.TH "SRC/zhptrd.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME SRC/zhptrd.f .SH SYNOPSIS .br .PP .SS "Functions/Subroutines" .in +1c .ti -1c .RI "subroutine \fBzhptrd\fP (uplo, n, ap, d, e, tau, info)" .br .RI "\fBZHPTRD\fP " .in -1c .SH "Function/Subroutine Documentation" .PP .SS "subroutine zhptrd (character uplo, integer n, complex*16, dimension( * ) ap, double precision, dimension( * ) d, double precision, dimension( * ) e, complex*16, dimension( * ) tau, integer info)" .PP \fBZHPTRD\fP .PP \fBPurpose:\fP .RS 4 .PP .nf 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\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. N >= 0\&. .fi .PP .br \fIAP\fP .PP .nf 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 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 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\&. .fi .PP .br \fID\fP .PP .nf D is DOUBLE PRECISION array, dimension (N) The diagonal elements of the tridiagonal matrix T: D(i) = A(i,i)\&. .fi .PP .br \fIE\fP .PP .nf E is 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'\&. .fi .PP .br \fITAU\fP .PP .nf TAU is COMPLEX*16 array, dimension (N-1) The scalar factors of the elementary reflectors (see Further Details)\&. .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBFurther Details:\fP .RS 4 .PP .nf 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**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: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**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)\&. .fi .PP .RE .PP .PP Definition at line \fB150\fP of file \fBzhptrd\&.f\fP\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.