pptrf(3)

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version 3.12.1 · 9 versions
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Hey bestie! You’re reading pptrf(3) from the Library Functions Manual — welcome to the triangular-factor group chat 💅✨

💖 NAME 💖

pptrf — pptrf: triangular factor 🎀

✨ SYNOPSIS ✨

💅 Functions

  • subroutine cpptrf (uplo, n, ap, info) — CPPTRF
  • subroutine dpptrf (uplo, n, ap, info) — DPPTRF
  • subroutine spptrf (uplo, n, ap, info) — SPPTRF
  • subroutine zpptrf (uplo, n, ap, info) — ZPPTRF

🌈 Detailed Description 🌈

Okay so this page is all about the triangular factor vibe — the full function documentation is right below, bestie 🫶

🌸 Function Documentation 🌸

💅 subroutine cpptrf (character uplo, integer n, complex, dimension( * ) ap, integer info)

CPPTRF

Purpose:

CPPTRF computes the Cholesky factorization of a complex Hermitian positive definite matrix A stored in packed format. No cap, that’s the whole assignment 💖

The factorization has the form

A = U**H * U,  if UPLO = 'U', or
A = L  * L**H,  if UPLO = 'L',

where U is an upper triangular matrix and L is lower triangular. Periodt 🌟

Parameters

  • UPLO — UPLO is CHARACTER*1. = 'U': the upper triangle of A is stored; = 'L': the lower triangle of A is stored. Pick your fighter, bestie 🎀
  • N — N is INTEGER. The order of the matrix A. N >= 0.
  • AP — AP is COMPLEX array, dimension (N*(N+1)/2). On entry, it’s the upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP like this: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. See below for further details 👀 On exit, if INFO = 0, you get the triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, in the same storage format as A. Slay 💅
  • INFO — INFO is INTEGER. = 0: successful exit ✨ < 0: if INFO = -i, the i-th argument had an illegal value 🙈 > 0: if INFO = i, the leading principal minor of order i is not positive definite, and the factorization could not be completed 😭

Author

  • Univ. of Tennessee
  • Univ. of California Berkeley
  • Univ. of Colorado Denver
  • NAG Ltd.

Further Details:

The packed storage scheme is illustrated by the following example when N = 4, UPLO = 'U':

Two-dimensional storage of the Hermitian matrix A:

     a11 a12 a13 a14
         a22 a23 a24
             a33 a34     (aij = conjg(aji))
                 a44

Packed storage of the upper triangle of A:

AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]

Definition at line 118 of file cpptrf.f.

💅 subroutine dpptrf (character uplo, integer n, double precision, dimension( * ) ap, integer info)

DPPTRF

Purpose:

DPPTRF computes the Cholesky factorization of a real symmetric positive definite matrix A stored in packed format. We love a real symmetric moment 🦋

The factorization has the form

A = U**T * U,  if UPLO = 'U', or
A = L  * L**T,  if UPLO = 'L',

where U is an upper triangular matrix and L is lower triangular. Iconic 🌟

Parameters

  • UPLO — UPLO is CHARACTER*1. = 'U': the upper triangle of A is stored; = 'L': the lower triangle of A is stored. Choose wisely, bestie 🎀
  • N — N is INTEGER. The order of the matrix A. N >= 0.
  • AP — AP is DOUBLE PRECISION array, dimension (N*(N+1)/2). On entry, it’s the upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP like this: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. See below for further details 👀 On exit, if INFO = 0, you get the triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, in the same storage format as A. Ate 💅
  • INFO — INFO is INTEGER. = 0: successful exit ✨ < 0: if INFO = -i, the i-th argument had an illegal value 🙈 > 0: if INFO = i, the leading principal minor of order i is not positive, and the factorization could not be completed 😭

Author

  • Univ. of Tennessee
  • Univ. of California Berkeley
  • Univ. of Colorado Denver
  • NAG Ltd.

Further Details:

The packed storage scheme is illustrated by the following example when N = 4, UPLO = 'U':

Two-dimensional storage of the symmetric matrix A:

     a11 a12 a13 a14
         a22 a23 a24
             a33 a34     (aij = aji)
                 a44

Packed storage of the upper triangle of A:

AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]

Definition at line 118 of file dpptrf.f.

💅 subroutine spptrf (character uplo, integer n, real, dimension( * ) ap, integer info)

SPPTRF

Purpose:

SPPTRF computes the Cholesky factorization of a real symmetric positive definite matrix A stored in packed format. Same real-symmetric energy, single-precision edition 💖

The factorization has the form

A = U**T * U,  if UPLO = 'U', or
A = L  * L**T,  if UPLO = 'L',

where U is an upper triangular matrix and L is lower triangular. Periodt 🌟

Parameters

  • UPLO — UPLO is CHARACTER*1. = 'U': the upper triangle of A is stored; = 'L': the lower triangle of A is stored. It’s giving “pick a triangle” 🎀
  • N — N is INTEGER. The order of the matrix A. N >= 0.
  • AP — AP is REAL array, dimension (N*(N+1)/2). On entry, it’s the upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP like this: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. See below for further details 👀 On exit, if INFO = 0, you get the triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, in the same storage format as A. Slay 💅
  • INFO — INFO is INTEGER. = 0: successful exit ✨ < 0: if INFO = -i, the i-th argument had an illegal value 🙈 > 0: if INFO = i, the leading principal minor of order i is not positive, and the factorization could not be completed 😭

Author

  • Univ. of Tennessee
  • Univ. of California Berkeley
  • Univ. of Colorado Denver
  • NAG Ltd.

Further Details:

The packed storage scheme is illustrated by the following example when N = 4, UPLO = 'U':

Two-dimensional storage of the symmetric matrix A:

     a11 a12 a13 a14
         a22 a23 a24
             a33 a34     (aij = aji)
                 a44

Packed storage of the upper triangle of A:

AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]

Definition at line 118 of file spptrf.f.

💅 subroutine zpptrf (character uplo, integer n, complex*16, dimension( * ) ap, integer info)

ZPPTRF

Purpose:

ZPPTRF computes the Cholesky factorization of a complex Hermitian positive definite matrix A stored in packed format. Double-complex Hermitian bestie, we are obsessed 🦋

The factorization has the form

A = U**H * U,  if UPLO = 'U', or
A = L  * L**H,  if UPLO = 'L',

where U is an upper triangular matrix and L is lower triangular. Literally iconic 🌟

Parameters

  • UPLO — UPLO is CHARACTER*1. = 'U': the upper triangle of A is stored; = 'L': the lower triangle of A is stored. Pick your triangle, bestie 🎀
  • N — N is INTEGER. The order of the matrix A. N >= 0.
  • AP — AP is COMPLEX*16 array, dimension (N*(N+1)/2). On entry, it’s the upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP like this: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. See below for further details 👀 On exit, if INFO = 0, you get the triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, in the same storage format as A. Ate and left no crumbs 💅
  • INFO — INFO is INTEGER. = 0: successful exit ✨ < 0: if INFO = -i, the i-th argument had an illegal value 🙈 > 0: if INFO = i, the leading principal minor of order i is not positive definite, and the factorization could not be completed 😭

Author

  • Univ. of Tennessee
  • Univ. of California Berkeley
  • Univ. of Colorado Denver
  • NAG Ltd.

Further Details:

The packed storage scheme is illustrated by the following example when N = 4, UPLO = 'U':

Two-dimensional storage of the Hermitian matrix A:

     a11 a12 a13 a14
         a22 a23 a24
             a33 a34     (aij = conjg(aji))
                 a44

Packed storage of the upper triangle of A:

AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]

Definition at line 118 of file zpptrf.f.

👑 Author 👑

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