posv(3)

📦

version 3.12.1 · 9 versions

3.12.1 · arch rolling (latest)
3.12.0 · opensuse-leap 16.0
3.12.1 · ubuntu stonking
3.12.1 · ubuntu questing
3.12.0 · ubuntu noble
3.12.0 · ubuntu noble
3.12.0 · centos-stream 10, fedora 43, fedora 44
3.12.1 · ubuntu resolute
3.12.1 · debian trixie

💖 posv(3) — Library Functions Manual 💖

okay bestie, so this is posv — the factor-and-solve girlie from the Library Functions Manual. She comes in four flavors (cposv, dposv, sposv, zposv) and they all do the exact same iconic thing: take your A * X = B situation, factor A with Cholesky, and hand you back X. No cap. Let's get into it 💅

✨ NAME ✨

posv — posv: factor and solve 🎀

🌸 SYNOPSIS 🌸

🌈 Functions 🌈

subroutine cposv (uplo, n, nrhs, a, lda, b, ldb, info) — CPOSV computes the solution to system of linear equations A * X = B for PO matrices
subroutine dposv (uplo, n, nrhs, a, lda, b, ldb, info) — DPOSV computes the solution to system of linear equations A * X = B for PO matrices
subroutine sposv (uplo, n, nrhs, a, lda, b, ldb, info) — SPOSV computes the solution to system of linear equations A * X = B for PO matrices
subroutine zposv (uplo, n, nrhs, a, lda, b, ldb, info) — ZPOSV computes the solution to system of linear equations A * X = B for PO matrices

🦋 DETAILED DESCRIPTION 🦋

So the page has a Detailed Description section and it is lowkey just a heading doing main character energy with nothing under it 💀 — the actual tea is all in Function Documentation right below. Every single function gets the full treatment there. Scroll with me 🫶

👑 FUNCTION DOCUMENTATION 👑

💜 subroutine cposv

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

CPOSV computes the solution to system of linear equations A * X = B for PO matrices

🌟 Purpose

ok so picture this: CPOSV computes the solution to a complex system of linear equations

A * X = B,

where A is an N-by-N Hermitian positive definite matrix and X and B are N-by-NRHS matrices. obsessed.

The Cholesky decomposition is used to factor A as

A = U**H* U,  if UPLO = 'U', or
A = L * L**H,  if UPLO = 'L',

where U is an upper triangular matrix and L is a lower triangular matrix. Then the factored form of A is used to solve the system of equations A * X = B. literally the whole pipeline ✨

💅 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 number of linear equations, i.e., 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).
- On entry, the Hermitian matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. like, don't even look at it 🙈
- On exit, if INFO = 0, the factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H.
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 N-by-NRHS right hand side matrix B.
- On exit, if INFO = 0, the N-by-NRHS solution matrix X. she ate 💅
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 of A is not positive, so the factorization could not be completed, and the solution has not been computed. 💀 so yeah, check your INFO, bestie.

🫶 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

📖 Definition

Definition at line 129 of file cposv.f.

💙 subroutine dposv

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

DPOSV computes the solution to system of linear equations A * X = B for PO matrices

🌟 Purpose

DPOSV computes the solution to a real system of linear equations

A * X = B,

where A is an N-by-N symmetric positive definite matrix and X and B are N-by-NRHS matrices.

The Cholesky decomposition is used to factor A as

A = U**T* U,  if UPLO = 'U', or
A = L * L**T,  if UPLO = 'L',

where U is an upper triangular matrix and L is a lower triangular matrix. The factored form of A is then used to solve the system of equations A * X = B. same energy, but real numbers this time 🍓

💅 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 number of linear equations, i.e., 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).
- On entry, the symmetric matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced.
- On exit, if INFO = 0, the factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T.
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 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 of A is not positive, so the factorization could not be completed, and the solution has not been computed.

🫶 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

📖 Definition

Definition at line 129 of file dposv.f.

💚 subroutine sposv

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

SPOSV computes the solution to system of linear equations A * X = B for PO matrices

🌟 Purpose

SPOSV computes the solution to a real system of linear equations

A * X = B,

where A is an N-by-N symmetric positive definite matrix and X and B are N-by-NRHS matrices.

The Cholesky decomposition is used to factor A as

A = U**T* U,  if UPLO = 'U', or
A = L * L**T,  if UPLO = 'L',

where U is an upper triangular matrix and L is a lower triangular matrix. The factored form of A is then used to solve the system of equations A * X = B. single precision said "I'm also here" 🌸

💅 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 number of linear equations, i.e., 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).
- On entry, the symmetric matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced.
- On exit, if INFO = 0, the factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T.
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 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 of A is not positive, so the factorization could not be completed, and the solution has not been computed.

🫶 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

📖 Definition

Definition at line 129 of file sposv.f.

💖 subroutine zposv

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

ZPOSV computes the solution to system of linear equations A * X = B for PO matrices

🌟 Purpose

🦋 (...and this is exactly where part 1 runs out of runway — zposv's Purpose section keeps going in part 2, so don't go anywhere bestie) 🦋

ZPOSV is literally here to compute the solution to a complex system of linear equations

A * X = B

where A is an N-by-N Hermitian positive definite matrix and X and B are N-by-NRHS matrices. 💅✨

The Cholesky decomposition is used to factor A as

A = U**H* U,  if UPLO = 'U', or
A = L * L**H,  if UPLO = 'L',

where U is an upper triangular matrix and L is a lower triangular matrix. The factored form of A is then used to solve the system of equations A * X = B. 🫶

✨ Parameters ✨

UPLO — is CHARACTER*1.
- = 'U': Upper triangle of A is stored;
- = 'L': Lower triangle of A is stored. 🦋
N — is INTEGER. The number of linear equations, i.e., 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). On entry, the Hermitian matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced.

On exit, if INFO = 0, the factor U or L from the Cholesky factorization A = U**H *U or A = L*L**H. 🔥

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 N-by-NRHS right hand side matrix B. On exit, if INFO = 0, the N-by-NRHS solution matrix X. 🎀
LDB — is INTEGER. The leading dimension of the array B. LDB >= max(1,N). 💜
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 of A is not positive, so the factorization could not be completed, and the solution has not been computed. 😭

🫶 Author 🫶

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

Definition at line 129 of file zposv.f. 📜

🌸 Author 🌸

Generated automatically by Doxygen for LAPACK from the source code. 🧚

And that's the footer tea, bestie: source/version/date energy is LAPACK, Version 3.12.0, posv(3) — iconic, no cap. 👑🌈

📦 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