chetrd - onal form T by a unitary similarity transformation
SUBROUTINE CHETRD(UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO) CHARACTER*1 UPLO COMPLEX A(LDA,*), TAU(*), WORK(*) INTEGER N, LDA, LWORK, INFO REAL D(*), E(*) SUBROUTINE CHETRD_64(UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO) CHARACTER*1 UPLO COMPLEX A(LDA,*), TAU(*), WORK(*) INTEGER*8 N, LDA, LWORK, INFO REAL D(*), E(*) F95 INTERFACE SUBROUTINE HETRD(UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX, DIMENSION(:) :: TAU, WORK COMPLEX, DIMENSION(:,:) :: A INTEGER :: N, LDA, LWORK, INFO REAL, DIMENSION(:) :: D, E SUBROUTINE HETRD_64(UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX, DIMENSION(:) :: TAU, WORK COMPLEX, DIMENSION(:,:) :: A INTEGER(8) :: N, LDA, LWORK, INFO REAL, DIMENSION(:) :: D, E C INTERFACE #include <sunperf.h> void chetrd(char uplo, int n, complex *a, int lda, float *d, float *e, complex *tau, int *info); void chetrd_64(char uplo, long n, complex *a, long lda, float *d, float *e, complex *tau, long *info);
Oracle Solaris Studio Performance Library chetrd(3P)
NAME
chetrd - reduce a complex Hermitian matrix A to real symmetric tridiag-
onal form T by a unitary similarity transformation
SYNOPSIS
SUBROUTINE CHETRD(UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO)
CHARACTER*1 UPLO
COMPLEX A(LDA,*), TAU(*), WORK(*)
INTEGER N, LDA, LWORK, INFO
REAL D(*), E(*)
SUBROUTINE CHETRD_64(UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO)
CHARACTER*1 UPLO
COMPLEX A(LDA,*), TAU(*), WORK(*)
INTEGER*8 N, LDA, LWORK, INFO
REAL D(*), E(*)
F95 INTERFACE
SUBROUTINE HETRD(UPLO, N, A, LDA, D, E, TAU, WORK, LWORK,
INFO)
CHARACTER(LEN=1) :: UPLO
COMPLEX, DIMENSION(:) :: TAU, WORK
COMPLEX, DIMENSION(:,:) :: A
INTEGER :: N, LDA, LWORK, INFO
REAL, DIMENSION(:) :: D, E
SUBROUTINE HETRD_64(UPLO, N, A, LDA, D, E, TAU, WORK, LWORK,
INFO)
CHARACTER(LEN=1) :: UPLO
COMPLEX, DIMENSION(:) :: TAU, WORK
COMPLEX, DIMENSION(:,:) :: A
INTEGER(8) :: N, LDA, LWORK, INFO
REAL, DIMENSION(:) :: D, E
C INTERFACE
#include <sunperf.h>
void chetrd(char uplo, int n, complex *a, int lda, float *d, float *e,
complex *tau, int *info);
void chetrd_64(char uplo, long n, complex *a, long lda, float *d, float
*e, complex *tau, long *info);
PURPOSE
chetrd reduces a complex Hermitian matrix A to real symmetric tridiago-
nal form T by a unitary similarity transformation: Q**H * A * Q = T.
ARGUMENTS
UPLO (input)
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) The order of the matrix A. N >= 0.
A (input/output)
On entry, the Hermitian matrix A. If UPLO = 'U', the leading
N-by-N upper triangular part of A contains the upper triangu-
lar part of the matrix A, and the strictly lower triangular
part of A is not referenced. If UPLO = 'L', the leading N-
by-N lower triangular part of A contains the lower triangular
part of the matrix A, and the strictly upper triangular part
of A is not referenced. On exit, if UPLO = 'U', the diagonal
and first superdiagonal of A are overwritten by the corre-
sponding elements of the tridiagonal matrix T, and the ele-
ments above the first superdiagonal, with the array TAU, rep-
resent the unitary matrix Q as a product of elementary
reflectors; if UPLO = 'L', the diagonal and first subdiagonal
of A are over- written by the corresponding elements of the
tridiagonal matrix T, and the elements below the first subdi-
agonal, with the array TAU, represent the unitary matrix Q as
a product of elementary reflectors. See Further Details.
LDA (input)
The leading dimension of the array A. LDA >= max(1,N).
D (output)
The diagonal elements of the tridiagonal matrix T: D(i) =
A(i,i).
E (output)
The off-diagonal elements of the tridiagonal matrix T: E(i) =
A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'.
TAU (output)
The scalar factors of the elementary reflectors (see Further
Details).
WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input)
The dimension of the array WORK. LWORK >= 1. For optimum
performance LWORK >= N*NB, where NB is the optimal blocksize.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
FURTHER DETAILS
If UPLO = 'U', the matrix Q is represented as a product of elementary
reflectors
Q = H(n-1) . . . H(2) H(1).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with v(i+1:n)
= 0 and v(i) = 1; v(1:i-1) is stored on exit in
A(1:i-1,i+1), and tau in TAU(i).
If UPLO = 'L', the matrix Q is represented as a product of elementary
reflectors
Q = H(1) H(2) . . . H(n-1).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a complex scalar, and v is a complex vector with v(1:i) =
0 and v(i+1) = 1; v(i+2:n) is stored on exit in A(i+2:n,i), and tau in
TAU(i).
The contents of A on exit are illustrated by the following examples
with n = 5:
if UPLO = 'U': if UPLO = 'L':
( d e v2 v3 v4 ) ( d )
( d e v3 v4 ) ( e d )
( d e v4 ) ( v1 e d )
( d e ) ( v1 v2 e d )
( d ) ( v1 v2 v3 e d )
where d and e denote diagonal and off-diagonal elements of T, and vi
denotes an element of the vector defining H(i).
7 Nov 2015 chetrd(3P)