TESTING/LIN/dtpt03.f(3)

🌸 NAME 🌸

TESTING/LIN/dtpt03.f — hey bestie, this is the manual page for the dtpt03 routine in LAPACK’s TESTING/LIN corner, straight outta the Library Functions Manual 💅

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🦋 SYNOPSIS 🦋

✨ Functions/Subroutines ✨

subroutine dtpt03 (uplo, trans, diag, n, nrhs, ap, scale, cnorm, tscal,
    x, ldx, b, ldb, work, resid)
    DTPT03

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🎀 Function/Subroutine Documentation 🎀

subroutine dtpt03 (character uplo, character trans, character diag, integer
    n, integer nrhs, double precision, dimension( * ) ap, 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)
    DTPT03

💖 Purpose 💖

Okay so DTPT03 computes the residual for the solution to a scaled triangular system of equations A*x = s*b or A'*x = s*b when the triangular matrix A is stored in packed format. Here 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.

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💅 Parameters 💅

• UPLO — CHARACTER*1. Tells whether the matrix A is upper or lower triangular.
  • = 'U': Upper triangular
  • = 'L': Lower triangular
• TRANS — CHARACTER*1. Tells what operation is 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 — CHARACTER*1. Tells whether or not the matrix A is unit triangular.
  • = 'N': Non-unit triangular
  • = 'U': Unit triangular
• N — INTEGER. The order of the matrix A. N >= 0.
• NRHS — INTEGER. The number of right hand sides, i.e., the number of columns of the matrices X and B. NRHS >= 0.
• AP — DOUBLE PRECISION array, dimension (N*(N+1)/2). The upper or lower triangular matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows:

if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
if UPLO = 'L',
   AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.

• SCALE — DOUBLE PRECISION. The scaling factor s used in solving the triangular system.
• CNORM — DOUBLE PRECISION array, dimension (N). The 1-norms of the columns of A, not counting the diagonal.
• TSCAL — DOUBLE PRECISION. The scaling factor used in computing the 1-norms in CNORM. CNORM actually contains the column norms of TSCAL*A.
• X — DOUBLE PRECISION array, dimension (LDX,NRHS). The computed solution vectors for the system of linear equations.
• LDX — INTEGER. The leading dimension of the array X. LDX >= max(1,N).
• B — DOUBLE PRECISION array, dimension (LDB,NRHS). The right hand side vectors for the system of linear equations.
• LDB — INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• WORK — DOUBLE PRECISION array, dimension (N).
• RESID — DOUBLE PRECISION. The maximum over the number of right hand sides of:

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

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👑 Author 👑

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

🧚 Definition at line 🧚

Definition at line 159 of file dtpt03.f.

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🩷 Author 🩷

Generated automatically by Doxygen for LAPACK from the source code.

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That’s the whole page, bestie! Sending you LAPACK Version 3.12.0 vibes and a little wave from <code>TESTING/LIN/dtpt03.f(3)</code>. 💖✨