ZTPT02(3)

💅 ZTPT02(3) — Library Functions Manual

okay so bestie, welcome to ZTPT02(3) from the Library Functions Manual. This is the page for the ZTPT02 subroutine, and yes it's lowkey iconic for residual-checking a packed triangular solve ✨.

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🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/TESTING/LIN/ztpt02.f

that's the file path, periodt.

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✨ SYNOPSIS ✨

🧚 Functions/Subroutines

       subroutine ZTPT02 (uplo, trans, diag, n, nrhs, ap, x, ldx, b, ldb, work,
           rwork, resid)
           ZTPT02

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📚 Function/Subroutine Documentation 📚

okay, deep breath, here's the full signature:

   subroutine ZTPT02 (character uplo, character trans, character diag, integer
       n, integer nrhs, complex*16, dimension( * ) ap, complex*16, dimension(
       ldx, * ) x, integer ldx, complex*16, dimension( ldb, * ) b, integer ldb,
       complex*16, dimension( * ) work, double precision, dimension( * ) rwork,
       double precision resid)
       ZTPT02

🎯 Purpose

ZTPT02 computes the residual for the computed solution to a triangular system of linear equations op(A)*X = B, when the triangular matrix A is stored in packed format. The test ratio is the maximum over:

norm(b - op(A)*x) / ( ||op(A)||_1 * norm(x) * EPS ),

where op(A) = A, A**T, or A**H, b is the column of B, x is the solution vector, and EPS is the machine epsilon. That's the whole math vibe 🧮✨.

🎛️ Parameters

Every single param, no cap:

• UPLO — UPLO is CHARACTER*1. Specifies whether the matrix A is upper or lower triangular.
  • = 'U': Upper triangular
  • = 'L': Lower triangular
• TRANS — TRANS is CHARACTER*1. Specifies the operation applied to A.
  • = 'N': A * X = B (No transpose)
  • = 'T': A**T * X = B (Transpose)
  • = 'C': A**H * X = B (Conjugate transpose)
• DIAG — DIAG is CHARACTER*1. Specifies whether or not the matrix A is unit triangular.
  • = 'N': Non-unit triangular
  • = 'U': Unit triangular
• N — N is INTEGER. The order of the matrix A. N >= 0.
• NRHS — NRHS is INTEGER. The number of right hand sides, i.e., the number of columns of the matrices X and B. NRHS >= 0.
• AP — AP is COMPLEX*16 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.

• X — X is COMPLEX*16 array, dimension (LDX,NRHS). The computed solution vectors for the system of linear equations.
• LDX — LDX is INTEGER. The leading dimension of the array X. LDX >= max(1,N).
• B — B is COMPLEX*16 array, dimension (LDB,NRHS). The right hand side vectors for the system of linear equations.
• LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• WORK — WORK is COMPLEX*16 array, dimension (N).
• RWORK — RWORK is DOUBLE PRECISION array, dimension (N).
• RESID — RESID is DOUBLE PRECISION. The maximum over the number of right hand sides of:

norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ).

🫶 Author

shoutout to the institutions behind it:

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

Definition at line 145 of file ztpt02.f.

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👑 Author

Generated automatically by Doxygen for LAPACK from the source code.

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okay bestie, that's the whole page. Signed off with LAPACK Version 3.12.0 and the source path /home/abui...IN/ztpt02.f(3). mwah 💋✨