SRC/sptsv.f(3)

💖 NAME 💖

Okay so welcome to SRC/sptsv.f(3), bestie — this is the Library Functions Manual page for SRC/sptsv.f. That’s the whole name. No cap, it’s a Fortran source page for an LAPACK routine, and it’s lowkey iconic. 🫶

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✨ SYNOPSIS ✨

🫶 Functions/Subroutines 🫶

• subroutine sptsv (n, nrhs, d, e, b, ldb, info) — the main character. SPTSV computes the solution to system of linear equations A * X = B for PT matrices. Periodt. 💅

Here’s the synopsis exactly as it appears:

       subroutine sptsv (n, nrhs, d, e, b, ldb, info)
            SPTSV computes the solution to system of linear equations A * X = B
           for PT matrices

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🦋 Function/Subroutine Documentation 🦋

Here’s the full signature with types, exactly as written:

   subroutine sptsv (integer n, integer nrhs, real, dimension( * ) d, real,
       dimension( * ) e, real, dimension( ldb, * ) b, integer ldb, integer
       info)
        SPTSV computes the solution to system of linear equations A * X = B for
       PT matrices

And yes, the source marks the purpose and parameter blurbs with !> comment prefixes — Doxygen’s little emo bangs — but here’s the clean tea. 🍓

🎀 Purpose 🎀

Okay so SPTSV computes the solution to a real system of linear equations A*X = B, where A is an N-by-N symmetric positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices.

A is factored as A = L*D*L**T, and the factored form of A is then used to solve the system of equations. That’s the whole plot, and it ate. 🔥

🌸 Parameters 🌸

Each parameter blurb in the original is also !>-prefixed; this is the un-styled version, bestie.

N

• N is INTEGER — the order of the matrix A. N >= 0.

NRHS

• NRHS is INTEGER — the number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 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 factorization A = L*D*L**T.

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.)

B

• B is REAL array, dimension (LDB,NRHS) — on entry, the N-by-NRHS right hand side matrix B. On exit, if INFO = 0, the N-by-NRHS solution matrix X.

LDB

• LDB is INTEGER — the leading dimension of the array B. LDB >= max(1,N).

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 solution has not been computed. The factorization has not been completed unless i = N.

Important caveat tea: if INFO comes back positive, the solution has not been computed, and the factorization has not been completed unless i = N. No cap, that’s a real warning. 💀

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👑 Author 👑

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

Definition at line 113 of file sptsv.f.

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🤖 Author (generated) 🤖

Generated automatically by Doxygen for LAPACK from the source code.

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💜 Cute little sign-off: this page is from LAPACK, Version 3.12.0, and it’s SRC/sptsv.f(3). The footer is giving source/version energy, no date drama, just vibes. Slay, bestie. 🎀✨