TESTING/LIN/dtrt03.f(3)

🎀 TESTING/LIN/dtrt03.f(3) 🎀

hey bestie, welcome to the TESTING/LIN/dtrt03.f(3) page from the Library Functions Manual. it’s giving “LAPACK test routine with main character energy,” and we’re gonna get through every detail together, no cap. 💖

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🌸 NAME 🌸

TESTING/LIN/dtrt03.f — yes, that’s the file, bestie. iconic name, zero notes. 💅

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✨ SYNOPSIS ✨

🎀 Functions/Subroutines 🎀

       subroutine dtrt03 (uplo, trans, diag, n, nrhs, a, lda, scale, cnorm,
           tscal, x, ldx, b, ldb, work, resid)
           DTRT03

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💖 Function/Subroutine Documentation 💖

   subroutine dtrt03 (character uplo, character trans, character diag, integer
       n, integer nrhs, double precision, dimension( lda, * ) a, integer lda,
       double precision scale, double precision, dimension( * ) cnorm, double
       precision tscal, double precision, dimension( ldx, * ) x, integer ldx,
       double precision, dimension( ldb, * ) b, integer ldb, double precision,
       dimension( * ) work, double precision resid)
       DTRT03

okay so, DTRT03 is the routine name, and it’s literally right there at the end. 🫶

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🦋 Purpose 🦋

DTRT03 computes the residual for the solution to a scaled triangular system of equations. The two vibes are:

A*x = s*b  or  A'*x = s*b

Here A is a triangular matrix, A' is the transpose of A, s is a scalar, and x and b are N by NRHS matrices. 🌈

The test ratio is the maximum over the number of right hand sides of:

norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),

where op(A) denotes A or A' and EPS is the machine epsilon. periodt. 💫

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🌈 Parameters 🌈

💅 UPLO 💅

UPLO is CHARACTER*1. It specifies whether the matrix A is upper or lower triangular:

• = 'U': Upper triangular
• = 'L': Lower triangular

💅 TRANS 💅

TRANS is CHARACTER*1. It specifies the operation applied to A:

• = 'N': A *x = s*b (No transpose)
• = 'T': A'*x = s*b (Transpose)
• = 'C': A'*x = s*b (Conjugate transpose = Transpose)

💅 DIAG 💅

DIAG is CHARACTER*1. It specifies whether or not the matrix A is unit triangular:

• = 'N': Non-unit triangular
• = 'U': Unit triangular

💅 N 💅

N is INTEGER. It’s the order of the matrix A. And the rule is: N >= 0. ✨

💅 NRHS 💅

NRHS is INTEGER. It’s the number of right hand sides, i.e., the number of columns of the matrices X and B. And: NRHS >= 0. 🦋

💅 A 💅

A is a DOUBLE PRECISION array, dimension (LDA,N). It’s the triangular matrix A, bestie. Here’s the tea:

• If UPLO = 'U', the leading n by n upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced.
• If UPLO = 'L', the leading n by n lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced.
• If DIAG = 'U', the diagonal elements of A are also not referenced and are assumed to be 1.

💅 LDA 💅

LDA is INTEGER. It’s the leading dimension of the array A. The rule: LDA >= max(1,N). 💀 do not mess this up.

💅 SCALE 💅

SCALE is DOUBLE PRECISION. It’s the scaling factor s used in solving the triangular system. 🌸

💅 CNORM 💅

CNORM is a DOUBLE PRECISION array, dimension (N). It holds the 1-norms of the columns of A, not counting the diagonal. 👑

💅 TSCAL 💅

TSCAL is DOUBLE PRECISION. It’s the scaling factor used in computing the 1-norms in CNORM. And just so you know: CNORM actually contains the column norms of TSCAL*A. 🫶

💅 X 💅

X is a DOUBLE PRECISION array, dimension (LDX,NRHS). It’s the computed solution vectors for the system of linear equations. ✨

💅 LDX 💅

LDX is INTEGER. It’s the leading dimension of the array X. The rule: LDX >= max(1,N). 💖

💅 B 💅

B is a DOUBLE PRECISION array, dimension (LDB,NRHS). It’s the right hand side vectors for the system of linear equations. 🌈

💅 LDB 💅

LDB is INTEGER. It’s the leading dimension of the array B. The rule: LDB >= max(1,N). 🎀

💅 WORK 💅

WORK is a DOUBLE PRECISION array, dimension (N). that’s the whole description, bestie — no extra lore. 🫡

💅 RESID 💅

RESID is DOUBLE PRECISION. It’s the maximum over the number of right hand sides of:

norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).

literally the residual moment. 🔥

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👑 Author 👑

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

Definition at line 167 of file dtrt03.f. 📌

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🫶 Author 🫶

Generated automatically by Doxygen for LAPACK from the source code. 🤖✨

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okay that’s the whole page, bestie — source/version sign-off: LAPACK, Version 3.12.0, and the page is TESTING/LIN/dtrt03.f(3). slay, and good luck with those residuals 💅💖🎀