SPTSVX(3)

💖 SPTSVX(3) — tridiagonal solver, but make it fashion 💅

okay so this page lives in the Library Functions Manual, and it’s all about /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/sptsvx.f. yes, that whole path is literally the NAME section’s main character. no cap.

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🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/sptsvx.f — that’s the file, bestie. that’s the name. iconic behavior.

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✨ SYNOPSIS ✨

🫶 Functions/Subroutines

subroutine SPTSVX (fact, n, nrhs, d, e, df, ef, b, ldb, x, ldx, rcond,
    ferr, berr, work, info)

SPTSVX computes the solution to system of linear equations A * X = B for PT matrices. periodt.

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🦋 Function/Subroutine Documentation 🦋

subroutine SPTSVX (character fact, integer n, integer nrhs, real, dimension(
* ) d, real, dimension( * ) e, real, dimension( * ) df, real, dimension(
* ) ef, real, dimension( ldb, * ) b, integer ldb, real, dimension( ldx,
* ) x, integer ldx, real rcond, real, dimension( * ) ferr, real,
dimension( * ) berr, real, dimension( * ) work, integer info)

SPTSVX computes the solution to system of linear equations A * X = B for PT matrices. we love a consistent queen.

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💜 Purpose 💜

okay so SPTSVX uses the factorization A = L*D*L**T to compute 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.

error bounds on the solution and a condition estimate are also provided. fancy, but make it math.

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🌈 Description 🌈

the following steps are performed, in this exact order, no skipping:

1. if FACT = 'N', the matrix A is factored as A = L*D*L**T, where L is a unit lower bidiagonal matrix and D is diagonal. the factorization can also be regarded as having the form A = U**T*D*U.
2. if the leading principal minor of order i is not positive, then the routine returns with INFO = i. otherwise, the factored form of A is used to estimate the condition number of the matrix A. if the reciprocal of the condition number is less than machine precision, INFO = N+1 is returned as a warning, but the routine still goes on to solve for X and compute error bounds as described below. she warns you but she keeps going. 💅
3. the system of equations is solved for X using the factored form of A.
4. iterative refinement is applied to improve the computed solution matrix and calculate error bounds and backward error estimates for it.

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🎀 Parameters 🎀

• FACT — CHARACTER*1. specifies whether or not the factored form of A has been supplied on entry.
  • = 'F': on entry, DF and EF contain the factored form of A. D, E, DF, and EF will not be modified.
  • = 'N': the matrix A will be copied to DF and EF and factored.
• N — INTEGER. the order of the matrix A. N >= 0.
• NRHS — INTEGER. the number of right hand sides, i.e., the number of columns of the matrices B and X. NRHS >= 0.
• D — REAL array, dimension (N). the n diagonal elements of the tridiagonal matrix A.
• E — REAL array, dimension (N-1). the (n-1) subdiagonal elements of the tridiagonal matrix A.
• DF — REAL array, dimension (N). if FACT = 'F', then DF is an input argument and on entry contains the n diagonal elements of the diagonal matrix D from the L*D*L**T factorization of A. if FACT = 'N', then DF is an output argument and on exit contains the n diagonal elements of the diagonal matrix D from the L*D*L**T factorization of A.
• EF — REAL array, dimension (N-1). if FACT = 'F', then EF is an input argument and on entry contains the (n-1) subdiagonal elements of the unit bidiagonal factor L from the L*D*L**T factorization of A. if FACT = 'N', then EF is an output argument and on exit contains the (n-1) subdiagonal elements of the unit bidiagonal factor L from the L*D*L**T factorization of A.
• B — REAL array, dimension (LDB,NRHS). the N-by-NRHS right hand side matrix B.
• LDB — INTEGER. the leading dimension of the array B. LDB >= max(1,N).
• X — REAL array, dimension (LDX,NRHS). if INFO = 0 of INFO = N+1 (that’s literally what it says 😭), the N-by-NRHS solution matrix X.
• LDX — INTEGER. the leading dimension of the array X. LDX >= max(1,N).
• RCOND — REAL. the reciprocal condition number of the matrix A. if RCOND is less than the machine precision (in particular, if RCOND = 0), the matrix is singular to working precision. this condition is indicated by a return code of INFO > 0.
• FERR — REAL array, dimension (NRHS). the forward error bound for each solution vector X(j) (the j-th column of the solution matrix X). if XTRUE is the true solution corresponding to X(j), FERR(j) is an estimated upper bound for the magnitude of the largest element in (X(j) - XTRUE) divided by the magnitude of the largest element in X(j).
• BERR — REAL array, dimension (NRHS). the componentwise relative backward error of each solution vector X(j) (i.e., the smallest relative change in any element of A or B that makes X(j) an exact solution).
• WORK — REAL array, dimension (2*N).
• INFO — 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 leading principal minor of order i of A is not positive, so the factorization could not be completed, and the solution has not been computed. RCOND = 0 is returned.
    • = N+1: U is nonsingular, but RCOND is less than machine precision, meaning that the matrix is singular to working precision. nevertheless, the solution and error bounds are computed because there are a number of situations where the computed solution can be more accurate than the value of RCOND would suggest.

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👑 Author 👑

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

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🧚 Definition at line 🧚

Definition at line 226 of file sptsvx.f.

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⭐ Author (generated edition) ⭐

generated automatically by Doxygen for LAPACK from the source code. she’s meta like that.

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and that’s the whole vibe, bestie — LAPACK Version 3.12.0, footer path /home/abui...RC/sptsvx.f(3), generated automatically by Doxygen for LAPACK from the source code. mwah 💋✨