ptsv(3)

📦

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💖 ptsv(3) — Library Functions Manual 💖

okay so bestie, this is the ptsv(3) page from the Library Functions Manual — it’s giving “factor and solve,” and we’re keeping every deet. 💅

✨ NAME ✨

ptsv - ptsv: factor and solve 🎀

✨ SYNOPSIS ✨

🎀 Functions 🎀

subroutine cptsv (n, nrhs, d, e, b, ldb, info) — CPTSV computes the solution to system of linear equations A * X = B for PT matrices. 💖
subroutine dptsv (n, nrhs, d, e, b, ldb, info) — DPTSV computes the solution to system of linear equations A * X = B for PT matrices. ✨
subroutine sptsv (n, nrhs, d, e, b, ldb, info) — SPTSV computes the solution to system of linear equations A * X = B for PT matrices. 🦋
subroutine zptsv (n, nrhs, d, e, b, ldb, info) — ZPTSV computes the solution to system of linear equations A * X = B for PT matrices. 🌸

✨ Detailed Description ✨

(no extra details listed here in this part 💜)

🫶 FUNCTION DOCUMENTATION 🫶

okay bestie, this is the part where we actually meet the four routines. they're quadruplets, basically — same job, different precision. s and d do the real symmetric thing, c and z do the complex Hermitian thing. slay 💅

subroutine `cptsv`

subroutine cptsv (integer n, integer nrhs, real, dimension( * ) d, complex,
    dimension( * ) e, complex, dimension( ldb, * ) b, integer ldb, integer
    info)

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

💖 Purpose

so like, CPTSV computes the solution to a complex system of linear equations A*X = B, okay? where A is an N-by-N Hermitian positive definite tridiagonal matrix, and X and B are N-by-NRHS matrices. yes, all of that. iykyk.

A is factored as A = L*D*L**H, and the factored form of A is then used to solve the system of equations. iconic behaviour honestly 👑

🎀 Parameters

N — N is INTEGER. the order of the matrix A. N >= 0. no cap, it can be zero, she's flexible 💅
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**H. glow-up moment fr fr ✨
E — E is COMPLEX 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**H factorization of A. E can also be regarded as the superdiagonal of the unit bidiagonal factor U from the U**H*D*U factorization of A. she contains multitudes 🦋
B — B is COMPLEX 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. literally the whole point of the function, main character energy 👑
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. 💀 so yeah, that's a real "not me breaking linear algebra" moment

🌸 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 114 of file cptsv.f.

subroutine `dptsv`

subroutine dptsv (integer n, integer nrhs, double precision, dimension( * )
    d, double precision, dimension( * ) e, double precision, dimension( ldb,
    * ) b, integer ldb, integer info)

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

💖 Purpose

DPTSV 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. same vibe, double the precision, zero notes 💅

A is factored as A = L*D*L**T, and the factored form of A is then used to solve the system of equations. slay 🔥

🎀 Parameters

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 DOUBLE PRECISION 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 DOUBLE PRECISION 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.) yes the parentheses are canon, i don't make the rules 🫶
B — B is DOUBLE PRECISION 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. she solved it 💖
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. so close yet so far 😭

🌸 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 113 of file dptsv.f.

subroutine `sptsv`

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 ✨

💖 Purpose

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. the single-precision sister of DPTSV, same energy, smaller floats 🎀

A is factored as A = L*D*L**T, and the factored form of A is then used to solve the system of equations. ate and left no crumbs 🔥

🎀 Parameters

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.) same parenthetical, still real, still iconic 🦋
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. 💀

🌸 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 113 of file sptsv.f.

subroutine `zptsv`

subroutine zptsv (integer n, integer nrhs, double precision, dimension( * )
    d, complex*16, dimension( * ) e, complex*16, dimension( ldb, * ) b,
    integer ldb, integer info)

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

💖 Purpose

ZPTSV computes 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. double precision complex, aka the final boss of the tridiagonal family 👑

A is factored as A = L*D*L**H, and the factored form of A is then used to solve the system of equations. periodt. 🎀

🎀 Parameters

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 DOUBLE PRECISION 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**H. note that D stays real even though everything around her is complex — she's the grounded one 💅
E — E is COMPLEX*16 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**H factorization of A. E can also be regarded as the superdiagonal of the unit bidiagonal factor U from the U**H*D*U factorization of A.
B — B is COMPLEX*16 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. bestie she solved it in complex double 🫶
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. screaming, crying, throwing up 😭

🌸 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 114 of file zptsv.f.

🌟 Author 🌟

generated automatically by Doxygen for LAPACK from the source code. yes, a robot wrote this and we're all just living in its house 🤖💖

okay that's the whole page bestie, go forth and solve your tridiagonal systems 💅✨ — this little doc-drop is from LAPACK, Version 3.12.0, filed under ptsv(3). mwah 🫶🎀

📦 where this page comes from

arch rolling: lapack-doc 3.12.1-2 · custom
💖 girlified by deepseek-ai/DeepSeek-V4.1-Flash-1017 on 2026-11-04: a language model's rewrite of the original, under its terms