TESTING/LIN/cpbt02.f(3)

🎀 TESTING/LIN/cpbt02.f 🎀

okay so bestie, this is the TESTING/LIN/cpbt02.f page from the Library Functions Manual. It’s giving tiny subroutine, big residual energy, and we are going to go through every single bit. 💅✨

✨ NAME ✨

TESTING/LIN/cpbt02.f — that’s the page name, and the main character is the cpbt02 routine. No cap. 👑

🌸 SYNOPSIS 🌸

💖 Functions/Subroutines 💖

• subroutine cpbt02 (uplo, n, kd, nrhs, a, lda, x, ldx, b, ldb, rwork, resid) — CPBT02.

🦋 Function/Subroutine Documentation 🦋

Here’s the full signature, bestie — copy it exactly, okay? 🫶

subroutine cpbt02 (character uplo, integer n, integer kd, integer nrhs,
     complex, dimension( lda, * ) a, integer lda, complex, dimension( ldx, *
     ) x, integer ldx, complex, dimension( ldb, * ) b, integer ldb, real,
     dimension( * ) rwork, real resid)

CPBT02

🎯 Purpose 🎯

CPBT02 computes the residual for a solution of a Hermitian banded system of equations A*x = b:

RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS)

where EPS is the machine precision. Slay, that’s the whole point. ✨

🧚 Parameters 🧚

• UPLO — UPLO is CHARACTER*1. Tells you whether the upper or lower triangular part of the Hermitian matrix A is stored:
  • = 'U': Upper triangular
  • = 'L': Lower triangular
• N — N is INTEGER. The number of rows and columns of the matrix A. N >= 0.
• KD — KD is INTEGER. The number of super-diagonals of the matrix A if UPLO = 'U', or the number of sub-diagonals if UPLO = 'L'. KD >= 0.
• NRHS — NRHS is INTEGER. The number of right hand sides. NRHS >= 0.
• A — A is COMPLEX array, dimension (LDA,N). The original Hermitian band matrix A. If UPLO = 'U', the upper triangular part of A is stored as a band matrix; if UPLO = 'L', the lower triangular part of A is stored. The columns of the appropriate triangle are stored in the columns of A and the diagonals of the triangle are stored in the rows of A. See CPBTRF for further details.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,KD+1).
• X — X is COMPLEX 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 array, dimension (LDB,NRHS). On entry, the right hand side vectors for the system of linear equations. On exit, B is overwritten with the difference B - A*X.
• LDB — LDB is INTEGER. The leading dimension of the array B. LDB >= max(1,N).
• RWORK — RWORK is REAL array, dimension (N)
• RESID — RESID is REAL. The maximum over the number of right hand sides of norm(B - A*X) / ( norm(A) * norm(X) * EPS ).

👑 Author 👑

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

Definition at line 134 of file cpbt02.f.

👑 Author 👑

Generated automatically by Doxygen for LAPACK from the source code.

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