tptrs(3)

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version 3.12.1 · 9 versions
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✨ tptrs(3) — triangular solve ✨

okay bestie, buckle up, this is the tptrs family from the Library Functions Manual and it's literally the glow-up squad for triangular solves 💅

We've got four routines here — one per data type — and they all do the same iconic thing: solve a triangular system where A is triangular and stored in packed format. No cap.

🌸 NAME 🌸

tptrs — tptrs: triangular solve

That's it. That's the whole name. Short, sweet, main character energy 👑

🎀 SYNOPSIS 🎀

Functions

  • subroutine ctptrs (uplo, trans, diag, n, nrhs, ap, b, ldb, info) — CTPTRS
  • subroutine dtptrs (uplo, trans, diag, n, nrhs, ap, b, ldb, info) — DTPTRS
  • subroutine stptrs (uplo, trans, diag, n, nrhs, ap, b, ldb, info) — STPTRS
  • subroutine ztptrs (uplo, trans, diag, n, nrhs, ap, b, ldb, info) — ZTPTRS

Same argument list every single time, bestie. The only thing that changes is the flavour of the numbers inside. Obsessed with the consistency 🫶

🦋 Detailed Description 🦋

This page is the whole tptrs friend group: CTPTRS, DTPTRS, STPTRS and ZTPTRS. They solve triangular systems with the matrix packed columnwise into one flat array, and every one of them has the exact same parameter lineup — <italic>uplo</italic>, <italic>trans</italic>, <italic>diag</italic>, <italic>n</italic>, <italic>nrhs</italic>, <italic>ap</italic>, <italic>b</italic>, <italic>ldb</italic>, <italic>info</italic>. Periodt.

🔥 Function Documentation 🔥

⭐ subroutine ctptrs ⭐

subroutine ctptrs (character uplo, character trans, character diag, integer
    n, integer nrhs, complex, dimension( * ) ap, complex, dimension( ldb, *
    ) b, integer ldb, integer info)

CTPTRS

Purpose

okay so CTPTRS solves a triangular system of the form

A * X = B,  A**T * X = B,  or  A**H * X = B,

where A is a triangular matrix of order N stored in packed format, and B is an N-by-NRHS matrix.

🚨 lowkey important: this subroutine verifies that A is nonsingular, but callers should note that only exact singularity is detected. It is conceivable for one or more diagonal elements of A to be subnormally tiny numbers without this subroutine signalling an error. Like, it will not catch that for you 💀

If a possible loss of numerical precision due to near-singular matrices is a concern, the caller should verify that A is nonsingular within some tolerance before calling this subroutine. Fr fr, do your own vibe check first 🙈

Parameters

  • UPLO — UPLO is CHARACTER*1
    • = 'U': A is upper triangular;
    • = 'L': A is lower triangular.
  • TRANS — TRANS is CHARACTER*1. Specifies the form of the system of equations:
    • = 'N': A * X = B (No transpose)
    • = 'T': A**T * X = B (Transpose)
    • = 'C': A**H * X = B (Conjugate transpose)
  • DIAG — DIAG is CHARACTER*1
    • = 'N': A is non-unit triangular;
    • = 'U': A is unit triangular.
  • 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 upper or lower triangular matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows:
    • if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
    • if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
  • B — B is COMPLEX array, dimension (LDB,NRHS). On entry, the right hand side matrix B. On exit, if INFO = 0, the solution matrix X. it's giving transformation arc ✨
  • 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 i-th diagonal element of A is exactly zero, indicating that the matrix is singular and the solutions X have not been computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 134 of file ctptrs.f.

⭐ subroutine dtptrs ⭐

subroutine dtptrs (character uplo, character trans, character diag, integer
    n, integer nrhs, double precision, dimension( * ) ap, double precision,
    dimension( ldb, * ) b, integer ldb, integer info)

DTPTRS

Purpose

DTPTRS solves a triangular system of the form

A * X = B  or  A**T * X = B,

where A is a triangular matrix of order N stored in packed format, and B is an N-by-NRHS matrix.

🚨 same warning, bestie: this subroutine verifies that A is nonsingular, but callers should note that only exact singularity is detected. It is conceivable for one or more diagonal elements of A to be subnormally tiny numbers without this subroutine signalling an error. Sneaky little subnormal numbers, no cap 😭

If a possible loss of numerical precision due to near-singular matrices is a concern, the caller should verify that A is nonsingular within some tolerance before calling this subroutine. Do it yourself, don't make it everyone else's problem 💅

Parameters

  • UPLO — UPLO is CHARACTER*1
    • = 'U': A is upper triangular;
    • = 'L': A is lower triangular.
  • TRANS — TRANS is CHARACTER*1. Specifies the form of the system of equations:
    • = 'N': A * X = B (No transpose)
    • = 'T': A**T * X = B (Transpose)
    • = 'C': A**H * X = B (Conjugate transpose = Transpose) ← note the extra "= Transpose", she's different 💫
  • DIAG — DIAG is CHARACTER*1
    • = 'N': A is non-unit triangular;
    • = 'U': A is unit triangular.
  • 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 upper or lower triangular matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows:
    • if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
    • if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
  • B — B is DOUBLE PRECISION array, dimension (LDB,NRHS). On entry, the right hand side matrix B. On exit, if INFO = 0, 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
    • > 0: if INFO = i, the i-th diagonal element of A is exactly zero, indicating that the matrix is singular and the solutions X have not been computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 134 of file dtptrs.f.

⭐ subroutine stptrs ⭐

subroutine stptrs (character uplo, character trans, character diag, integer
    n, integer nrhs, real, dimension( * ) ap, real, dimension( ldb, * ) b,
    integer ldb, integer info)

STPTRS

Purpose

STPTRS solves a triangular system of the form

A * X = B  or  A**T * X = B,

where A is a triangular matrix of order N stored in packed format, and B is an N-by-NRHS matrix.

🚨 again for the people in the back: this subroutine verifies that A is nonsingular, but callers should note that only exact singularity is detected. It is conceivable for one or more diagonal elements of A to be subnormally tiny numbers without this subroutine signalling an error. it's giving "technically correct but numerically stressful" 💀

If a possible loss of numerical precision due to near-singular matrices is a concern, the caller should verify that A is nonsingular within some tolerance before calling this subroutine. Your tolerance, your problem, bestie 🫶

Parameters

  • UPLO — UPLO is CHARACTER*1
    • = 'U': A is upper triangular;
    • = 'L': A is lower triangular.
  • TRANS — TRANS is CHARACTER*1. Specifies the form of the system of equations:
    • = 'N': A * X = B (No transpose)
    • = 'T': A**T * X = B (Transpose)
    • = 'C': A**H * X = B (Conjugate transpose = Transpose)
  • DIAG — DIAG is CHARACTER*1
    • = 'N': A is non-unit triangular;
    • = 'U': A is unit triangular.
  • 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 upper or lower triangular matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows:
    • if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
    • if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
  • B — B is REAL array, dimension (LDB,NRHS). On entry, the right hand side matrix B. On exit, if INFO = 0, 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
    • > 0: if INFO = i, the i-th diagonal element of A is exactly zero, indicating that the matrix is singular and the solutions X have not been computed.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 134 of file stptrs.f.

⭐ subroutine ztptrs ⭐

subroutine ztptrs (character uplo, character trans, character diag, integer
    n, integer nrhs, complex*16, dimension( * ) ap, complex*16, dimension(
    ldb, * ) b, integer ldb, integer info)

ZTPTRS

Purpose

✨ and this is where part 1 wraps — ZTPTRS's purpose is coming at you in part 2, stay tuned bestie ✨

✨ Parameters ✨

Okay bestie, here's the tea on every single argument — no skipping, no cap. 💅

  • UPLO — CHARACTER*1. This one tells us which triangle of A we're working with:
    • = 'U': A is upper triangular;
    • = 'L': A is lower triangular.
  • TRANS — CHARACTER*1. Specifies the form of the system of equations, iykyk:
    • = 'N': A * X = B (No transpose)
    • = 'T': A**T * X = B (Transpose)
    • = 'C': A**H * X = B (Conjugate transpose)
  • DIAG — CHARACTER*1. Are we dealing with a unit triangular matrix or not? That's the question:
    • = 'N': A is non-unit triangular;
    • = 'U': A is unit triangular.
  • N — INTEGER. The order of the matrix A. The vibe check here is N >= 0.
  • NRHS — INTEGER. The number of right hand sides, i.e., the number of columns of the matrix B. Gotta have NRHS >= 0.
  • AP — COMPLEX*16 array, dimension (N*(N+1)/2). The upper or lower triangular matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows:
    • if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
    • if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
  • B — COMPLEX*16 array, dimension (LDB,NRHS). On entry, the right hand side matrix B. On exit, if INFO = 0, the solution matrix X. It's giving glow-up. ✨
  • LDB — INTEGER. The leading dimension of the array B. Respect the constraint: LDB >= max(1,N).
  • INFO — INTEGER. The receipts:
    • = 0: successful exit
    • < 0: if INFO = -i, the i-th argument had an illegal value
    • > 0: if INFO = i, the i-th diagonal element of A is exactly zero, indicating that the matrix is singular and the solutions X have not been computed. 💀

👑 Author 👑

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

Definition at line 134 of file ztptrs.f.

Author: Generated automatically by Doxygen for LAPACK from the source code.

That's the whole page, bestie! 🫶 This lil' icon is from LAPACK, Version 3.12.0, and it's tptrs(3) — go slay some triangular systems. 🌈💖

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