trtrs(3)

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version 3.12.1 · 9 versions
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✨ trtrs(3) ✨ — the LAPACK triangular-solve girlies (Library Functions Manual)

okay so bestie. welcome to trtrs, the family of routines that solve triangular systems. it's giving "i have a triangle, i have a right-hand side, and i need the X". this is part 1 of the page so buckle up, we're going through every single routine and every single parameter, no skips, no cap 💅

🎀 NAME 🎀

trtrs — trtrs: triangular solve

🦋 SYNOPSIS 🦋

🌸 Functions 🌸

  • subroutine ctrtrs (uplo, trans, diag, n, nrhs, a, lda, b, ldb, info) — CTRTRS
  • subroutine dtrtrs (uplo, trans, diag, n, nrhs, a, lda, b, ldb, info) — DTRTRS
  • subroutine strtrs (uplo, trans, diag, n, nrhs, a, lda, b, ldb, info) — STRTRS
  • subroutine ztrtrs (uplo, trans, diag, n, nrhs, a, lda, b, ldb, info) — ZTRTRS

🌈 Detailed Description 🌈

yeah so there's not really a big intro blurb here, the docs go straight into the function documentation. iconic behaviour honestly, she doesn't waste your time 💅

👑 Function Documentation 👑

🧚 ctrtrs — CTRTRS 🧚

subroutine ctrtrs (character uplo, character trans, character diag, integer
n, integer nrhs, complex, dimension( lda, * ) a, integer lda, complex,
dimension( ldb, * ) b, integer ldb, integer info)

💖 Purpose

so CTRTRS 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, and B is an N-by-NRHS matrix.

ngl this next bit matters: 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 😭

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. like, do the vibe check yourself 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.
  • A — A is COMPLEX array, dimension (LDA,N), the triangular matrix A. if UPLO = 'U', the leading N-by-N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. if UPLO = 'L', the leading N-by-N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. if DIAG = 'U', the diagonal elements of A are also not referenced and are assumed to be 1.
  • LDA — LDA is INTEGER, the leading dimension of the array A. LDA >= max(1,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. ✨
  • 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 144 of file ctrtrs.f.

🦋 dtrtrs — DTRTRS 🦋

subroutine dtrtrs (character uplo, character trans, character diag, integer
n, integer nrhs, double precision, dimension( lda, * ) a, integer lda,
double precision, dimension( ldb, * ) b, integer ldb, integer info)

💖 Purpose

DTRTRS solves a triangular system of the form

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

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

same disclaimer, 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 😭

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. periodt.

🌟 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.
  • A — A is DOUBLE PRECISION array, dimension (LDA,N), the triangular matrix A. if UPLO = 'U', the leading N-by-N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. if UPLO = 'L', the leading N-by-N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. if DIAG = 'U', the diagonal elements of A are also not referenced and are assumed to be 1.
  • LDA — LDA is INTEGER, the leading dimension of the array A. LDA >= max(1,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 144 of file dtrtrs.f.

🌸 strtrs — STRTRS 🌸

subroutine strtrs (character uplo, character trans, character diag, integer
n, integer nrhs, real, dimension( lda, * ) a, integer lda, real,
dimension( ldb, * ) b, integer ldb, integer info)

💖 Purpose

STRTRS solves a triangular system of the form

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

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

okay so this is the single-precision one and the caveat is still the same: 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 😭

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. iykyk 🫶

🌟 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.
  • A — A is REAL array, dimension (LDA,N), the triangular matrix A. if UPLO = 'U', the leading N-by-N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. if UPLO = 'L', the leading N-by-N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. if DIAG = 'U', the diagonal elements of A are also not referenced and are assumed to be 1.
  • LDA — LDA is INTEGER, the leading dimension of the array A. LDA >= max(1,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 — 🫶 hold that thought, INFO keeps going in part 2
  • INFO is INTEGER — the final vibe check:
    • = 0: successful exit, we slayed ✨
    • < 0: if INFO = -i, the i-th argument had an illegal value, so something you passed was lowkey not it 🙈
    • > 0: if INFO = i, the i-th diagonal element of A is exactly zero — that means the matrix is singular and the solutions X have not been computed, so no results for you 💀

Author

Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd. — the absolute icons who wrote this 👑

Definition

Definition at line 144 of file strtrs.f.

💅 subroutine ztrtrs (ZTRTRS)

subroutine ztrtrs (character uplo, character trans, character diag, integer
    n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda,
    complex*16, dimension( ldb, * ) b, integer ldb, integer info)

ZTRTRS

✨ Purpose ✨

Okay so ZTRTRS 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, and B is an N-by-NRHS matrix. Slay.

This subroutine verifies that A is nonsingular, but bestie, listen: 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. So like, it's not a full vibe check on near-singularity.

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. No cap, that's on you.

Parameters

  • UPLO is CHARACTER*1 — tells us the triangular vibe:
    • = 'U': A is upper triangular;
    • = 'L': A is lower triangular.
  • 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 is CHARACTER*1 — unit or non-unit diagonal:
    • = 'N': A is non-unit triangular;
    • = 'U': A is unit triangular.
  • N is INTEGER — the order of the matrix A. N >= 0.
  • NRHS is INTEGER — the number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
  • A is COMPLEX*16 array, dimension (LDA,N) — the triangular matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If DIAG = 'U', the diagonal elements of A are also not referenced and are assumed to be 1.
  • LDA is INTEGER — the leading dimension of the array A. LDA >= max(1,N).
  • B is COMPLEX*16 array, dimension (LDB,NRHS) — on entry, the right hand side matrix B. On exit, if INFO = 0, the solution matrix X.
  • LDB is INTEGER — the leading dimension of the array B. LDB >= max(1,N).
  • INFO is INTEGER — the results:
    • = 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. — same iconic squad 🫶

Definition

Definition at line 144 of file ztrtrs.f.

Author

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And that's the tea! This page is from LAPACK version 3.12.0 (the date wasn't in the footer, but you know it's giving timeless 💅). Stay slaying those triangular systems, bestie! 🎀✨

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