zhetrd - onal form T by a unitary similarity transformation
SUBROUTINE ZHETRD(UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO) CHARACTER*1 UPLO DOUBLE COMPLEX A(LDA,*), TAU(*), WORK(*) INTEGER N, LDA, LWORK, INFO DOUBLE PRECISION D(*), E(*) SUBROUTINE ZHETRD_64(UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO) CHARACTER*1 UPLO DOUBLE COMPLEX A(LDA,*), TAU(*), WORK(*) INTEGER*8 N, LDA, LWORK, INFO DOUBLE PRECISION D(*), E(*) F95 INTERFACE SUBROUTINE HETRD(UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX(8), DIMENSION(:) :: TAU, WORK COMPLEX(8), DIMENSION(:,:) :: A INTEGER :: N, LDA, LWORK, INFO REAL(8), DIMENSION(:) :: D, E SUBROUTINE HETRD_64(UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX(8), DIMENSION(:) :: TAU, WORK COMPLEX(8), DIMENSION(:,:) :: A INTEGER(8) :: N, LDA, LWORK, INFO REAL(8), DIMENSION(:) :: D, E C INTERFACE #include <sunperf.h> void zhetrd(char uplo, int n, doublecomplex *a, int lda, double *d, double *e, doublecomplex *tau, int *info); void zhetrd_64(char uplo, long n, doublecomplex *a, long lda, double *d, double *e, doublecomplex *tau, long *info);
Oracle Solaris Studio Performance Library zhetrd(3P) NAME zhetrd - reduce a complex Hermitian matrix A to real symmetric tridiag- onal form T by a unitary similarity transformation SYNOPSIS SUBROUTINE ZHETRD(UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO) CHARACTER*1 UPLO DOUBLE COMPLEX A(LDA,*), TAU(*), WORK(*) INTEGER N, LDA, LWORK, INFO DOUBLE PRECISION D(*), E(*) SUBROUTINE ZHETRD_64(UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO) CHARACTER*1 UPLO DOUBLE COMPLEX A(LDA,*), TAU(*), WORK(*) INTEGER*8 N, LDA, LWORK, INFO DOUBLE PRECISION D(*), E(*) F95 INTERFACE SUBROUTINE HETRD(UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX(8), DIMENSION(:) :: TAU, WORK COMPLEX(8), DIMENSION(:,:) :: A INTEGER :: N, LDA, LWORK, INFO REAL(8), DIMENSION(:) :: D, E SUBROUTINE HETRD_64(UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX(8), DIMENSION(:) :: TAU, WORK COMPLEX(8), DIMENSION(:,:) :: A INTEGER(8) :: N, LDA, LWORK, INFO REAL(8), DIMENSION(:) :: D, E C INTERFACE #include <sunperf.h> void zhetrd(char uplo, int n, doublecomplex *a, int lda, double *d, double *e, doublecomplex *tau, int *info); void zhetrd_64(char uplo, long n, doublecomplex *a, long lda, double *d, double *e, doublecomplex *tau, long *info); PURPOSE zhetrd 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 zhetrd(3P)