SRC/zhbtrd.f(3)

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version 3.12.1 · 4 versions
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✨ SRC/zhbtrd.f ✨

okay so this page is from the Library Functions Manual, and the header title is literally SRC/zhbtrd.f(3). It is giving “deep Fortran lore” and we are seated. 🫶

🌸 NAME 🌸

SRC/zhbtrd.f — that’s the name, bestie, no cap. 💅

✨ SYNOPSIS ✨

Functions/Subroutines

subroutine zhbtrd (vect, uplo, n, kd, ab, ldab, d, e, q, ldq, work,
    info)
    ZHBTRD

🦋 Function/Subroutine Documentation 🦋

subroutine zhbtrd (character vect, character uplo, integer n, integer kd,
    complex*16, dimension( ldab, * ) ab, integer ldab, double precision,
    dimension( * ) d, double precision, dimension( * ) e, complex*16,
    dimension( ldq, * ) q, integer ldq, complex*16, dimension( * ) work,
    integer info)
ZHBTRD

Purpose

okay so here’s the main-character plot: ZHBTRD reduces a complex Hermitian band matrix A to real symmetric tridiagonal form T by a unitary similarity transformation: Q**H * A * Q = T. iconic behavior, honestly. 👑

Parameters

VECT

VECT is CHARACTER*1.

  • = 'N': do not form Q;
  • = 'V': form Q;
  • = 'U': update a matrix X, by forming X*Q.

UPLO

UPLO is CHARACTER*1.

  • = '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.

KD

KD is INTEGER.

The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >= 0.

AB

AB is COMPLEX*16 array, dimension (LDAB,N).

On entry, the upper or lower triangle of the Hermitian band matrix A, stored in the first KD+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows:

if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).

On exit, the diagonal elements of AB are overwritten by the diagonal elements of the tridiagonal matrix T; if KD > 0, the elements on the first superdiagonal (if UPLO = 'U') or the first subdiagonal (if UPLO = 'L') are overwritten by the off-diagonal elements of T; the rest of AB is overwritten by values generated during the reduction. 💀

LDAB

LDAB is INTEGER.

The leading dimension of the array AB. LDAB >= KD+1.

D

D is DOUBLE PRECISION array, dimension (N).

The diagonal elements of the tridiagonal matrix T.

E

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

The off-diagonal elements of the tridiagonal matrix T:

E(i) = T(i,i+1) if UPLO = 'U'; E(i) = T(i+1,i) if UPLO = 'L'.

Q

Q is COMPLEX*16 array, dimension (LDQ,N).

On entry, if VECT = 'U', then Q must contain an N-by-N matrix X; if VECT = 'N' or 'V', then Q need not be set.

On exit:

  • if VECT = 'V', Q contains the N-by-N unitary matrix Q;
  • if VECT = 'U', Q contains the product X*Q;
  • if VECT = 'N', the array Q is not referenced.

LDQ

LDQ is INTEGER.

The leading dimension of the array Q. LDQ >= 1, and LDQ >= N if VECT = 'V' or 'U'.

WORK

WORK is COMPLEX*16 array, dimension (N).

INFO

INFO is INTEGER.

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

👑 Author 👑

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

🌈 Further Details 🌈

Modified by Linda Kaufman, Bell Labs.

Definition at line 161 of file zhbtrd.f.

🎀 Author 🎀

Generated automatically by Doxygen for LAPACK from the source code.

mwah 💋 this whole cutie is from LAPACK, Version 3.12.0, and the source page is SRC/zhbtrd.f(3). The footer doesn’t print a separate date, bestie, so I’m not inventing one — periodt. 🌟

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