potrs(3)

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version 3.12.1 · 9 versions
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💅 potrs(3) — the LAPACK girlies' triangular solve, bestie edition ✨

Okay so this is the potrs manual page from LAPACK, and no cap, it's literally four subroutines that all do the same iconic thing in different precisions. It's giving "Cholesky round two, electric boogaloo" and I'm obsessed. Let's get into it 🎀

🌸 NAME 🌸

potrs — potrs: triangular solve using factor 💖

✨ SYNOPSIS ✨

🦋 Functions 🦋

  • subroutine cpotrs (uplo, n, nrhs, a, lda, b, ldb, info) — CPOTRS
  • subroutine dpotrs (uplo, n, nrhs, a, lda, b, ldb, info) — DPOTRS
  • subroutine spotrs (uplo, n, nrhs, a, lda, b, ldb, info) — SPOTRS
  • subroutine zpotrs (uplo, n, nrhs, a, lda, b, ldb, info) — ZPOTRS

🌈 Detailed Description 🌈

Bestie, this page is literally just the function docs, one for each precision. Every single one of them solves A*X = B where A is a positive definite matrix that you already Cholesky-factored (via CPOTRF / DPOTRF / SPOTRF / ZOTRF, iykyk). Scroll for your fave 💅

👑 Function Documentation 👑

💜 subroutine cpotrs (character uplo, integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldb, * ) b, integer ldb, integer info)

CPOTRS

🍓 Purpose:

!>
!> CPOTRS solves a system of linear equations A*X = B with a Hermitian
!> positive definite matrix A using the Cholesky factorization
!> A = U**H*U or A = L*L**H computed by CPOTRF.
!>

🌸 Parameters 🌸

  • UPLO
!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangle of A is stored;
!>          = 'L':  Lower triangle of A is stored.
!>
  • 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 factor U or L from the Cholesky factorization
!>          A = U**H*U or A = L*L**H, as computed by CPOTRF.
!>
  • 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, 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 109 of file cpotrs.f.

💜 subroutine dpotrs (character uplo, integer n, integer nrhs, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldb, * ) b, integer ldb, integer info)

DPOTRS

🍓 Purpose:

!>
!> DPOTRS solves a system of linear equations A*X = B with a symmetric
!> positive definite matrix A using the Cholesky factorization
!> A = U**T*U or A = L*L**T computed by DPOTRF.
!>

🌸 Parameters 🌸

  • UPLO
!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangle of A is stored;
!>          = 'L':  Lower triangle of A is stored.
!>
  • 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 factor U or L from the Cholesky factorization
!>          A = U**T*U or A = L*L**T, as computed by DPOTRF.
!>
  • 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, 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 109 of file dpotrs.f.

💜 subroutine spotrs (character uplo, integer n, integer nrhs, real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, integer info)

SPOTRS

🍓 Purpose:

!>
!> SPOTRS solves a system of linear equations A*X = B with a symmetric
!> positive definite matrix A using the Cholesky factorization
!> A = U**T*U or A = L*L**T computed by SPOTRF.
!>

🌸 Parameters 🌸

  • UPLO
!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangle of A is stored;
!>          = 'L':  Lower triangle of A is stored.
!>
  • 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 factor U or L from the Cholesky factorization
!>          A = U**T*U or A = L*L**T, as computed by SPOTRF.
!>
  • 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, 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 109 of file spotrs.f.

💜 subroutine zpotrs (character uplo, integer n, integer nrhs, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb, integer info)

ZPOTRS

🍓 Purpose:

!>
!> ZPOTRS solves a system of linear equations A*X = B with a Hermitian
!> positive definite matrix A using the Cholesky factorization
!> A = U**H * U or A = L * L**H computed by ZPOTRF.
!>

🌸 Parameters 🌸

  • UPLO
!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangle of A is stored;
!>          = 'L':  Lower triangle of A is stored.
!>
  • 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*16 array, dimension (LDA,N)
!>          The triangular factor U or L from the Cholesky factorization
!>          A = U**H * U or A = L * L**H, as computed by ZPOTRF.
!>
  • LDA
!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,N).
!>
  • B
!>          B is COMPLEX*16 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 109 of file zpotrs.f.

⭐ Author ⭐

Generated automatically by Doxygen for LAPACK from the source code. (Not a human, not a vibe, just a robot doing its thing 🤖✨)

Heads up bestie: c = complex, d = double precision, s = real, z = complex*16 — pick the one that matches your factorization and slay 💅

That's the whole page, periodt! 🫶 This absolute icon of a manpage is from LAPACK, Version 3.12.0, and it's serving potrs(3) realness. Go solve those systems, queen 👑💖

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