hptrs(3)

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version 3.12.1 · 9 versions
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💖 hptrs(3) 💖

(Library Functions Manual — yes bestie, we're in the packed-solve era 💅)

✨ NAME ✨

hptrs — {hp,sp}trs: triangular solve using factor 🎀

🌸 SYNOPSIS 🌸

🌟 Functions 🌟

  • subroutine chptrs (uplo, n, nrhs, ap, ipiv, b, ldb, info) — CHPTRS
  • subroutine csptrs (uplo, n, nrhs, ap, ipiv, b, ldb, info) — CSPTRS
  • subroutine dsptrs (uplo, n, nrhs, ap, ipiv, b, ldb, info) — DSPTRS
  • subroutine ssptrs (uplo, n, nrhs, ap, ipiv, b, ldb, info) — SSPTRS
  • subroutine zhptrs (uplo, n, nrhs, ap, ipiv, b, ldb, info) — ZHPTRS
  • subroutine zsptrs (uplo, n, nrhs, ap, ipiv, b, ldb, info) — ZSPTRS

🦋 Detailed Description 🦋

Okay so this page is the glow-up for the packed triangular solves. The full function-by-function tea is right below 👇

👑 Function Documentation 👑

🎀 chptrs 🎀

subroutine chptrs (character uplo, integer n, integer nrhs, complex, dimension( * ) ap, integer, dimension( * ) ipiv, complex, dimension( ldb, * ) b, integer ldb, integer info)

CHPTRS

💫 Purpose

CHPTRS solves a system of linear equations A*X = B with a complex Hermitian matrix A stored in packed format using the factorization A = U*D*U**H or A = L*D*L**H computed by CHPTRF. 💖

🧚 Parameters

  • UPLO — UPLO is CHARACTER*1. Specifies whether the details of the factorization are stored as an upper or lower triangular matrix. = 'U': Upper triangular, form is A = U*D*U**H; = 'L': Lower triangular, form is A = L*D*L**H.
  • 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.
  • AP — AP is COMPLEX array, dimension (N*(N+1)/2). The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by CHPTRF, stored as a packed triangular matrix.
  • IPIV — IPIV is INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by CHPTRF.
  • B — B is COMPLEX array, dimension (LDB,NRHS). On entry, the right hand side matrix B. On exit, the 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.

🌈 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 114 of file chptrs.f.

🎀 csptrs 🎀

subroutine csptrs (character uplo, integer n, integer nrhs, complex, dimension( * ) ap, integer, dimension( * ) ipiv, complex, dimension( ldb, * ) b, integer ldb, integer info)

CSPTRS

💫 Purpose

CSPTRS solves a system of linear equations A*X = B with a complex symmetric matrix A stored in packed format using the factorization A = U*D*U**T or A = L*D*L**T computed by CSPTRF. 💖

🧚 Parameters

  • UPLO — UPLO is CHARACTER*1. Specifies whether the details of the factorization are stored as an upper or lower triangular matrix. = 'U': Upper triangular, form is A = U*D*U**T; = 'L': Lower triangular, form is A = L*D*L**T.
  • 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.
  • AP — AP is COMPLEX array, dimension (N*(N+1)/2). The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by CSPTRF, stored as a packed triangular matrix.
  • IPIV — IPIV is INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by CSPTRF.
  • B — B is COMPLEX array, dimension (LDB,NRHS). On entry, the right hand side matrix B. On exit, the 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.

🌈 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 114 of file csptrs.f.

🎀 dsptrs 🎀

subroutine dsptrs (character uplo, integer n, integer nrhs, double precision, dimension( * ) ap, integer, dimension( * ) ipiv, double precision, dimension( ldb, * ) b, integer ldb, integer info)

DSPTRS

💫 Purpose

DSPTRS solves a system of linear equations A*X = B with a real symmetric matrix A stored in packed format using the factorization A = U*D*U**T or A = L*D*L**T computed by DSPTRF. 💖

🧚 Parameters

  • UPLO — UPLO is CHARACTER*1. Specifies whether the details of the factorization are stored as an upper or lower triangular matrix. = 'U': Upper triangular, form is A = U*D*U**T; = 'L': Lower triangular, form is A = L*D*L**T.
  • 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.
  • AP — AP is DOUBLE PRECISION array, dimension (N*(N+1)/2). The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by DSPTRF, stored as a packed triangular matrix.
  • IPIV — IPIV is INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by DSPTRF.
  • B — B is DOUBLE PRECISION array, dimension (LDB,NRHS). On entry, the right hand side matrix B. On exit, the 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.

🌈 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 114 of file dsptrs.f.

🎀 ssptrs 🎀

subroutine ssptrs (character uplo, integer n, integer nrhs, real, dimension( * ) ap, integer, dimension( * ) ipiv, real, dimension( ldb, * ) b, integer ldb, integer info)

SSPTRS

💫 Purpose

SSPTRS solves a system of linear equations A*X = B with a real symmetric matrix A stored in packed format using the factorization A = U*D*U**T or A = L*D*L**T computed by SSPTRF. 💖

🧚 Parameters

  • UPLO — UPLO is CHARACTER*1. Specifies whether the details of the factorization are stored as an upper or lower triangular matrix. = 'U': Upper triangular, form is A = U*D*U**T; = 'L': Lower triangular, form is A = L*D*L**T.
  • 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.
  • AP — AP is REAL array, dimension (N*(N+1)/2). The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by SSPTRF, stored as a packed triangular matrix.
  • IPIV — IPIV is INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by SSPTRF.
  • B — B is REAL array, dimension (LDB,NRHS). On entry, the right hand side matrix B. On exit, the 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.

🌈 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 114 of file ssptrs.f.

🎀 zhptrs 🎀

subroutine zhptrs (character uplo, integer n, integer nrhs, complex*16, dimension( * ) ap, integer, dimension( * ) ipiv, complex*16, dimension( ldb, * ) b, integer ldb, integer info)

ZHPTRS

💫 Purpose

ZHPTRS solves a system of linear equations A*X = B with a complex Hermitian matrix A stored in packed format using the factorization A = U*D*U**H or A = L*D*L**H computed by ZHPTRF. 💖

🧚 Parameters

  • UPLO — UPLO is CHARACTER*1. Specifies whether the details of the factorization are stored as an upper or lower triangular matrix. = 'U': Upper triangular, form is A = U*D*U**H; = 'L': Lower triangular, form is A = L*D*L**H.
  • 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.
  • AP —

💅 the rest of the zhptrs params (yes bestie we're still going, hydrate)

  • AP — COMPLEX*16 array, dimension (N*(N+1)/2). This is where the block diagonal matrix D lives, plus the multipliers you used to get the factor U or L, exactly as ZHPTRF computed them, all squished into a packed triangular matrix. It's giving "everything in one bag" energy 👜
  • IPIV — INTEGER array, dimension (N). The receipts for the interchanges and the block structure of D, as determined by ZHPTRF. iykyk 🔍
  • B — COMPLEX*16 array, dimension (LDB,NRHS). On entry: the right hand side matrix B. On exit: plot twist, it's the solution matrix X 😭✨
  • LDB — INTEGER. The leading dimension of the array B. Constraint era: LDB >= max(1,N). Respect it or the routine is gonna be so disappointed in you 💀
  • INFO — INTEGER. The vibe check at the end:
    • = 0: successful exit, slay 🎉
    • < 0: if INFO = -i, the i-th argument had an illegal value — so like, one of your args was Not It 🙈

Author — Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd. (the whole academic squad, respectfully 🫶)

Definition at line 114 of file zhptrs.f. — yes, that exact line, no cap.

🌈 zsptrs (ZSPTRS) — the symmetric sibling 🌈

Okay so bestie, now we pivot to zsptrs, and the signature is a whole meal:

subroutine zsptrs (character uplo, integer n, integer nrhs, complex*16,
    dimension( * ) ap, integer, dimension( * ) ipiv, complex*16, dimension(
    ldb, * ) b, integer ldb, integer info)

✨ Purpose ✨

ZSPTRS solves a system of linear equations A*X = B with a complex symmetric matrix A stored in packed format, using the factorization A = U*D*U**T or A = L*D*L**T computed by ZSPTRF. Notice it's **T not **H — she's symmetric, not Hermitian, and she knows it 💅

🎀 Parameters 🎀

  • UPLO — CHARACTER*1. Tells us whether the details of the factorization are stored as an upper or lower triangular matrix.
    • = 'U': Upper triangular, form is A = U*D*U**T
    • = 'L': Lower triangular, form is A = L*D*L**T
  • N — INTEGER. The order of the matrix A. N >= 0. Zero is valid bestie, she's inclusive 🫶
  • NRHS — INTEGER. The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. Same energy, also inclusive.
  • AP — COMPLEX*16 array, dimension (N*(N+1)/2). Again: the block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by ZSPTRF, stored as a packed triangular matrix. Packed! Iconic behavior ✨
  • IPIV — INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by ZSPTRF. The lore 🗂️
  • B — COMPLEX*16 array, dimension (LDB,NRHS). On entry, the right hand side matrix B. On exit, the solution matrix X. Same glow-up as before, main character transformation 😌
  • LDB — INTEGER. The leading dimension of the array B. LDB >= max(1,N). Non-negotiable, fr fr.
  • INFO — INTEGER. The final verdict:
    • = 0: successful exit 🔥
    • < 0: if INFO = -i, the i-th argument had an illegal value. Somebody's getting read to filth 💀

Author — Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd. (same iconic four, we love consistency 💜)

Definition at line 114 of file zsptrs.f. — line 114 hive rise up ⭐

One lil' note before you go: a bad INFO < 0 isn't a scandal, it literally just points at which argument was illegal — check the index i and go fix that arg, bestie. No panic spiraling needed 🧚

and that's the whole page, mwah 💖

Author: Generated automatically by Doxygen for LAPACK from the source code. (yes, the doc wrote itself, queen behavior 👑)

Sign-off: This absolute gem is LAPACK, Version 3.12.0, and you're reading the hptrs(3) page — go forth and solve your packed systems, you've got this 🦋🌸

📦 where this page comes from