DSPOSV(3)

💖 DSPOSV(3) — LAPACK Library Functions Manual 💖

🌸 NAME 🌸

/home/abuild/rpmbuild/BUILD/lapack-static-3.12.0-build/lapack-3.12.0/SRC/dsposv.f — bestie, this is the full source-file path for DSPOSV, the LAPACK routine that solves a real linear system A * X = B for PO matrices. The path is literally giving main-character energy in the NAME section. 💅

✨ SYNOPSIS ✨

🧚 Functions/Subroutines

subroutine DSPOSV (uplo, n, nrhs, a, lda, b, ldb, x, ldx, work, swork, iter, info)

DSPOSV computes the solution to system of linear equations A * X = B for PO matrices

🦋 Function/Subroutine Documentation 🦋

subroutine DSPOSV (character uplo, integer n, integer nrhs, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( ldx, * ) x, integer ldx, double precision, dimension( n, * ) work, real, dimension( * ) swork, integer iter, integer info)

DSPOSV computes the solution to system of linear equations A * X = B for PO matrices

🎯 Purpose

Okay so DSPOSV computes the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric positive definite matrix and X and B are N-by-NRHS matrices. 💖

First it attempts to factorize the matrix in SINGLE PRECISION and use that factorization inside an iterative refinement procedure to produce a solution with DOUBLE PRECISION normwise backward error quality (see below). If the approach fails, the method switches to a DOUBLE PRECISION factorization and solve. ✨

The iterative refinement is not going to be a winning strategy if the ratio of SINGLE PRECISION performance over DOUBLE PRECISION performance is too small. A reasonable strategy should take the number of right-hand sides and the size of the matrix into account. This might be done with a call to ILAENV in the future. Up to now, we always try iterative refinement. 👑

The iterative refinement process is stopped if

ITER > ITERMAX

or for all the RHS we have:

RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX

where

• ITER is the number of the current iteration in the iterative refinement process
• RNRM is the infinity-norm of the residual
• XNRM is the infinity-norm of the solution
• ANRM is the infinity-operator-norm of the matrix A
• EPS is the machine epsilon returned by DLAMCH('Epsilon')

The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00 respectively. 🎀

🧚 Parameters

• UPLO — UPLO is CHARACTER*1
  • = 'U': Upper triangle of A is stored;
  • = 'L': Lower triangle of A is stored.
• N — N is INTEGER
  • The number of linear equations, i.e., 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 matrix B. NRHS >= 0. 🌸
• A — A is DOUBLE PRECISION array, dimension (LDA,N)
  • On entry, the symmetric matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced.
  • On exit, if iterative refinement has been successfully used (INFO = 0 and ITER >= 0, see description below), then A is unchanged. If double precision factorization has been used (INFO = 0 and ITER < 0, see description below), then the array A contains the factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T. 💜
• LDA — LDA is INTEGER
  • The leading dimension of the array A. LDA >= max(1,N). ✨
• B — B is DOUBLE PRECISION array, dimension (LDB,NRHS)
  • The N-by-NRHS right hand side matrix B. 🫶
• LDB — LDB is INTEGER
  • The leading dimension of the array B. LDB >= max(1,N). 🎀
• X — X is DOUBLE PRECISION array, dimension (LDX,NRHS)
  • If INFO = 0, the N-by-NRHS solution matrix X. 🌈
• LDX — LDX is INTEGER
  • The leading dimension of the array X. LDX >= max(1,N). ⭐
• WORK — WORK is DOUBLE PRECISION array, dimension (N,NRHS)
  • This array is used to hold the residual vectors. 🧚
• SWORK — SWORK is REAL array, dimension (N*(N+NRHS))
  • This array is used to use the single precision matrix and the right-hand sides or solutions in single precision. 💅
• ITER — ITER is INTEGER
  • < 0: iterative refinement has failed, double precision factorization has been performed
    • -1 : the routine fell back to full precision for implementation- or machine-specific reasons
    • -2 : narrowing the precision induced an overflow, the routine fell back to full precision
    • -3 : failure of SPOTRF
    • -31: stop the iterative refinement after the 30th iterations
  • > 0: iterative refinement has been successfully used. Returns the number of iterations 🔥
• INFO — INFO is INTEGER
  • = 0: successful exit
  • < 0: if INFO = -i, the i-th argument had an illegal value
  • > 0: if INFO = i, the leading principal minor of order i of (DOUBLE PRECISION) A is not positive, so the factorization could not be completed, and the solution has not been computed. 💀

🫶 Author

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

Definition at line 197 of file dsposv.f. 🌸

🌈 Author

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

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Okay bestie, that's the whole DSPOSV tea ☕💖. Cute sign-off from the footer: LAPACK, Version 3.12.0, and /home/abui...RC/dsposv.f(3) — that's the source/version and the footer as printed, no separate date shown. Slay. 💅✨