hetrs_aa(3)

📦
version 3.12.1 · 9 versions
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🌸 hetrs_aa 🌸

okay so bestie, buckle up — this is the manual page for hetrs_aa(3), from the Library Functions Manual. it's giving "the whole {he,sy}trs_aa family in one place" and honestly? iconic. 💅

✨ NAME ✨

hetrs_aa — {he,sy}trs_aa: triangular solve using factor

like, you already did the factorization thing. now we use it. slay. 🎀

🦋 SYNOPSIS 🦋

💖 Functions

  • subroutine chetrs_aa (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info) — CHETRS_AA
  • subroutine csytrs_aa (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info) — CSYTRS_AA
  • subroutine dsytrs_aa (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info) — DSYTRS_AA
  • subroutine ssytrs_aa (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info) — SSYTRS_AA
  • subroutine zhetrs_aa (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info) — ZHETRS_AA
  • subroutine zsytrs_aa (uplo, n, nrhs, a, lda, ipiv, b, ldb, work, lwork, info) — ZSYTRS_AA

six of them. one vibe. the whole alphabet of precisions, fr fr. 🌈

🔥 Detailed Description 🔥

so this section exists in the original and it's… literally empty. no cap. the heading sits there with nothing under it, like a group chat after someone says "we need to talk." 💀

we move.

👑 Function Documentation 👑

🧚 subroutine chetrs_aa (character uplo, integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( * ) work, integer lwork, integer info)

CHETRS_AA

⭐ Purpose:

CHETRS_AA solves a system of linear equations A*X = B with a complex hermitian matrix A, using the factorization A = U**H*T*U or A = L*T*L**H computed by CHETRF_AA.

that's it. that's the whole job. you hand it the factors, it hands you the answer. 🫶

🌸 Parameters

  • UPLO — UPLO is CHARACTER*1. says whether the details of the factorization are stored as an upper or lower triangular matrix.
    • = 'U': upper triangular, form is A = U**H*T*U;
    • = 'L': lower triangular, form is A = L*T*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). details of factors computed by CHETRF_AA.
  • 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 as computed by CHETRF_AA.
  • B — B is COMPLEX array, dimension (LDB,NRHS). on entry, the right hand side matrix B. on exit, the solution matrix X. ✨ (it literally becomes your answer, main character energy)
  • LDB — LDB is INTEGER. the leading dimension of the array B. LDB >= max(1,N).
  • WORK — WORK is COMPLEX array, dimension (MAX(1,LWORK)).
  • LWORK — LWORK is INTEGER. the dimension of the array WORK. if MIN(N,NRHS) = 0, LWORK >= 1, else LWORK >= 3*N-2.
    • if LWORK = -1, then a workspace query is assumed; the routine only calculates the minimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. 🔍
  • 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 135 of file chetrs_aa.f.

🦋 subroutine csytrs_aa (character uplo, integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( ldb, * ) b, integer ldb, complex, dimension( * ) work, integer lwork, integer info)

CSYTRS_AA

⭐ Purpose:

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

note: symmetric, not hermitian. transposes, not conjugate transposes. mind the difference bestie, it matters. 👀

🌸 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**T*T*U;
    • = 'L': lower triangular, form is A = L*T*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). details of factors computed by CSYTRF_AA.
  • 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 as computed by CSYTRF_AA.
  • 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).
  • WORK — WORK is COMPLEX array, dimension (MAX(1,LWORK)).
  • LWORK — LWORK is INTEGER. the dimension of the array WORK. LWORK >= max(1,3*N-2).
  • INFO — INFO is INTEGER.
    • = 0: successful exit
    • < 0: if INFO = -i, the i-th argument had an illegal value
and yeah — this one's LWORK section has no workspace-query paragraph. don't come for me, that's literally how it's written. 🙈

🎀 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 129 of file csytrs_aa.f.

💜 subroutine dsytrs_aa (character uplo, integer n, integer nrhs, double precision, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( * ) work, integer lwork, integer info)

DSYTRS_AA

⭐ Purpose:

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

double precision, real symmetric, same energy. 🍓

🌸 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**T*T*U;
    • = 'L': lower triangular, form is A = L*T*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). details of factors computed by DSYTRF_AA.
  • 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 as computed by DSYTRF_AA.
  • 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).
  • WORK — WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)).
  • LWORK — LWORK is INTEGER. the dimension of the array WORK. if MIN(N,NRHS) = 0, LWORK >= 1, else LWORK >= 3*N-2.
    • if LWORK = -1, then a workspace query is assumed; the routine only calculates the minimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.
  • 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 135 of file dsytrs_aa.f.

🌈 subroutine ssytrs_aa (character uplo, integer n, integer nrhs, real, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, real, dimension( ldb, * ) b, integer ldb, real, dimension( * ) work, integer lwork, integer info)

SSYTRS_AA

⭐ Purpose:

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

single precision edition. same routine, lighter baggage. ⭐

🌸 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**T*T*U;
    • = 'L': lower triangular, form is A = L*T*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). details of factors computed by SSYTRF_AA.
  • 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 as computed by SSYTRF_AA.
  • 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).

WORK

okay bestie, here's the real workspace tea: WORK is WORK is REAL array, dimension (MAX(1,LWORK)). That’s the real-valued scratch space, no cap 💅

LWORK

LWORK is LWORK is INTEGER — it’s the dimension of the array WORK.

So here’s the size check, literally: if MIN(N,NRHS) = 0, then LWORK >= 1, else LWORK >= 3*N-2. 🫶

And if LWORK = -1, then a workspace query is assumed; the routine only calculates the minimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. Iconic lazy-girl behavior, honestly.

INFO

INFO is 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 135 of file ssytrs_aa.f.

zhetrs_aa — ZHETRS_AA

Purpose

okay so ZHETRS_AA solves a system of linear equations A*X = B with a complex hermitian matrix A using the factorization A = U**H*T*U or A = L*T*L**H computed by ZHETRF_AA. That’s the whole main-character plot 💜

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

Parameters

  • UPLO — UPLO is CHARACTER*1. It specifies whether the details of the factorization are stored as an upper or lower triangular matrix. = 'U': Upper triangular, form is A = U**H*T*U; = 'L': Lower triangular, form is A = L*T*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). Details of factors computed by ZHETRF_AA.
  • 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 as computed by ZHETRF_AA.
  • 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).
  • WORK — WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)).
  • LWORK — LWORK is INTEGER. The dimension of the array WORK. If MIN(N,NRHS) = 0, LWORK >= 1, else LWORK >= 3*N-2. If LWORK = -1, then a workspace query is assumed; the routine only calculates the minimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. 🫶
  • 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 136 of file zhetrs_aa.f.

zsytrs_aa — ZSYTRS_AA

Purpose

and ZSYTRS_AA solves a system of linear equations A*X = B with a complex symmetric matrix A using the factorization A = U**T*T*U or A = L*T*L**T computed by ZSYTRF_AA. Same slay, different symmetry vibe 🌈

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

Parameters

  • UPLO — UPLO is CHARACTER*1. It specifies whether the details of the factorization are stored as an upper or lower triangular matrix. = 'U': Upper triangular, form is A = U**T*T*U; = 'L': Lower triangular, form is A = L*T*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). Details of factors computed by ZSYTRF_AA.
  • 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 as computed by ZSYTRF_AA.
  • 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).
  • WORK — WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)).
  • LWORK — LWORK is INTEGER. The dimension of the array WORK. LWORK >= max(1,3*N-2).
  • 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 129 of file zsytrs_aa.f.

Author

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