TESTING/EIG/ssyt22.f(3)

okay bestie, this is the TESTING/EIG/ssyt22.f page from the Library Functions Manual, and it’s giving extremely specific Fortran test-subroutine energy. buckle up 💅

🌸 NAME 🌸

TESTING/EIG/ssyt22.f

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✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

subroutine ssyt22 (itype, uplo, n, m, kband, a, lda, d, e, u, ldu, v,
     ldv, tau, work, result)

SSYT22 — that’s the routine, no cap.

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🦋 Function/Subroutine Documentation 🦋

subroutine ssyt22 (integer itype, character uplo, integer n, integer m, 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)

subroutine ssyt22 (integer itype, character uplo, integer n, integer m,
     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)

SSYT22

💖 Purpose 💖

okay so SSYT22 generally checks a decomposition of the form

A U = U S

where A is symmetric, the columns of U are orthonormal, and S is diagonal (if KBAND=0) or symmetric tridiagonal (if KBAND=1). If ITYPE=1, then U is represented as a dense matrix, otherwise the U is expressed as a product of Householder transformations, whose vectors are stored in the array and whose scaling constants are in — the source then literally says “we shall use the letter” to refer to the product of Householder transformations (which should be equal to U).

Specifically, if ITYPE=1, then:

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

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okay, parameter time. every single one, exactly as written:

• ITYPE — 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 )

• UPLO — CHARACTER. If UPLO='U', the upper triangle of A will be used and the (strictly) lower triangle will not be referenced. If UPLO='L', the lower triangle of A will be used and the (strictly) upper triangle will not be referenced. Not modified.
• N — INTEGER. The size of the matrix. If it is zero, SSYT22 does nothing. It must be at least zero. Not modified.
• M — INTEGER. The number of columns of U. If it is zero, SSYT22 does nothing. It must be at least zero. Not modified.
• KBAND — 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. Not modified.
• A — 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. Not modified.
• LDA — INTEGER. The leading dimension of A. It must be at least 1 and at least N. Not modified.
• D — REAL array, dimension (N). The diagonal of the (symmetric tri-) diagonal matrix. Not modified.
• E — REAL array, dimension (N). The off-diagonal of the (symmetric tri-) diagonal matrix. E(1) is ignored, E(2) is the (1,2) and (2,1) element, etc. Not referenced if KBAND=0. Not modified.
• U — 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. Not modified.
• LDU — INTEGER. The leading dimension of U. LDU must be at least N and at least 1. Not modified.
• V — REAL array, dimension (LDV, N). If ITYPE=2 or 3, the lower triangle of this array contains the Householder vectors used to describe the orthogonal matrix in the decomposition. If ITYPE=1, then it is not referenced. Not modified.
• LDV — INTEGER. The leading dimension of V. LDV must be at least N and at least 1. Not modified.
• TAU — 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. Not modified.
• WORK — REAL array, dimension (2*N**2). Workspace. Modified.
• RESULT — 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 LDU is at least N. Modified.

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👑 Author 👑

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

Definition at line 155 of file ssyt22.f.

🌈 Author 🌈

Generated automatically by Doxygen for LAPACK from the source code.

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xoxo, bestie 💖 — source/version: LAPACK, Version 3.12.0; footer page tag: TESTING/EIG/ssyt22.f(3). periodt.