SSYT21(3)

Welcome to SSYT21(3), bestie! This page lives in the Library Functions Manual, and the source file is /home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/ssyt21.f. Buckle up 💅

✨ NAME ✨

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/EIG/ssyt21.f — the source file for the SSYT21 subroutine, aka the vibe-checker for a symmetric decomposition. 💖

🦋 SYNOPSIS 🦋

Functions/Subroutines

subroutine SSYT21 (itype, uplo, n, kband, a, lda, d, e, u, ldu, v, ldv,
    tau, work, result)
    SSYT21

💖 Function/Subroutine Documentation 💖

subroutine SSYT21 (integer itype, character uplo, integer n, integer kband,
    real, dimension( lda, * ) a, integer lda, real, dimension( * ) d, real,
    dimension( * ) e, real, dimension( ldu, * ) u, integer ldu, real,
    dimension( ldv, * ) v, integer ldv, real, dimension( * ) tau, real,
    dimension( * ) work, real, dimension( 2 ) result)
    SSYT21

🌸 Purpose 🌸

Okay so SSYT21 generally checks a decomposition shaped like this:

A = U S U**T

where **T means transpose, A is symmetric, U is orthogonal, and S is diagonal (if KBAND=0) or symmetric tridiagonal (if KBAND=1). Periodt.

If ITYPE=1, then U is represented as a dense matrix; otherwise U is expressed as a product of Householder transformations, whose vectors are stored in the array [blank in the source] and whose scaling constants are in [blank in the source]. We shall use the letter [blank in the source] to refer to the product of Householder transformations (which should be equal to U). Yes, the source really leaves those names blank — we are not inventing anything 🙈.

Specifically, if ITYPE=1, then:

RESULT(1) = | A - U S U**T | / ( |A| n ulp ) and
RESULT(2) = | I - U U**T | / ( n ulp )

If ITYPE=2, then:

RESULT(1) = | A - V S V**T | / ( |A| n ulp )

If ITYPE=3, then:

RESULT(1) = | I - V U**T | / ( n ulp )

For ITYPE > 1, the transformation U is expressed as a product V = H(1)...H(n-2), where H(j) = I - tau(j) v(j) v(j)**T and each vector v(j) has its first j elements 0 and the remaining n-j elements stored in V(j+1:n,j).

🎀 Parameters 🎀

• ITYPE — ITYPE is INTEGER. Specifies the type of tests to be performed.
  • 1: U expressed as a dense orthogonal matrix: RESULT(1) = | A - U S U**T | / ( |A| n ulp ) and RESULT(2) = | I - U U**T | / ( n ulp )
  • 2: U expressed as a product V of Housholder transformations: RESULT(1) = | A - V S V**T | / ( |A| n ulp )
  • 3: U expressed both as a dense orthogonal matrix and as a product of Housholder transformations: RESULT(1) = | I - V U**T | / ( n ulp )
• UPLO — UPLO is CHARACTER. If UPLO='U', the upper triangle of A and V will be used and the (strictly) lower triangle will not be referenced. If UPLO='L', the lower triangle of A and V will be used and the (strictly) upper triangle will not be referenced.
• N — N is INTEGER. The size of the matrix. If it is zero, SSYT21 does nothing. It must be at least zero.
• KBAND — KBAND is INTEGER. The bandwidth of the matrix. It may only be zero or one. If zero, then S is diagonal, and E is not referenced. If one, then S is symmetric tri-diagonal.
• A — A is REAL array, dimension (LDA, N). The original (unfactored) matrix. It is assumed to be symmetric, and only the upper (UPLO='U') or only the lower (UPLO='L') will be referenced.
• LDA — LDA is INTEGER. The leading dimension of A. It must be at least 1 and at least N.
• D — D is REAL array, dimension (N). The diagonal of the (symmetric tri-) diagonal matrix.
• E — E is REAL array, dimension (N-1). The off-diagonal of the (symmetric tri-) diagonal matrix. E(1) is the (1,2) and (2,1) element, E(2) is the (2,3) and (3,2) element, etc. Not referenced if KBAND=0.
• U — U is REAL array, dimension (LDU, N). If ITYPE=1 or 3, this contains the orthogonal matrix in the decomposition, expressed as a dense matrix. If ITYPE=2, then it is not referenced.
• LDU — LDU is INTEGER. The leading dimension of U. LDU must be at least N and at least 1.
• V — V is REAL array, dimension (LDV, N). If ITYPE=2 or 3, the columns of this array contain the Householder vectors used to describe the orthogonal matrix in the decomposition. If UPLO='L', then the vectors are in the lower triangle, if UPLO='U', then in the upper triangle. NOTE If ITYPE=2 or 3, V is modified and restored. The subdiagonal (if UPLO='L') or the superdiagonal (if UPLO='U') is set to one, and later reset to its original value, during the course of the calculation. If ITYPE=1, then it is neither referenced nor modified.
• LDV — LDV is INTEGER. The leading dimension of V. LDV must be at least N and at least 1.
• TAU — TAU is REAL array, dimension (N). If ITYPE >= 2, then TAU(j) is the scalar factor of v(j) v(j)**T in the Householder transformation H(j) of the product U = H(1)...H(n-2). If ITYPE < 2, then TAU is not referenced.
• WORK — WORK is REAL array, dimension (2*N**2).
• RESULT — RESULT is REAL array, dimension (2). The values computed by the two tests described above. The values are currently limited to 1/ulp, to avoid overflow. RESULT(1) is always modified. RESULT(2) is modified only if ITYPE=1.

🌟 Author 🌟

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

Definition at line 205 of file ssyt21.f.

🌟 Author 🌟

Generated automatically by Doxygen for LAPACK from the source code.

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Catch you later, bestie 🫶 This page is from LAPACK, Version 3.12.0, and the footer path is /home/abui...IG/ssyt21.f(3). No date appears in the footer, so we are not inventing one 🙈💖