CHPTRD(3)

chptrd.f(3) — Library Functions Manual

okay so welcome to the chptrd.f(3) page, bestie — this is the Library Functions Manual and it’s giving serious LAPACK main-character energy. 💅✨

NAME

The NAME section is literally just this source path, no cap:

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/chptrd.f

SYNOPSIS

🛠️ Functions/Subroutines

subroutine CHPTRD (uplo, n, ap, d, e, tau, info)
    CHPTRD

CHPTRD — that’s the subroutine, periodt.

Function/Subroutine Documentation

Here’s the full signature again, because documentation loves a repeat:

subroutine CHPTRD (character uplo, integer n, complex, dimension( * ) ap,
       real, dimension( * ) d, real, dimension( * ) e, complex, dimension( * )
       tau, integer info)

🎯 Purpose:

CHPTRD 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.

🧸 Parameters

UPLO

UPLO is CHARACTER*1, and it’s literally picking which triangle we’re storing:

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

N

N is INTEGER — the order of the matrix A. N >= 0.

AP

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

On entry, it’s 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 a REAL array, dimension (N).

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

E

E is a REAL 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

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

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

👑 Author

The author squad is:

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

🔍 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).

📌 Definition at line 150 of file chptrd.f.

🤖 Author

Generated automatically by Doxygen for LAPACK from the source code.

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