hegs2(3)

📦
version 3.12.1 · 9 versions
, in arch rolling

💅 hegs2(3) — Library Functions Manual 💅

✨ NAME ✨

hegs2 - {he,sy}gs2: reduction to standard form, level 2. 🎀

✨ SYNOPSIS ✨

Okay bestie, here's the function lineup. All four are giving unblocked algorithm energy. 💅

🌟 Functions 🌟

  • subroutine chegs2 (itype, uplo, n, a, lda, b, ldb, info) — CHEGS2 reduces a Hermitian definite generalized eigenproblem to standard form, using the factorization results obtained from cpotrf (unblocked algorithm).
  • subroutine dsygs2 (itype, uplo, n, a, lda, b, ldb, info) — DSYGS2 reduces a symmetric definite generalized eigenproblem to standard form, using the factorization results obtained from spotrf (unblocked algorithm).
  • subroutine ssygs2 (itype, uplo, n, a, lda, b, ldb, info) — SSYGS2 reduces a symmetric definite generalized eigenproblem to standard form, using the factorization results obtained from spotrf (unblocked algorithm).
  • subroutine zhegs2 (itype, uplo, n, a, lda, b, ldb, info) — ZHEGS2 reduces a Hermitian definite generalized eigenproblem to standard form, using the factorization results obtained from cpotrf (unblocked algorithm).

🌸 Detailed Description 🌸

This is the detailed description zone, and honestly? We're about to go function by function, parameter by parameter, no skipping, no summarizing. Periodt. 🫶

💖 Function Documentation 💖

💖 chegs2 — the complex Hermitian one 💖

subroutine chegs2 (integer itype, character uplo, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldb, * ) b, integer ldb, integer info)

CHEGS2 reduces a Hermitian definite generalized eigenproblem to standard form, using the factorization results obtained from cpotrf (unblocked algorithm). 💅

✨ Purpose ✨

Bestie, here's the whole point: CHEGS2 reduces a complex Hermitian-definite generalized eigenproblem to standard form. 🌈

  • If ITYPE = 1, the problem is A*x = lambda*B*x, and A is overwritten by inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H).
  • If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or B*A*x = lambda*x, and A is overwritten by U*A*U**H or L**H *A*L.
  • B must have been previously factorized as U**H *U or L*L**H by ZPOTRF. (Yes, it says ZPOTRF right there, bestie — we are not editing the lore. 💀)

🌸 Parameters 🌸

  • ITYPE — INTEGER; = 1: compute inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H); = 2 or 3: compute U*A*U**H or L**H *A*L.
  • UPLO — CHARACTER*1; specifies whether the upper or lower triangular part of the Hermitian matrix A is stored, and how B has been factorized. = 'U': Upper triangular; = 'L': Lower triangular.
  • N — INTEGER; the order of the matrices A and B. N >= 0.
  • A — 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.

On exit, if INFO = 0, the transformed matrix, stored in the same format as A.

  • LDA — INTEGER; the leading dimension of the array A. LDA >= max(1,N).
  • B — COMPLEX array, dimension (LDB,N). The triangular factor from the Cholesky factorization of B, as returned by CPOTRF. B is modified by the routine but restored on exit. 🫶
  • LDB — INTEGER; the leading dimension of the array B. LDB >= max(1,N).
  • INFO — 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 127 of file chegs2.f.

💙 dsygs2 — the DOUBLE PRECISION one 💙

subroutine dsygs2 (integer itype, character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldb, * ) b, integer ldb, integer info)

DSYGS2 reduces a symmetric definite generalized eigenproblem to standard form, using the factorization results obtained from spotrf (unblocked algorithm). ✨

✨ Purpose ✨

DSYGS2 reduces a real symmetric-definite generalized eigenproblem to standard form. 🌸

  • If ITYPE = 1, the problem is A*x = lambda*B*x, and A is overwritten by inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T).
  • If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or B*A*x = lambda*x, and A is overwritten by U*A*U**T or L**T *A*L.
  • B must have been previously factorized as U**T *U or L*L**T by DPOTRF.

🌸 Parameters 🌸

  • ITYPE — INTEGER; = 1: compute inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T); = 2 or 3: compute U*A*U**T or L**T *A*L.
  • UPLO — CHARACTER*1; specifies whether the upper or lower triangular part of the symmetric matrix A is stored, and how B has been factorized. = 'U': Upper triangular; = 'L': Lower triangular.
  • N — INTEGER; the order of the matrices A and B. N >= 0.
  • A — 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 transformed matrix, stored in the same format as A.

  • LDA — INTEGER; the leading dimension of the array A. LDA >= max(1,N).
  • B — DOUBLE PRECISION array, dimension (LDB,N). The triangular factor from the Cholesky factorization of B, as returned by DPOTRF.
  • LDB — INTEGER; the leading dimension of the array B. LDB >= max(1,N).
  • INFO — 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 126 of file dsygs2.f.

🌈 ssygs2 — the REAL one 🌈

subroutine ssygs2 (integer itype, character uplo, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, integer info)

SSYGS2 reduces a symmetric definite generalized eigenproblem to standard form, using the factorization results obtained from spotrf (unblocked algorithm). 🦋

✨ Purpose ✨

SSYGS2 reduces a real symmetric-definite generalized eigenproblem to standard form. 💜

  • If ITYPE = 1, the problem is A*x = lambda*B*x, and A is overwritten by inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T).
  • If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or B*A*x = lambda*x, and A is overwritten by U*A*U**T or L**T *A*L.
  • B must have been previously factorized as U**T *U or L*L**T by SPOTRF.

🌸 Parameters 🌸

  • ITYPE — INTEGER; = 1: compute inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T); = 2 or 3: compute U*A*U**T or L**T *A*L.
  • UPLO — CHARACTER*1; specifies whether the upper or lower triangular part of the symmetric matrix A is stored, and how B has been factorized. = 'U': Upper triangular; = 'L': Lower triangular.
  • N — INTEGER; the order of the matrices A and B. N >= 0.
  • A — 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 transformed matrix, stored in the same format as A.

  • LDA — INTEGER; the leading dimension of the array A. LDA >= max(1,N).
  • B — REAL array, dimension (LDB,N). The triangular factor from the Cholesky factorization of B, as returned by SPOTRF.
  • LDB — INTEGER; the leading dimension of the array B. LDB >= max(1,N).
  • INFO — 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 126 of file ssygs2.f.

🦋 zhegs2 — the COMPLEX*16 one 🦋

subroutine zhegs2 (integer itype, character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb, integer info)

ZHEGS2 reduces a Hermitian definite generalized eigenproblem to standard form, using the factorization results obtained from cpotrf (unblocked algorithm). 💖

✨ Purpose ✨

🎀 Parameters 🎀

Okay bestie, this is the part where we meet the whole cast 💅 every single one of them matters, no skipping.

  • ITYPE — ITYPE is INTEGER. Think of it as the "which flavor of problem are we solving" switch:
    • = 1: compute inv(U**H)*A*inv(U) or inv(L)*A*inv(L**H)
    • = 2 or 3: compute U*A*U**H or L**H *A*L
  • UPLO — UPLO is CHARACTER*1. This one tells us whether the upper or lower triangular chunk of the Hermitian matrix A is the part actually stored, and like, also how B got factorized. Two moods only:
    • = 'U': Upper triangular
    • = 'L': Lower triangular
  • N — N is INTEGER. The order of the matrices A and B. Constraint era: N >= 0. 🫶
  • A — A is COMPLEX*16 array, dimension (LDA,N). On entry, this is the Hermitian matrix A, and where the good stuff lives depends on your UPLO:
    • If UPLO = 'U', the leading n by n upper triangular part of A holds the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced (it's giving background character energy, nobody's looking at it 🙈).
    • If UPLO = 'L', the leading n by n lower triangular part of A holds the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced.

On exit, if INFO = 0, you get the transformed matrix, stored in the same format as A. Same fit, new vibe ✨

  • LDA — LDA is INTEGER. The leading dimension of the array A. Rule: LDA >= max(1,N). Not optional, bestie, it's the law 🫡
  • B — B is COMPLEX*16 array, dimension (LDB,N). This is the triangular factor from the Cholesky factorization of B, exactly as returned by ZPOTRF. And listen 👀 B is modified by the routine but restored on exit — so she goes out, has her little main character moment, and comes back exactly as she was. Iconic behavior honestly.
  • LDB — LDB is INTEGER. The leading dimension of the array B. Rule: LDB >= max(1,N). Same energy as LDA, equally non-negotiable 💀
  • INFO — INFO is INTEGER. The vibe check at the end:
    • = 0: successful exit. Slay 🎉
    • < 0: if INFO = -i, the i-th argument had an illegal value. So basically it's pointing at whoever misbehaved, and it's telling you which argument. Rude but helpful.

👑 Author

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

Definition at line 127 of file zhegs2.f.

🌸 Author (the meta one) 🌸

Generated automatically by Doxygen for LAPACK from the source code.

And that's the whole page, bestie!! 🦋 You made it to the end, I'm so proud 😭 This was LAPACK Version 3.12.0, hegs2(3), and it was generated automatically by Doxygen for LAPACK from the source code — so like, no human wrote that closing bit, the robot did it for us 🤖💖 mwah, go forth and factorize responsibly 🎀✨

📦 where this page comes from