SRC/zhptrd.f(3)

💖 SRC/zhptrd.f(3) — Library Functions Manual

okay bestie, this page is from the Library Functions Manual and it's all about SRC/zhptrd.f. no cap, it's giving “LAPACK source documentation” energy and I'm obsessed. 🎀

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🌸 NAME

SRC/zhptrd.f — that's the name, that's the whole name, and it's literally the file this page is documenting. 💅

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✨ SYNOPSIS

🧚 Functions/Subroutines

• subroutine zhptrd (uplo, n, ap, d, e, tau, info) — the callable routine, right here, ready to slay.
• ZHPTRD — the routine's name, loud and clear.

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👑 Function/Subroutine Documentation

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

💡 Purpose:

bestie, here's the whole vibe: 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. 🦋

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🎀 Parameters

UPLO

UPLO is CHARACTER*1.

• = 'U' — Upper triangle of A is stored;
• = 'L' — Lower triangle of A is stored.

N

N is INTEGER. It's the order of the matrix A. N >= 0. periodt. ✨

AP

AP is COMPLEX*16 array, dimension (N*(N+1)/2).

On entry, it holds 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. 👑

D

D is DOUBLE PRECISION array, dimension (N).

It holds the diagonal elements of the tridiagonal matrix T: D(i) = A(i,i). 💜

E

E is DOUBLE PRECISION array, dimension (N-1).

It holds 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

TAU is COMPLEX*16 array, dimension (N-1).

These are the scalar factors of the elementary reflectors (see Further Details). 🧚

INFO

INFO is INTEGER.

• = 0 — successful exit
• < 0 — if INFO = -i, the i-th argument had an illegal value

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🌟 Author

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

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🦋 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**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). 💫

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📜 Definition at line 150 of file zhptrd.f.

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🫶 Author

Generated automatically by Doxygen for LAPACK from the source code.

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okay that's the whole page, bestie 🎀✨ LAPACK Version 3.12.0 and SRC/zhptrd.f(3) — mwah, bye! 🦋💅