dlansf - norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric matrix in RFP format
DOUBLE PRECISION FUNCTION DLANSF(NORM, TRANSR, UPLO, N, A, WORK) CHARACTER*1 NORM, TRANSR, UPLO INTEGER N DOUBLE PRECISION A(0: *), WORK(0: *) DOUBLE PRECISION FUNCTION DLANSF_64(NORM, TRANSR, UPLO, N, A, WORK) CHARACTER*1 NORM, TRANSR, UPLO INTEGER*8 N DOUBLE PRECISION A(0: *), WORK(0: *) F95 INTERFACE REAL(8) FUNCTION LANSF(NORM, TRANSR, UPLO, N, A, WORK) INTEGER :: N CHARACTER(LEN=1) :: NORM, TRANSR, UPLO REAL(8), DIMENSION(:) :: A, WORK REAL(8) FUNCTION LANSF_64(NORM, TRANSR, UPLO, N, A, WORK) INTEGER(8) :: N CHARACTER(LEN=1) :: NORM, TRANSR, UPLO REAL(8), DIMENSION(:) :: A, WORK C INTERFACE #include <sunperf.h> double dlansf (char norm, char transr, char uplo, int n, double *a); double dlansf_64 (char norm, char transr, char uplo, long n, double *a);
Oracle Solaris Studio Performance Library dlansf(3P)
NAME
dlansf - return the value of the 1-norm, or the Frobenius norm, or the
infinity norm, or the element of largest absolute value of a symmetric
matrix in RFP format
SYNOPSIS
DOUBLE PRECISION FUNCTION DLANSF(NORM, TRANSR, UPLO, N, A, WORK)
CHARACTER*1 NORM, TRANSR, UPLO
INTEGER N
DOUBLE PRECISION A(0: *), WORK(0: *)
DOUBLE PRECISION FUNCTION DLANSF_64(NORM, TRANSR, UPLO, N, A, WORK)
CHARACTER*1 NORM, TRANSR, UPLO
INTEGER*8 N
DOUBLE PRECISION A(0: *), WORK(0: *)
F95 INTERFACE
REAL(8) FUNCTION LANSF(NORM, TRANSR, UPLO, N, A, WORK)
INTEGER :: N
CHARACTER(LEN=1) :: NORM, TRANSR, UPLO
REAL(8), DIMENSION(:) :: A, WORK
REAL(8) FUNCTION LANSF_64(NORM, TRANSR, UPLO, N, A, WORK)
INTEGER(8) :: N
CHARACTER(LEN=1) :: NORM, TRANSR, UPLO
REAL(8), DIMENSION(:) :: A, WORK
C INTERFACE
#include <sunperf.h>
double dlansf (char norm, char transr, char uplo, int n, double *a);
double dlansf_64 (char norm, char transr, char uplo, long n, double
*a);
PURPOSE
dlansf returns the value of the one norm, or the Frobenius norm, or the
infinity norm, or the element of largest absolute value of a real sym-
metric matrix A in RFP format.
DLANSF = ( 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*1
Specifies the value to be returned in DLANSF as described
above.
TRANSR (input)
TRANSR is CHARACTER*1
Specifies whether the RFP format of A is normal or transposed
format.
= 'N': RFP format is Normal;
= 'T': RFP format is Transpose.
UPLO (input)
UPLO is CHARACTER*1
On entry, UPLO specifies whether the RFP matrix A came from
an upper or lower triangular matrix as follows:
= 'U': RFP A came from an upper triangular matrix;
= '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, DLANSF is set
to zero.
A (input)
A is DOUBLE PRECISION array, dimension ( N*(N+1)/2 );
On entry, the upper (if UPLO = 'U') or lower (if UPLO = 'L')
part of the symmetric matrix A stored in RFP format. See the
"Notes" below for more details.
Unchanged on exit.
WORK (output)
WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
WORK is not referenced.
FURTHER DETAILS
We first consider Rectangular Full Packed (RFP) 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
the 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
the transpose of the last three columns of AP lower.
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 = 'T'. RFP A in both UPLO cases is just the
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 then consider Rectangular Full Packed (RFP) 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
the 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
the transpose of the last two columns of AP lower.
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 = 'T'. RFP A in both UPLO cases is just the
transpose of RFP A above. One therefore gets:
RFP A RFP A
00 33 34 30 31 32
01 11 44 40 41 42
Now let TRANSR = 'T'. RFP A in both UPLO cases is just the
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 dlansf(3P)