LAPACK
3.4.2
LAPACK: Linear Algebra PACKage

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Functions/Subroutines  
subroutine  zhptrd (UPLO, N, AP, D, E, TAU, INFO) 
ZHPTRD 
subroutine zhptrd  (  character  UPLO, 
integer  N,  
complex*16, dimension( * )  AP,  
double precision, dimension( * )  D,  
double precision, dimension( * )  E,  
complex*16, dimension( * )  TAU,  
integer  INFO  
) 
ZHPTRD
Download ZHPTRD + dependencies [TGZ] [ZIP] [TXT]ZHPTRD reduces a complex Hermitian matrix A stored in packed form to real symmetric tridiagonal form T by a unitary similarity transformation: Q**H * A * Q = T.
[in]  UPLO  UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. 
[in]  N  N is INTEGER The order of the matrix A. N >= 0. 
[in,out]  AP  AP is 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 jth column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j1)*(2*nj)/2) = A(i,j) for j<=i<=n. On exit, if UPLO = 'U', the diagonal and first superdiagonal of A are overwritten 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 elements 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. 
[out]  D  D is DOUBLE PRECISION array, dimension (N) The diagonal elements of the tridiagonal matrix T: D(i) = A(i,i). 
[out]  E  E is DOUBLE PRECISION array, dimension (N1) The offdiagonal elements of the tridiagonal matrix T: E(i) = A(i,i+1) if UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'. 
[out]  TAU  TAU is COMPLEX*16 array, dimension (N1) The scalar factors of the elementary reflectors (see Further Details). 
[out]  INFO  INFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value 
If UPLO = 'U', the matrix Q is represented as a product of elementary reflectors Q = H(n1) . . . H(2) H(1). Each H(i) has the form H(i) = I  tau * v * v**H where tau is a complex scalar, and v is a complex vector with v(i+1:n) = 0 and v(i) = 1; v(1:i1) is stored on exit in AP, overwriting A(1:i1,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(n1). Each H(i) has the form H(i) = I  tau * v * v**H 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).
Definition at line 152 of file zhptrd.f.