SRC/ssptrf.f(3)

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version 3.12.1 · 7 versions
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💜 SRC/ssptrf.f — from the Library Functions Manual, bestie ✨

okay so picture this: you're deep in LAPACK land (the Library Functions Manual section, obviously) and you meet SRC/ssptrf.f. she's a Fortran girlie and she's about to factor a real symmetric matrix for you. no cap. let's get into it 🫶

✨ NAME ✨

SRC/ssptrf.f — that's her, that's the file 💅

🦋 SYNOPSIS 🦋

Functions/Subroutines

  • subroutine ssptrf (uplo, n, ap, ipiv, info) — honestly just read it, the whole vibe is right there 👑

🌸 Function/Subroutine Documentation 🌸

subroutine ssptrf (character uplo, integer n, real, dimension( * ) ap, integer, dimension( * ) ipiv, integer info)

SSPTRF — say it with your chest 💖

🎀 Purpose 🎀

!> !> SSPTRF computes the factorization of a real symmetric matrix A stored !> in packed format using the Bunch-Kaufman diagonal pivoting method: !>
!>    A = U*D*U**T  or  A = L*D*L**T
!> !> where U (or L) is a product of permutation and unit upper (lower) !> triangular matrices, and D is symmetric and block diagonal with !> 1-by-1 and 2-by-2 diagonal blocks. !>

⭐ Parameters ⭐

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. !>

AP

!> AP is REAL array, dimension (N*(N+1)/2) !> On entry, 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 as follows: !> 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. !> !> On exit, the block diagonal matrix D and the multipliers used !> to obtain the factor U or L, stored as a packed triangular !> matrix overwriting A (see below for further details). !>

IPIV

!> IPIV is INTEGER array, dimension (N) !> Details of the interchanges and the block structure of D. !> If IPIV(k) > 0, then rows and columns k and IPIV(k) were !> interchanged and D(k,k) is a 1-by-1 diagonal block. !> If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and !> columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) !> is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = !> IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were !> interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. !>

INFO

!> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> > 0: if INFO = i, D(i,i) is exactly zero. The factorization !> has been completed, but the block diagonal matrix D is !> exactly singular, and division by zero will occur if it !> is used to solve a system of equations. !>
🚨 heads up bestie: that < 0 case means you fed her a bad argument (the i-th one, specifically), and the > 0 case means D(i,i) is exactly zero — the factorization finished, but D is exactly singular and you will get division by zero if you try to solve a system with it. not her fault, she told you 💀

👑 Author 👑

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

the whole squad, honestly 🫶

🌈 Further Details:

!> !> 5-96 - Based on modifications by J. Lewis, Boeing Computer Services !> Company !> !> If UPLO = 'U', then A = U*D*U**T, where !> U = P(n)*U(n)* ... *P(k)U(k)* ..., !> i.e., U is a product of terms P(k)*U(k), where k decreases from n to !> 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 !> and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as !> defined by IPIV(k), and U(k) is a unit upper triangular matrix, such !> that if the diagonal block D(k) is of order s (s = 1 or 2), then !> !> ( I v 0 ) k-s !> U(k) = ( 0 I 0 ) s !> ( 0 0 I ) n-k !> k-s s n-k !> !> If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k). !> If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), !> and A(k,k), and v overwrites A(1:k-2,k-1:k). !> !> If UPLO = 'L', then A = L*D*L**T, where !> L = P(1)*L(1)* ... *P(k)*L(k)* ..., !> i.e., L is a product of terms P(k)*L(k), where k increases from 1 to !> n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 !> and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as !> defined by IPIV(k), and L(k) is a unit lower triangular matrix, such !> that if the diagonal block D(k) is of order s (s = 1 or 2), then !> !> ( I 0 0 ) k-1 !> L(k) = ( 0 I 0 ) s !> ( 0 v I ) n-k-s+1 !> k-1 s n-k-s+1 !> !> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k). !> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k), !> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1). !>

like, the way she just lays out the whole U and L decomposition with the block diagrams? ate. no crumbs. 📐✨

Definition at line 156 of file ssptrf.f. — she's literally on line 156, go say hi 🦋

💌 Author (the meta one) 💌

Generated automatically by Doxygen for LAPACK from the source code.

okay that's the whole page, bestie — every flag, every formula, every warning, not one detail dropped 💅

and for the cute sign-off: this whole thing is brought to you by LAPACK, Version 3.12.0, straight out of SRC/ssptrf.f(3). mwah 💖🎀✨

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