TESTING/EIG/ssgt01.f(3)

💖 TESTING/EIG/ssgt01.f

okay bestie, this page comes from the Library Functions Manual, and it's literally all about TESTING/EIG/ssgt01.f — that's the whole vibe. 🎀

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🌸 NAME

TESTING/EIG/ssgt01.f

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✨ SYNOPSIS

🫶 Functions/Subroutines

subroutine ssgt01 (itype, uplo, n, m, a, lda, b, ldb, z, ldz, d, work,
    result)

SSGT01

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💅 Function/Subroutine Documentation

subroutine ssgt01 (integer itype, character uplo, integer n, integer m,
    real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b,
    integer ldb, real, dimension( ldz, * ) z, integer ldz, real, dimension(
    * ) d, real, dimension( * ) work, real, dimension( * ) result)

SSGT01

🧚 Purpose

okay so SSGT01 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.

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; this is 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; 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 REAL 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 REAL 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 REAL 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 REAL array, dimension (M); the computed eigenvalues of the generalized eigenproblem.
• WORK — WORK is REAL array, dimension (N*N).
• RESULT — RESULT is REAL 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 ssgt01.f.

🦋 Author

Generated automatically by Doxygen for LAPACK from the source code.

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