
zlanhf 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.
ZLANHF = ( 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.
ARGUMENTS
NORM (input)
NORM is CHARACTER
Specifies the value to be returned in ZLANHF as described
above.
TRANSR (input)
TRANSR is CHARACTER
Specifies whether the RFP format of A is normal or conjugate-
transposed format.
= 'N': RFP format is Normal
= 'C': RFP format is Conjugate-transposed
UPLO (input)
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
N (input)
N is INTEGER
The order of the matrix A. N >= 0. When N = 0, ZLANHF is set
to zero.
A (input)
A is COMPLEX*16 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:K-1) when N is even; K=N/2. RFP A is
(0:N-1,0:K) when N is odd; K=N/2. If TRANSR = 'C' then RFP is
the Conjugate-transpose 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 conjugate-transpose For-
mat. If UPLO = 'L' the RFP A contains the ( N*(N+1) /2 ) ele-
ments of lower packed A either in normal or conjugate-trans-
pose 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.
WORK (output)
WORK is DOUBLE PRECISION array, dimension (LWORK),
where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
WORK is not referenced.
FURTHER DETAILS
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
conjugate-transpose 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
conjugate-transpose 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
conjugate-transpose 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
conjugate-transpose 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
7 Nov 2015 zlanhf(3P)