TESTING/EIG/sget51.f(3)

💅 TESTING/EIG/sget51.f 💅

okay bestie, this is the Library Functions Manual page for TESTING/EIG/sget51.f — yes, the whole file path is the name, we don't make the rules. It's giving LAPACK testing-core energy. 🦋

✨ NAME ✨

TESTING/EIG/sget51.f — the SGET51 test routine, and honestly that's the whole name section. Short, iconic, no notes. 🎀

🎀 SYNOPSIS 🎀

Functions/Subroutines

subroutine sget51 (itype, n, a, lda, b, ldb, u, ldu, v, ldv, work, result)

SGET51

💖 Function/Subroutine Documentation 💖

subroutine sget51 (integer itype, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, real, dimension( ldu, * ) u, integer ldu, real, dimension( ldv, * ) v, integer ldv, real, dimension( * ) work, real result)

SGET51

🦋 Purpose 🦋

The source doc block has a !> on basically every line — that's just the Fortran doc-comment aesthetic ✨ — but the actual tea is this: SGET51 generally checks a decomposition of the form

A = U B V'

where ' means transpose and U and V are orthogonal. No cap. 💅

Specifically, if ITYPE=1:

RESULT = | A - U B V' | / ( |A| n ulp )

If ITYPE=2, then:

RESULT = | A - B | / ( |A| n ulp )

If ITYPE=3, then:

RESULT = | I - UU' | / ( n ulp )

That's the whole vibe check. 🫶

🌸 Parameters 🌸

• ITYPE — ITYPE is INTEGER. It specifies the type of tests to be performed. The levels are:
  • =1: RESULT = | A - U B V' | / ( |A| n ulp )
  • =2: RESULT = | A - B | / ( |A| n ulp )
  • =3: RESULT = | I - UU' | / ( n ulp )
• N — N is INTEGER. It's the size of the matrix. If it is zero, SGET51 does nothing (respectfully, it clocks out). It must be at least zero.
• A — A is a REAL array, dimension (LDA, N). It's the original (unfactored) matrix.
• LDA — LDA is INTEGER. It's the leading dimension of A. It must be at least 1 and at least N.
• B — B is a REAL array, dimension (LDB, N). It's the factored matrix.
• LDB — LDB is INTEGER. It's the leading dimension of B. It must be at least 1 and at least N.
• U — U is a REAL array, dimension (LDU, N). It's the orthogonal matrix on the left-hand side in the decomposition. Not referenced if ITYPE=2.
• LDU — LDU is INTEGER. It's the leading dimension of U. LDU must be at least N and at least 1.
• V — V is a REAL array, dimension (LDV, N). It's the orthogonal matrix on the left-hand side in the decomposition. Not referenced if ITYPE=2.
• LDV — LDV is INTEGER. It's the leading dimension of V. LDV must be at least N and at least 1.
• WORK — WORK is a REAL array, dimension (2*N**2).
• RESULT — RESULT is REAL. These are the values computed by the test specified by ITYPE. The value is currently limited to 1/ulp, to avoid overflow. Errors are flagged by RESULT=10/ulp.

👑 Author 👑

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

Definition at line 147 of file sget51.f.

🧚 Author 🧚

Generated automatically by Doxygen for LAPACK from the source code. Doxygen really said “I’ll do it myself.” 😭

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okay bestie, that's the page 💖 source/version: LAPACK Version 3.12.0; footer page: TESTING/EIG/sget51.f(3). The footer date is not listed, so I'm not inventing one — we don't do fanfic facts here. Bye 🫶✨