zhptrd - reduce a complex Hermitian matrix A stored in packed form to real symmetric tridiagonal form T by a unitary similarity transforma- tion
SUBROUTINE ZHPTRD(UPLO, N, AP, D, E, TAU, INFO) CHARACTER*1 UPLO DOUBLE COMPLEX AP(*), TAU(*) INTEGER N, INFO DOUBLE PRECISION D(*), E(*) SUBROUTINE ZHPTRD_64(UPLO, N, AP, D, E, TAU, INFO) CHARACTER*1 UPLO DOUBLE COMPLEX AP(*), TAU(*) INTEGER*8 N, INFO DOUBLE PRECISION D(*), E(*) F95 INTERFACE SUBROUTINE HPTRD(UPLO, N, AP, D, E, TAU, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX(8), DIMENSION(:) :: AP, TAU INTEGER :: N, INFO REAL(8), DIMENSION(:) :: D, E SUBROUTINE HPTRD_64(UPLO, N, AP, D, E, TAU, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX(8), DIMENSION(:) :: AP, TAU INTEGER(8) :: N, INFO REAL(8), DIMENSION(:) :: D, E C INTERFACE #include <sunperf.h> void zhptrd(char uplo, int n, doublecomplex *ap, double *d, double *e, doublecomplex *tau, int *info); void zhptrd_64(char uplo, long n, doublecomplex *ap, double *d, double *e, doublecomplex *tau, long *info);
Oracle Solaris Studio Performance Library zhptrd(3P) NAME zhptrd - reduce a complex Hermitian matrix A stored in packed form to real symmetric tridiagonal form T by a unitary similarity transforma- tion SYNOPSIS SUBROUTINE ZHPTRD(UPLO, N, AP, D, E, TAU, INFO) CHARACTER*1 UPLO DOUBLE COMPLEX AP(*), TAU(*) INTEGER N, INFO DOUBLE PRECISION D(*), E(*) SUBROUTINE ZHPTRD_64(UPLO, N, AP, D, E, TAU, INFO) CHARACTER*1 UPLO DOUBLE COMPLEX AP(*), TAU(*) INTEGER*8 N, INFO DOUBLE PRECISION D(*), E(*) F95 INTERFACE SUBROUTINE HPTRD(UPLO, N, AP, D, E, TAU, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX(8), DIMENSION(:) :: AP, TAU INTEGER :: N, INFO REAL(8), DIMENSION(:) :: D, E SUBROUTINE HPTRD_64(UPLO, N, AP, D, E, TAU, INFO) CHARACTER(LEN=1) :: UPLO COMPLEX(8), DIMENSION(:) :: AP, TAU INTEGER(8) :: N, INFO REAL(8), DIMENSION(:) :: D, E C INTERFACE #include <sunperf.h> void zhptrd(char uplo, int n, doublecomplex *ap, double *d, double *e, doublecomplex *tau, int *info); void zhptrd_64(char uplo, long n, doublecomplex *ap, double *d, double *e, doublecomplex *tau, long *info); PURPOSE zhptrd reduces a complex Hermitian matrix A stored in packed form to real symmetric tridiagonal form T by a unitary similarity transforma- tion: 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. AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2) On entry, the upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. On exit, if UPLO = 'U', the diagonal and first superdiagonal of A are overwrit- ten by the corresponding elements of the tridiagonal matrix T, and the elements above the first superdiagonal, with the array TAU, represent 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 ele- ments of the tridiagonal matrix T, and the elements below the first subdiagonal, with the array TAU, represent the unitary matrix Q as a product of elementary reflectors. See Further Details. D (output) DOUBLE PRECISION array, dimension (N) The diagonal elements of the tridiagonal matrix T: D(i) = A(i,i). E (output) DOUBLE PRECISION array, dimension (N-1) 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) COMPLEX*16 array, dimension (N-1) The scalar factors of the elementary reflectors (see Further Details). 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 AP, overwriting A(1:i-1,i+1), and tau is stored 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 AP, overwriting A(i+2:n,i), and tau is stored in TAU(i). 7 Nov 2015 zhptrd(3P)