DSBTRD(3)

💜 dsbtrd.f(3) — Library Functions Manual 💜

ok so bestie, this is a page from the LAPACK docs — manual name is dsbtrd.f(3), and the file it's documenting lives at:

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

(yeah it's a whole journey of a path, we love a deep directory tree 💅)

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✨ NAME ✨

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

that's it, that's the name, the manpage just names the file. iconique.

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🎀 SYNOPSIS 🎀

Functions/Subroutines

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

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🌸 Function/Subroutine Documentation 🌸

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

DSBTRD

💖 Purpose:

!>
!> DSBTRD reduces a real symmetric band matrix A to symmetric
!> tridiagonal form T by an orthogonal similarity transformation:
!> Q**T * A * Q = T.
!>

so basically it takes your symmetric band matrix A and squeezes it down into tridiagonal form T — no cap, that's the whole vibe check.

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🔥 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 DOUBLE PRECISION array, dimension (LDAB,N).

On entry, the upper or lower triangle of the symmetric 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.

⚠️ heads up bestie — AB gets absolutely demolished on exit. your original matrix? gone. she's been overwritten, periodt. 💀

• 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 DOUBLE PRECISION 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 orthogonal matrix Q;
if VECT = 'U', Q contains the product X*Q;
if VECT = 'N', the array Q is not referenced.

🫶 love that for VECT = 'N' honestly — she said "not my problem, don't even look at me."

• LDQ — LDQ is INTEGER. The leading dimension of the array Q. LDQ >= 1, and LDQ >= N if VECT = 'V' or 'U'.
• WORK — WORK is DOUBLE PRECISION array, dimension (N).
• 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: 🦋

!>
!>  Modified by Linda Kaufman, Bell Labs.
!>

shoutout Linda Kaufman from Bell Labs, the actual main character of this file fr fr 🎀

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Definition at line 161 of file dsbtrd.f.

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code. (yes queen, the robots wrote the docs, we're just vibing in their shadow ✨)

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LAPACK · Version 3.12.0 · /home/abui...RC/dsbtrd.f(3)

and that's the whole page bestie, mwah 💋 slay, go reduce some band matrices, ily 🫶💖