hetrs_rook(3)

📦

version 3.12.1 · 9 versions

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3.12.1 · ubuntu stonking
3.12.1 · ubuntu questing
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🦋 `hetrs_rook` — library functions manual 💅

okay so this is the hetrs_rook(3) page from your Library Functions Manual, bestie, and it's literally a whole family of subroutines that all do the same iconic thing: solve A*X = B after somebody already factored A for you. grab a snack, this one's long 🍓

✨ NAME ✨

hetrs_rook — {he,sy}trs_rook: triangular solve using factor

like, the whole vibe is "I already have the factorization, now gimme the answer" 🔥

🎀 SYNOPSIS 🎀

🌸 Functions

subroutine chetrs_rook (uplo, n, nrhs, a, lda, ipiv, b, ldb, info) — CHETRS_ROOK computes the solution to a system of linear equations A * X = B for HE matrices using factorization obtained with one of the bounded diagonal pivoting methods (max 2 interchanges)
subroutine csytrs_rook (uplo, n, nrhs, a, lda, ipiv, b, ldb, info) — CSYTRS_ROOK
subroutine dsytrs_rook (uplo, n, nrhs, a, lda, ipiv, b, ldb, info) — DSYTRS_ROOK
subroutine ssytrs_rook (uplo, n, nrhs, a, lda, ipiv, b, ldb, info) — SSYTRS_ROOK
subroutine zhetrs_rook (uplo, n, nrhs, a, lda, ipiv, b, ldb, info) — ZHETRS_ROOK computes the solution to a system of linear equations A * X = B for HE matrices using factorization obtained with one of the bounded diagonal pivoting methods (max 2 interchanges)
subroutine zsytrs_rook (uplo, n, nrhs, a, lda, ipiv, b, ldb, info) — ZSYTRS_ROOK

💜 Detailed Description 💜

bestie the original page leaves this section completely empty. no cap, there is nothing here. moving on 🫶

👑 Function Documentation 👑

⭐ `chetrs_rook`

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

CHETRS_ROOK computes the solution to a system of linear equations A * X = B for HE matrices using factorization obtained with one of the bounded diagonal pivoting methods (max 2 interchanges)

💖 Purpose

CHETRS_ROOK solves a system of linear equations A*X = B with a complex Hermitian matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by CHETRF_ROOK.

🧚 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.
A — A is COMPLEX array, dimension (LDA,N). The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by CHETRF_ROOK.
LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
IPIV — IPIV is INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by CHETRF_ROOK.
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.

🌸 Contributors

November 2013, Igor Kozachenko, Computer Science Division, University of California, Berkeley
September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, School of Mathematics, University of Manchester

Definition at line 134 of file chetrs_rook.f.

⭐ `csytrs_rook`

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

CSYTRS_ROOK

💖 Purpose

CSYTRS_ROOK solves a system of linear equations A*X = B with a complex symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by CSYTRF_ROOK.

🧚 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.
A — A is COMPLEX array, dimension (LDA,N). The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by CSYTRF_ROOK.
LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
IPIV — IPIV is INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by CSYTRF_ROOK.
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.

🌸 Contributors

December 2016, Igor Kozachenko, Computer Science Division, University of California, Berkeley
September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, School of Mathematics, University of Manchester

Definition at line 134 of file csytrs_rook.f.

⭐ `dsytrs_rook`

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

DSYTRS_ROOK

💖 Purpose

DSYTRS_ROOK solves a system of linear equations A*X = B with a real symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by DSYTRF_ROOK.

🧚 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.
A — A is DOUBLE PRECISION array, dimension (LDA,N). The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by DSYTRF_ROOK.
LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
IPIV — IPIV is INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by DSYTRF_ROOK.
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.

🌸 Contributors

April 2012, Igor Kozachenko, Computer Science Division, University of California, Berkeley
September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, School of Mathematics, University of Manchester

Definition at line 134 of file dsytrs_rook.f.

⭐ `ssytrs_rook`

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

SSYTRS_ROOK

💖 Purpose

SSYTRS_ROOK solves a system of linear equations A*X = B with a real symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by SSYTRF_ROOK.

🧚 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.
A — A is REAL array, dimension (LDA,N). The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by SSYTRF_ROOK.
LDA

LDA — LDA is INTEGER, and it's literally the leading dimension of the array A. Respect the boundary, bestie: LDA >= max(1,N). 💅

IPIV — IPIV is INTEGER array, dimension (N). It's carrying the details of the interchanges and the block structure of D as determined by SSYTRF_ROOK. iykyk 🫶

B — B is REAL array, dimension (LDB,NRHS). On entry, it's the right hand side matrix B; on exit, it's the solution matrix X. The glow-up is real. ✨

LDB — LDB is INTEGER. It's the leading dimension of the array B, no cap: LDB >= max(1,N). 🎀

INFO — INFO is INTEGER. = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. That's the tea. 💀

Author:

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

Contributors:

April 2012, Igor Kozachenko,
- Computer Science Division,
- University of California, Berkeley
September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
- School of Mathematics,
- University of Manchester

Definition at line 134 of file ssytrs_rook.f.

subroutine zhetrs_rook

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

Description: ZHETRS_ROOK computes the solution to a system of linear equations A * X = B for HE matrices using factorization obtained with one of the bounded diagonal pivoting methods (max 2 interchanges). 🔥

Purpose:

ZHETRS_ROOK solves a system of linear equations A*X = B with a complex Hermitian matrix A using the factorization A = U*D*U**H or A = L*D*L**H computed by ZHETRF_ROOK. 💜

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. 🎀
A — A is COMPLEX*16 array, dimension (LDA,N). The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by ZHETRF_ROOK. 🦋
LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N). 💅
IPIV — IPIV is INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by ZHETRF_ROOK. 🫶
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.

Contributors:

November 2013, Igor Kozachenko,
- Computer Science Division,
- University of California, Berkeley
September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
- School of Mathematics,
- University of Manchester

Definition at line 134 of file zhetrs_rook.f.

subroutine zsytrs_rook

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

Description: ZSYTRS_ROOK. That's the whole description line — iconic minimalism. 🫶

Purpose:

ZSYTRS_ROOK solves a system of linear equations A*X = B with a complex symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by ZSYTRF_ROOK. 🦋

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. 🎀
A — A is COMPLEX*16 array, dimension (LDA,N). The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by ZSYTRF_ROOK. 🦋
LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N). 💅
IPIV — IPIV is INTEGER array, dimension (N). Details of the interchanges and the block structure of D as determined by ZSYTRF_ROOK. 🫶
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.

Contributors:

December 2016, Igor Kozachenko,
- Computer Science Division,
- University of California, Berkeley
September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas,
- School of Mathematics,
- University of Manchester

Definition at line 134 of file zsytrs_rook.f.

Author

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And that's the whole page, bestie! Footer vibes: LAPACK Version 3.12.0, page hetrs_rook(3) — iconic, no cap. 🎀✨

📦 where this page comes from

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hetrs_rook(3)

🦋 hetrs_rook — library functions manual 💅

✨ NAME ✨

🎀 SYNOPSIS 🎀

🌸 Functions

💜 Detailed Description 💜

👑 Function Documentation 👑

⭐ chetrs_rook

💖 Purpose

🧚 Parameters

🌈 Author

🌸 Contributors

⭐ csytrs_rook

💖 Purpose

🧚 Parameters

🌈 Author

🌸 Contributors

⭐ dsytrs_rook

💖 Purpose

🧚 Parameters

🌈 Author

🌸 Contributors

⭐ ssytrs_rook

💖 Purpose

🧚 Parameters

subroutine zhetrs_rook

subroutine zsytrs_rook

Author

🦋 `hetrs_rook` — library functions manual 💅

⭐ `chetrs_rook`

⭐ `csytrs_rook`

⭐ `dsytrs_rook`

⭐ `ssytrs_rook`