ZPTSVX(3)

💖 ZPTSVX(3) 💖

okay so bestie, welcome to the LAPACK Library Functions Manual — this is the zptsvx.f(3) page, and it’s literally about solving a complex Hermitian positive definite tridiagonal system with error bounds and a condition estimate. Linear algebra main character energy, fr fr. 🫶

---

✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/zptsvx.f — that’s the source path, bestie. That’s the name this page is filed under, no cap.

---

🌸 SYNOPSIS 🌸

Functions/Subroutines

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

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

---

🦋 Function/Subroutine Documentation 🦋

subroutine ZPTSVX (character fact, integer n, integer nrhs, double
    precision, dimension( * ) d, complex*16, dimension( * ) e, double
    precision, dimension( * ) df, complex*16, dimension( * ) ef, complex*16,
    dimension( ldb, * ) b, integer ldb, complex*16, dimension( ldx, * ) x,
    integer ldx, double precision rcond, double precision, dimension( * )
    ferr, double precision, dimension( * ) berr, complex*16, dimension( * )
    work, double precision, dimension( * ) rwork, integer info)

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

💅 Purpose 💅

ZPTSVX uses the factorization A = L*D*L**H to compute the solution to a complex system of linear equations A*X = B, where A is an N-by-N Hermitian 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. Obsessed, honestly. ✨

🌈 Description 🌈

The following steps are performed:

1. If FACT = 'N', the matrix A is factored as A = L*D*L**H, where L is a unit lower bidiagonal matrix and D is diagonal. The factorization can also be regarded as having the form A = U**H*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.
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.

🎀 Parameters 🎀

• FACT — FACT is CHARACTER*1. It specifies whether or not the factored form of the matrix A is 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 — 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 matrices B and X. NRHS >= 0.
• D — D is DOUBLE PRECISION array, dimension (N). The n diagonal elements of the tridiagonal matrix A.
• E — E is COMPLEX*16 array, dimension (N-1). The (n-1) subdiagonal elements of the tridiagonal matrix A.
• DF — DF is DOUBLE PRECISION 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**H 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**H factorization of A.
• EF — EF is COMPLEX*16 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**H 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**H factorization of A.
• B — B is COMPLEX*16 array, dimension (LDB,NRHS). The N-by-NRHS right hand side matrix B.
• LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• X — X is COMPLEX*16 array, dimension (LDX,NRHS). If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X.
• LDX — LDX is INTEGER. The leading dimension of the array X. LDX >= max(1,N).
• RCOND — RCOND is DOUBLE PRECISION. 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 — FERR is DOUBLE PRECISION 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 — BERR is DOUBLE PRECISION 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 — WORK is COMPLEX*16 array, dimension (N).
• RWORK — RWORK is DOUBLE PRECISION array, dimension (N).
• INFO — INFO is 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.

👑 Author 👑

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

Definition at line 232 of file zptsvx.f.

---

🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code. It’s giving auto-generated but make it cute. 💅

---

that’s the whole page, bestie 🫶 — signed off by LAPACK Version 3.12.0 and the page path /home/abui...RC/zptsvx.f(3). mwah 💋