pttrf(3)

📦
version 3.12.1 · 9 versions
, in arch rolling

🌸 pttrf(3) 🌸

okay so this page is from the Library Functions Manual and it's literally all about pttrf — the triangular factor bestie 💅 four whole Fortran subroutines that do the same iconic thing in different flavors. grab a snack, we're getting into it 🍓

✨ NAME ✨

pttrf — pttrf: triangular factor. that's the whole name, no notes 💖

✨ SYNOPSIS ✨

🎀 Functions 🎀

  • subroutine cpttrf (n, d, e, info) — CPTTRF
  • subroutine dpttrf (n, d, e, info) — DPTTRF
  • subroutine spttrf (n, d, e, info) — SPTTRF
  • subroutine zpttrf (n, d, e, info) — ZPTTRF

like yes bestie, all four of them, same energy, different precision 🌈

✨ Detailed Description ✨

the actual details live down below in Function Documentation, one subroutine at a time 👑

💅 Function Documentation 💅

⭐ subroutine cpttrf (integer n, real, dimension( * ) d, complex, dimension( * ) e, integer info)

CPTTRF

Purpose:

!>
!> CPTTRF computes the L*D*L**H factorization of a complex Hermitian
!> positive definite tridiagonal matrix A.  The factorization may also
!> be regarded as having the form A = U**H *D*U.
!>

Parameters

  • N — N is INTEGER. The order of the matrix A. N >= 0.
  • D — D is REAL array, dimension (N). On entry, the n diagonal elements of the tridiagonal matrix A. On exit, the n diagonal elements of the diagonal matrix D from the L*D*L**H factorization of A.
  • E — E is COMPLEX array, dimension (N-1). On entry, the (n-1) subdiagonal elements of the tridiagonal matrix A. On exit, the (n-1) subdiagonal elements of the unit bidiagonal factor L from the L*D*L**H factorization of A. E can also be regarded as the superdiagonal of the unit bidiagonal factor U from the U**H *D*U factorization of A.
  • INFO — INFO is INTEGER:
    • = 0: successful exit 🎉
    • < 0: if INFO = -k, the k-th argument had an illegal value
    • > 0: if INFO = k, the leading principal minor of order k is not positive; if k < N, the factorization could not be completed, while if k = N, the factorization was completed, but D(N) <= 0.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 91 of file cpttrf.f.

⭐ subroutine dpttrf (integer n, double precision, dimension( * ) d, double precision, dimension( * ) e, integer info)

DPTTRF

Purpose:

!>
!> DPTTRF computes the L*D*L**T factorization of a real symmetric
!> positive definite tridiagonal matrix A.  The factorization may also
!> be regarded as having the form A = U**T*D*U.
!>

Parameters

  • N — N is INTEGER. The order of the matrix A. N >= 0.
  • D — D is DOUBLE PRECISION array, dimension (N). On entry, the n diagonal elements of the tridiagonal matrix A. On exit, the n diagonal elements of the diagonal matrix D from the L*D*L**T factorization of A.
  • E — E is DOUBLE PRECISION array, dimension (N-1). On entry, the (n-1) subdiagonal elements of the tridiagonal matrix A. On exit, the (n-1) subdiagonal elements of the unit bidiagonal factor L from the L*D*L**T factorization of A. E can also be regarded as the superdiagonal of the unit bidiagonal factor U from the U**T*D*U factorization of A.
  • INFO — INFO is INTEGER:
    • = 0: successful exit 🎉
    • < 0: if INFO = -k, the k-th argument had an illegal value
    • > 0: if INFO = k, the leading principal minor of order k is not positive; if k < N, the factorization could not be completed, while if k = N, the factorization was completed, but D(N) <= 0.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 90 of file dpttrf.f.

⭐ subroutine spttrf (integer n, real, dimension( * ) d, real, dimension( * ) e, integer info)

SPTTRF

Purpose:

!>
!> SPTTRF computes the L*D*L**T factorization of a real symmetric
!> positive definite tridiagonal matrix A.  The factorization may also
!> be regarded as having the form A = U**T*D*U.
!>

Parameters

  • N — N is INTEGER. The order of the matrix A. N >= 0.
  • D — D is REAL array, dimension (N). On entry, the n diagonal elements of the tridiagonal matrix A. On exit, the n diagonal elements of the diagonal matrix D from the L*D*L**T factorization of A.
  • E — E is REAL array, dimension (N-1). On entry, the (n-1) subdiagonal elements of the tridiagonal matrix A. On exit, the (n-1) subdiagonal elements of the unit bidiagonal factor L from the L*D*L**T factorization of A. E can also be regarded as the superdiagonal of the unit bidiagonal factor U from the U**T*D*U factorization of A.
  • INFO — INFO is INTEGER:
    • = 0: successful exit 🎉
    • < 0: if INFO = -k, the k-th argument had an illegal value
    • > 0: if INFO = k, the leading principal minor of order k is not positive; if k < N, the factorization could not be completed, while if k = N, the factorization was completed, but D(N) <= 0.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 90 of file spttrf.f.

⭐ subroutine zpttrf (integer n, double precision, dimension( * ) d, complex*16, dimension( * ) e, integer info)

ZPTTRF

Purpose:

!>
!> ZPTTRF computes the L*D*L**H factorization of a complex Hermitian
!> positive definite tridiagonal matrix A.  The factorization may also
!> be regarded as having the form A = U**H *D*U.
!>

Parameters

  • N — N is INTEGER. The order of the matrix A. N >= 0.
  • D — D is DOUBLE PRECISION array, dimension (N). On entry, the n diagonal elements of the tridiagonal matrix A. On exit, the n diagonal elements of the diagonal matrix D from the L*D*L**H factorization of A.
  • E — E is COMPLEX*16 array, dimension (N-1). On entry, the (n-1) subdiagonal elements of the tridiagonal matrix A. On exit, the (n-1) subdiagonal elements of the unit bidiagonal factor L from the L*D*L**H factorization of A. E can also be regarded as the superdiagonal of the unit bidiagonal factor U from the U**H *D*U factorization of A.
  • INFO — INFO is INTEGER:
    • = 0: successful exit 🎉
    • < 0: if INFO = -k, the k-th argument had an illegal value
    • > 0: if INFO = k, the leading principal minor of order k is not positive; if k < N, the factorization could not be completed, while if k = N, the factorization was completed, but D(N) <= 0.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 91 of file zpttrf.f.

🦋 Author 🦋

Generated automatically by Doxygen for LAPACK from the source code. (not a human wrote this bit, it's the robot intern 🤖✨)

okay that's the whole page bestie, you ate that 💅

signing off with the cute little footer deets: it's LAPACK, Version 3.12.0, and the page itself is pttrf(3) — mwah, periodt 🎀💖

📦 where this page comes from