CHBTRD(3)

CHBTRD(3) — Library Functions Manual 💅

okay bestie, this is CHBTRD(3) from the Library Functions Manual — header path /home/abui...RC/chbtrd.f(3), and the actual source is the full path below. buckle up, it’s giving linear algebra but make it cute ✨

🌸 NAME 🌸

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

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✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

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

CHBTRD

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💖 Function/Subroutine Documentation 💖

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 🌟

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

Q**H * A * Q = T.

literally iconic. 👑

💜 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 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 REAL array, dimension (N) The diagonal elements of the tridiagonal matrix T.
• E — E is REAL 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 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 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 chbtrd.f.

🎀 Author 🎀

Generated automatically by Doxygen for LAPACK from the source code.

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made with 💖 by LAPACK Version 3.12.0 — footer path says /home/abui...RC/chbtrd.f(3), and that’s the whole vibe check, bestie 🫶✨