SRC/chbtrd.f(3)

📦
version 3.12.1 · 4 versions
, in arch rolling

💖 NAME 💖

okay bestie, this is SRC/chbtrd.f — the whole page lives in the LAPACK manual as SRC/chbtrd.f(3), and it's about making a complex Hermitian band matrix get its life together.

📜 SYNOPSIS 📜

🌸 Functions/Subroutines 🌸

Here's the iconic little signature, no cap:

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

🧚 Function/Subroutine Documentation 🧚

The full glow-up signature is literally:

subroutine chbtrd (character vect, character uplo, integer n, integer kd,
     complex, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) d,
     real, dimension( * ) e, complex, dimension( ldq, * ) q, integer ldq,
     complex, dimension( * ) work, integer info)
CHBTRD

🎀 Purpose 🎀

CHBTRD reduces a complex Hermitian band matrix A to real symmetric tridiagonal form T by a unitary similarity transformation:

Q**H * A * Q = T

That's the whole main-character move. 💅

💅 Parameters 💅

VECT

VECT is CHARACTER*1, and it picks the vibe:

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

UPLO

UPLO is CHARACTER*1, and it says which triangle of A is stored:

  • '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. Constraint: N >= 0.

KD

KD is INTEGER.

It's the number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. Constraint: KD >= 0.

AB

AB is a COMPLEX array, dimension (LDAB,N).

On entry, it holds 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. So yeah, AB gets a full makeover. ✨

LDAB

LDAB is INTEGER.

It's the leading dimension of the array AB. Constraint: LDAB >= KD+1.

D

D is a REAL array, dimension (N).

It holds the diagonal elements of the tridiagonal matrix T.

E

E is a REAL array, dimension (N-1).

It holds 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 a COMPLEX 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.

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

WORK

WORK is a COMPLEX array, dimension (N).

That's it. It's just out here doing its work, literally. 🫶

INFO

INFO is INTEGER.

  • 0: successful exit;
  • < 0: if INFO = -i, the i-th argument had an illegal value.
If INFO = -i, bestie, argument i had an illegal value — that's the error vibe check. 🚨

👑 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 chbtrd.f. 📝

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

That's the page, bestie — LAPACK Version 3.12.0, from SRC/chbtrd.f(3). 💅✨

📦 where this page comes from