TESTING/LIN/spbt01.f(3)

🩰 TESTING/LIN/spbt01.f

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🌸 NAME

TESTING/LIN/spbt01.f

✨ SYNOPSIS

🔥 Functions/Subroutines

       subroutine spbt01 (uplo, n, kd, a, lda, afac, ldafac, rwork, resid)
           SPBT01

💖 Function/Subroutine Documentation

   subroutine spbt01 (character uplo, integer n, integer kd, real, dimension(
       lda, * ) a, integer lda, real, dimension( ldafac, * ) afac, integer
       ldafac, real, dimension( * ) rwork, real resid)
       SPBT01

🎀 Purpose

SPBT01 reconstructs a symmetric positive definite band matrix A from its L*L' or U'*U factorization and computes the residual:

norm( L*L' - A ) / ( N * norm(A) * EPS ) or
norm( U'*U - A ) / ( N * norm(A) * EPS )

where EPS is the machine epsilon, L' is the conjugate transpose of L, and U' is the conjugate transpose of U. ✨

🌈 Parameters

• UPLO — UPLO is CHARACTER*1. It tells you whether the upper or lower triangular part of the symmetric 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.
• A — A is REAL array, dimension (LDA,N). The original symmetric 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 SPBTRF for further details.
• LDA — LDA is INTEGER. The leading dimension of the array A. LDA >= max(1,KD+1).
• AFAC — AFAC is REAL array, dimension (LDAFAC,N). The factored form of the matrix A. AFAC contains the factor L or U from the L*L' or U'*U factorization in band storage format, as computed by SPBTRF.
• LDAFAC — LDAFAC is INTEGER. The leading dimension of the array AFAC. LDAFAC >= max(1,KD+1).
• RWORK — RWORK is REAL array, dimension (N).
• RESID — RESID is REAL. If UPLO = 'L', norm(L*L' - A) / ( N * norm(A) * EPS ). If UPLO = 'U', norm(U'*U - A) / ( N * norm(A) * EPS ).

👑 Author

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

Definition at line 117 of file spbt01.f.

🧚 Author

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