DPTEQR(3)

💅 DPTEQR 💅

okay so bestie, welcome to the dpteqr.f(3) page from the Library Functions Manual. Buckle up, we're doing LAPACK and it's giving very serious numerical energy. 💖

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🎀 NAME 🎀

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

yes, that whole path is the NAME section. iconic, honestly. ✨

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✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

• subroutine DPTEQR (compz, n, d, e, z, ldz, work, info) — DPTEQR

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💖 Function/Subroutine Documentation 💖

subroutine DPTEQR (character compz, integer n, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( ldz, * ) z, integer ldz, double precision, dimension( * ) work, integer info)

DPTEQR

🌸 Purpose 🌸

Okay so DPTEQR computes all eigenvalues and, optionally, eigenvectors of a symmetric positive definite tridiagonal matrix. It does this by first factoring the matrix using DPTTRF, and then calling DBDSQR to compute the singular values of the bidiagonal factor. periodt. 💅

This routine computes the eigenvalues of the positive definite tridiagonal matrix to high relative accuracy. Which means: if the eigenvalues range over many orders of magnitude in size, then the small eigenvalues and corresponding eigenvectors will be computed more accurately than, for example, with the standard QR method. slay accuracy, no cap. 🌟

The eigenvectors of a full or band symmetric positive definite matrix can also be found if DSYTRD, DSPTRD, or DSBTRD has been used to reduce this matrix to tridiagonal form. But listen: the reduction to tridiagonal form, however, may preclude the possibility of obtaining high relative accuracy in the small eigenvalues of the original matrix, if these eigenvalues range over many orders of magnitude. so that's the caveat, bestie. 🫶

💅 Parameters 💅

• COMPZ — COMPZ is CHARACTER*1
  • = 'N': Compute eigenvalues only.
  • = 'V': Compute eigenvectors of original symmetric matrix also. Array Z contains the orthogonal matrix used to reduce the original matrix to tridiagonal form.
  • = 'I': Compute eigenvectors of tridiagonal matrix also.
• N — N is INTEGER

The order of the matrix. N >= 0.

• D — D is DOUBLE PRECISION array, dimension (N)

On entry, the n diagonal elements of the tridiagonal matrix.

On normal exit, D contains the eigenvalues, in descending order.

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

On entry, the (n-1) subdiagonal elements of the tridiagonal matrix.

On exit, E has been destroyed.

• Z — Z is DOUBLE PRECISION array, dimension (LDZ, N)

On entry, if COMPZ = 'V', the orthogonal matrix used in the reduction to tridiagonal form.

On exit, if COMPZ = 'V', the orthonormal eigenvectors of the original symmetric matrix; if COMPZ = 'I', the orthonormal eigenvectors of the tridiagonal matrix.

If INFO > 0 on exit, Z contains the eigenvectors associated with only the stored eigenvalues.

If COMPZ = 'N', then Z is not referenced.

• LDZ — LDZ is INTEGER

The leading dimension of the array Z. LDZ >= 1, and if COMPZ = 'V' or 'I', LDZ >= max(1,N).

• WORK — WORK is DOUBLE PRECISION array, dimension (4*N)
• INFO — INFO is INTEGER
  • = 0: successful exit.
  • < 0: if INFO = -i, the i-th argument had an illegal value.
  • > 0: if INFO = i, and i is:
    • <= N: the Cholesky factorization of the matrix could not be performed because the leading principal minor of order i was not positive.
    • > N: the SVD algorithm failed to converge; if INFO = N+i, i off-diagonal elements of the bidiagonal factor did not converge to zero.

👑 Author 👑

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 144 of file dpteqr.f.

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📜 Author 📜

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