TESTING/EIG/dsgt01.f(3)

📦
version 3.12.1 · 3 versions
, in arch rolling

💖 NAME 💖

TESTING/EIG/dsgt01.f — okay bestie, you found the page for TESTING/EIG/dsgt01.f(3) in the Library Functions Manual. It’s giving one Fortran file, one subroutine, and a whole lot of eigenproblem energy. The subroutine is dsgt01, and yes, we’re keeping every detail. 🎀

✨ SYNOPSIS ✨

🦋 Functions/Subroutines 🦋

subroutine dsgt01 (itype, uplo, n, m, a, lda, b, ldb, z, ldz, d, work,
    result)
    DSGT01

DSGT01 is literally right there in the synopsis, bestie. 💅

🌸 Function/Subroutine Documentation 🌸

subroutine dsgt01 (integer itype, character uplo, integer n, integer m,
    double precision, dimension( lda, * ) a, integer lda, double precision,
    dimension( ldb, * ) b, integer ldb, double precision, dimension( ldz, *
    ) z, integer ldz, double precision, dimension( * ) d, double precision,
    dimension( * ) work, double precision, dimension( * ) result)

DSGT01

🔥 Purpose 🔥

Okay so the purpose block says DDGT01 checks a decomposition of the form:

A Z   =  B Z D or
A B Z =  Z D or
B A Z =  Z D

where A is a symmetric matrix, B is symmetric positive definite, Z is orthogonal, and D is diagonal. No cap. 🫶

One of the following test ratios is computed:

ITYPE = 1:  RESULT(1) = | A Z - B Z D | / ( |A| |Z| n ulp )

ITYPE = 2:  RESULT(1) = | A B Z - Z D | / ( |A| |Z| n ulp )

ITYPE = 3:  RESULT(1) = | B A Z - Z D | / ( |A| |Z| n ulp )

🌈 Parameters 🌈

  • ITYPE — ITYPE is INTEGER. It’s the form of the symmetric generalized eigenproblem:
= 1:  A*z = (lambda)*B*z
= 2:  A*B*z = (lambda)*z
= 3:  B*A*z = (lambda)*z
  • UPLO — UPLO is CHARACTER*1. It specifies whether the upper or lower triangular part of the symmetric matrices A and B is stored. = 'U': Upper triangular, = 'L': Lower triangular.
  • N — N is INTEGER. The order of the matrix A. N >= 0.
  • M — M is INTEGER. The number of eigenvalues found. 0 <= M <= N.
  • A — A is DOUBLE PRECISION array, dimension (LDA, N). The original symmetric matrix 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 original symmetric positive definite matrix B.
  • LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N).
  • Z — Z is DOUBLE PRECISION array, dimension (LDZ, M). The computed eigenvectors of the generalized eigenproblem.
  • LDZ — LDZ is INTEGER. The leading dimension of the array Z. LDZ >= max(1,N).
  • D — D is DOUBLE PRECISION array, dimension (M). The computed eigenvalues of the generalized eigenproblem.
  • WORK — WORK is DOUBLE PRECISION array, dimension (N*N)
  • RESULT — RESULT is DOUBLE PRECISION array, dimension (1). The test ratio as described above.

👑 Author 👑

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

Definition at line 144 of file dsgt01.f.

💫 Author 💫

Generated automatically by Doxygen for LAPACK from the source code.

That’s the whole manual page, bestie — LAPACK Version 3.12.0, TESTING/EIG/dsgt01.f(3), and all the eigenproblem tea. Slay and stay orthogonal. 💖✨

📦 where this page comes from