hetrs_aa_2stage(3)

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version 3.12.1 · 9 versions
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💖 hetrs_aa_2stage(3) — Library Functions Manual 💖

okay so bestie, welcome to the group chat. this page is literally the hetrs_aa_2stage(3) manual entry from the Library Functions Manual, and it's the whole {he,sy}trs_aa_2stage family — six subroutines that do a triangular solve using factors. grab a snack, we're reading all of it 🍓

✨ NAME ✨

hetrs_aa_2stage — {he,sy}trs_aa_2stage: triangular solve using factor

no cap, that's the whole vibe. one line, one job, iconic behavior 💅

🌸 SYNOPSIS 🌸

Functions

  • subroutine chetrs_aa_2stage (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, info) — CHETRS_AA_2STAGE
  • subroutine csytrs_aa_2stage (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, info) — CSYTRS_AA_2STAGE
  • subroutine dsytrs_aa_2stage (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, info) — DSYTRS_AA_2STAGE
  • subroutine ssytrs_aa_2stage (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, info) — SSYTRS_AA_2STAGE
  • subroutine zhetrs_aa_2stage (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, info) — ZHETRS_AA_2STAGE
  • subroutine zsytrs_aa_2stage (uplo, n, nrhs, a, lda, tb, ltb, ipiv, ipiv2, b, ldb, info) — ZSYTRS_AA_2STAGE

six of them. all the same shape. the prefixes are just the type-check letters — C/Z are complex, S/D are real, HE means hermitian and SY means symmetric. iykyk 🧚

🦋 Detailed Description 🦋

(this is where the page puts the heading, and then just... moves straight on into the functions. love that for us. no filler, periodt.)

👑 Function Documentation 👑

🎀 subroutine chetrs_aa_2stage (character uplo, integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, complex, dimension( ldb, * ) b, integer ldb, integer info)

subroutine chetrs_aa_2stage (character uplo, integer n, integer nrhs, &
    complex, dimension( lda, * ) a, integer lda, &
    complex, dimension( * ) tb, integer ltb, &
    integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, &
    complex, dimension( ldb, * ) b, integer ldb, integer info)

💜 Purpose:

!> !> CHETRS_AA_2STAGE solves a system of linear equations A*X = B with a real !> hermitian matrix A using the factorization A = U**T*T*U or !> A = L*T*L**T computed by CHETRF_AA_2STAGE. !>

(yeah, the page literally says "a real hermitian matrix" for the C routine — not me, that's what's written, we don't edit the docs, we just report them fr fr 🙈)

🌸 Parameters

  • UPLO — UPLO is CHARACTER*1. tells us how the factorization details are stored — upper or lower triangular. no ambiguity allowed, bestie:
    • = '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). the details of the factors computed by CHETRF_AA_2STAGE.
  • LDA — LDA is INTEGER. the leading dimension of the array A. LDA >= max(1,N).
  • TB — TB is COMPLEX array, dimension (LTB). the details of the factors computed by CHETRF_AA_2STAGE.
  • LTB — LTB is INTEGER. the size of the array TB. LTB >= 4*N.
  • IPIV — IPIV is INTEGER array, dimension (N). details of the interchanges as computed by CHETRF_AA_2STAGE.
  • IPIV2 — IPIV2 is INTEGER array, dimension (N). details of the interchanges as computed by CHETRF_AA_2STAGE.
  • B — B is COMPLEX array, dimension (LDB,NRHS). on entry, the right hand side matrix B. on exit, the solution matrix X. the glow-up is real ✨
  • 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

Definition at line 139 of file chetrs_aa_2stage.f.

🎀 subroutine csytrs_aa_2stage (character uplo, integer n, integer nrhs, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, complex, dimension( ldb, * ) b, integer ldb, integer info)

subroutine csytrs_aa_2stage (character uplo, integer n, integer nrhs, &
    complex, dimension( lda, * ) a, integer lda, &
    complex, dimension( * ) tb, integer ltb, &
    integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, &
    complex, dimension( ldb, * ) b, integer ldb, integer info)

💜 Purpose:

!> !> CSYTRS_AA_2STAGE 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_2STAGE. !>

🌸 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_2STAGE.
  • LDA — LDA is INTEGER. the leading dimension of the array A. LDA >= max(1,N).
  • TB — TB is COMPLEX array, dimension (LTB). details of factors computed by CSYTRF_AA_2STAGE.
  • LTB — LTB is INTEGER. the size of the array TB. LTB >= 4*N.
  • IPIV — IPIV is INTEGER array, dimension (N). details of the interchanges as computed by CSYTRF_AA_2STAGE.
  • IPIV2 — IPIV2 is INTEGER array, dimension (N). details of the interchanges as computed by CSYTRF_AA_2STAGE.
  • 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

Definition at line 137 of file csytrs_aa_2stage.f.

🎀 subroutine dsytrs_aa_2stage (character uplo, integer n, integer nrhs, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, double precision, dimension( ldb, * ) b, integer ldb, integer info)

subroutine dsytrs_aa_2stage (character uplo, integer n, integer nrhs, &
    double precision, dimension( lda, * ) a, integer lda, &
    double precision, dimension( * ) tb, integer ltb, &
    integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, &
    double precision, dimension( ldb, * ) b, integer ldb, integer info)

💜 Purpose:

!> !> DSYTRS_AA_2STAGE 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_2STAGE. !>

🌸 Parameters

  • UPLO — UPLO is CHARACTER*1. tells you whether the factorization details are stored as upper or lower triangular.
    • = '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_2STAGE.
  • LDA — LDA is INTEGER. the leading dimension of the array A. LDA >= max(1,N).
  • TB — TB is DOUBLE PRECISION array, dimension (LTB). details of factors computed by DSYTRF_AA_2STAGE.
  • LTB — LTB is INTEGER. the size of the array TB. LTB >= 4*N.
  • IPIV — IPIV is INTEGER array, dimension (N). details of the interchanges as computed by DSYTRF_AA_2STAGE.
  • IPIV2 — IPIV2 is INTEGER array, dimension (N). details of the interchanges as computed by DSYTRF_AA_2STAGE.
  • 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

Definition at line 137 of file dsytrs_aa_2stage.f.

🎀 subroutine ssytrs_aa_2stage (character uplo, integer n, integer nrhs, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, real, dimension( ldb, * ) b, integer ldb, integer info)

subroutine ssytrs_aa_2stage (character uplo, integer n, integer nrhs, &
    real, dimension( lda, * ) a, integer lda, &
    real, dimension( * ) tb, integer ltb, &
    integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, &
    real, dimension( ldb, * ) b, integer ldb, integer info)

💜 Purpose:

!> !> SSYTRS_AA_2STAGE 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_2STAGE. !>

🌸 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_2STAGE.
  • LDA — LDA is INTEGER. the leading dimension of the array A. LDA >= max(1,N).
  • TB
🦋 and that's exactly where this half of the page runs out — TB just vibing there with no description yet. the rest of SSYTRS_AA_2STAGE (and the Z routines) are living their best life in part 2, so don't go anywhere 👀

okay bestie, we’re still mid-parameter-list for ssytrs_aa_2stage — no need to re-intro the whole function, we’re just picking up at TB like it’s the next text in the group chat. 💬

  • TB — TB is a REAL array, dimension (LTB). It’s holding the details of factors computed by SSYTRF_AA_2STAGE. factorization receipts, basically.
  • LTB — LTB is INTEGER. It’s the size of the array TB. Must be LTB >= 4*N. respect the minimum, bestie.
  • IPIV — IPIV is an INTEGER array, dimension (N). Details of the interchanges as computed by SSYTRF_AA_2STAGE. the plot twists.
  • IPIV2 — IPIV2 is an INTEGER array, dimension (N). Details of the interchanges as computed by SSYTRF_AA_2STAGE. more plot twists, second volume.
  • B — B is a REAL array, dimension (LDB,NRHS). On entry, the right hand side matrix B. On exit, the solution matrix X. glow-up arc: RHS in, answers out.
  • LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N). do not fumble this one.
  • 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 137 of file ssytrs_aa_2stage.f.

💖 subroutine zhetrs_aa_2stage (a.k.a. ZHETRS_AA_2STAGE) — hermitian era

   subroutine zhetrs_aa_2stage (character uplo, integer n, integer nrhs,
       complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( *
       ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * )
       ipiv2, complex*16, dimension( ldb, * ) b, integer ldb, integer info)
       ZHETRS_AA_2STAGE

✨ Purpose

ZHETRS_AA_2STAGE solves a system of linear equations A*X = B with a hermitian matrix A using the factorization A = U**H*T*U or A = L*T*L**H computed by ZHETRF_AA_2STAGE. hermitian girlies, this is your moment. ✨

🌸 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**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. zero is valid, she’s just tiny.
  • 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 a COMPLEX*16 array, dimension (LDA,N). Details of factors computed by ZHETRF_AA_2STAGE. the main character array.
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
  • TB — TB is a COMPLEX*16 array, dimension (LTB). Details of factors computed by ZHETRF_AA_2STAGE.
  • LTB — LTB is INTEGER. The size of the array TB. LTB >= 4*N.
  • IPIV — IPIV is an INTEGER array, dimension (N). Details of the interchanges as computed by ZHETRF_AA_2STAGE.
  • IPIV2 — IPIV2 is an INTEGER array, dimension (N). Details of the interchanges as computed by ZHETRF_AA_2STAGE.
  • B — B is a COMPLEX*16 array, dimension (LDB,NRHS). On entry, the right hand side matrix B. On exit, the solution matrix X. same array, new destiny.
  • 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 139 of file zhetrs_aa_2stage.f.

💜 subroutine zsytrs_aa_2stage (a.k.a. ZSYTRS_AA_2STAGE) — complex symmetric bestie

   subroutine zsytrs_aa_2stage (character uplo, integer n, integer nrhs,
       complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( *
       ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * )
       ipiv2, complex*16, dimension( ldb, * ) b, integer ldb, integer info)
       ZSYTRS_AA_2STAGE

✨ Purpose

ZSYTRS_AA_2STAGE 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_2STAGE. transpose energy, but make it complex. 💅

🌸 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 a COMPLEX*16 array, dimension (LDA,N). Details of factors computed by ZSYTRF_AA_2STAGE.
  • LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,N).
  • TB — TB is a COMPLEX*16 array, dimension (LTB). Details of factors computed by ZSYTRF_AA_2STAGE.
  • LTB — LTB is INTEGER. The size of the array TB. LTB >= 4*N.
  • IPIV — IPIV is an INTEGER array, dimension (N). Details of the interchanges as computed by ZSYTRF_AA_2STAGE.
  • IPIV2 — IPIV2 is an INTEGER array, dimension (N). Details of the interchanges as computed by ZSYTRF_AA_2STAGE.
  • B — B is a COMPLEX*16 array, dimension (LDB,NRHS). On entry, the right hand side matrix B. On exit, the solution matrix X. RHS walks in, solution walks out.
  • 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 137 of file zsytrs_aa_2stage.f.

🎀 Author

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sign-off time, bestie: this whole page is serving LAPACK Version 3.12.0, and the page name is hetrs_aa_2stage(3) — date vibes are whatever Doxygen stamped, but the source/version flex is right there. mwah. 💋✨

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