SRC/dsygs2.f(3)

✨ SRC/dsygs2.f ✨

okay so bestie, we're in the Library Functions Manual today and this one is literally the girl who does the glow-up transformation on your generalized eigenproblem 💅 (also hi, this page is SRC/dsygs2.f, manual name checked, moving on)

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🌸 SYNOPSIS 🌸

Functions/Subroutines

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). no cap, that's the whole job 🫶

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🦋 Function/Subroutine Documentation 🦋

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.
!>

so like, it takes your spicy generalized problem and makes it a standard one, main character energy for the eigenproblem fr fr 🔥

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🎀 Parameters 🎀

ITYPE

!>          ITYPE is 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

!>          UPLO is 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

!>          N is INTEGER
!>          The order of the matrices A and B.  N >= 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 transformed matrix, stored in the
!>          same format as A.
!>

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,N).
!>

B

!>          B is DOUBLE PRECISION array, dimension (LDB,N)
!>          The triangular factor from the Cholesky factorization of B,
!>          as returned by DPOTRF.
!>

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.
!>

⚠️ heads up bestie: if INFO comes back negative it's giving "one of your arguments is sus" — specifically INFO = -i means the i-th argument had an illegal value. that's on you, not on her 🙈

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👑 Author 👑

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 126 of file dsygs2.f.

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🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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💖 and that's the whole page bestie — this iconic little write-up is from LAPACK, Version 3.12.0, signed, sealed, and auto-generated with love. slay, go transform some matrices, periodt ✨🎀🦋