ppcon(3)

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🎀 ppcon(3) — Library Functions Manual 💅

Okay bestie, welcome to ppcon(3) — the condition number estimate page. It’s giving linear algebra, it’s giving Cholesky factorization, and it’s honestly iconic ✨

🌸 NAME

ppcon — ppcon: condition number estimate 💖

✨ SYNOPSIS

📚 Functions

subroutine cppcon (uplo, n, ap, anorm, rcond, work, rwork, info)
    CPPCON
subroutine dppcon (uplo, n, ap, anorm, rcond, work, iwork, info)
    DPPCON
subroutine sppcon (uplo, n, ap, anorm, rcond, work, iwork, info)
    SPPCON
subroutine zppcon (uplo, n, ap, anorm, rcond, work, rwork, info)
    ZPPCON

🔍 Detailed Description

No extra description lives here, bestie — the full deets are in the function docs right below 👇💖

💖 Function Documentation

💅 subroutine cppcon — CPPCON

subroutine cppcon (character uplo, integer n, complex, dimension( * ) ap,
    real anorm, real rcond, complex, dimension( * ) work, real, dimension( *
    ) rwork, integer info)

CPPCON

Purpose

CPPCON estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite packed matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by CPPTRF 🔥

An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as:

RCOND = 1 / (ANORM * norm(inv(A)))

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 order of the matrix A. N >= 0 ✨
  • AP — AP is COMPLEX array, dimension (N*(N+1)/2). The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, packed columnwise in a linear array. The j-th column of U or L is stored in the array AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
  • ANORM — ANORM is REAL; the 1-norm (or infinity-norm) of the Hermitian matrix A 🦋
  • RCOND — RCOND is REAL; the reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine 💖
  • WORK — WORK is COMPLEX array, dimension (2*N) 🌸
  • RWORK — RWORK is REAL array, dimension (N) 🎀
  • INFO — INFO is INTEGER; = 0: successful exit; < 0: if INFO = -i, the i-th argument had an illegal value 👑

Author

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

Definition: at line 117 of file cppcon.f.

💅 subroutine dppcon — DPPCON

subroutine dppcon (character uplo, integer n, double precision, dimension( *
    ) ap, double precision anorm, double precision rcond, double precision,
    dimension( * ) work, integer, dimension( * ) iwork, integer info)

DPPCON

Purpose

DPPCON estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite packed matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by DPPTRF 🔥

An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as:

RCOND = 1 / (ANORM * norm(inv(A)))

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 order of the matrix A. N >= 0 ✨
  • AP — AP is DOUBLE PRECISION array, dimension (N*(N+1)/2). The triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, packed columnwise in a linear array. The j-th column of U or L is stored in the array AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
  • ANORM — ANORM is DOUBLE PRECISION; the 1-norm (or infinity-norm) of the symmetric matrix A 🦋
  • RCOND — RCOND is DOUBLE PRECISION; the reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine 💖
  • WORK — WORK is DOUBLE PRECISION array, dimension (3*N) 🌸
  • IWORK — IWORK is INTEGER array, dimension (N) 🎀
  • INFO — INFO is INTEGER; = 0: successful exit; < 0: if INFO = -i, the i-th argument had an illegal value 👑

Author

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

Definition: at line 117 of file dppcon.f.

💅 subroutine sppcon — SPPCON

subroutine sppcon (character uplo, integer n, real, dimension( * ) ap, real
    anorm, real rcond, real, dimension( * ) work, integer, dimension( * )
    iwork, integer info)

SPPCON

Purpose

SPPCON estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite packed matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPPTRF 🔥

An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as:

RCOND = 1 / (ANORM * norm(inv(A)))

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 order of the matrix A. N >= 0 ✨
  • AP — AP is REAL array, dimension (N*(N+1)/2). The triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, packed columnwise in a linear array. The j-th column of U or L is stored in the array AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
  • ANORM — ANORM is REAL; the 1-norm (or infinity-norm) of the symmetric matrix A 🦋
  • RCOND — RCOND is REAL; the reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine 💖
  • WORK — WORK is REAL array, dimension (3*N) 🌸
  • IWORK — IWORK is INTEGER array, dimension (N) 🎀
  • INFO — INFO is INTEGER; = 0: successful exit; < 0: if INFO = -i, the i-th argument had an illegal value 👑

Author

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

Definition: at line 117 of file sppcon.f.

💅 subroutine zppcon — ZPPCON

subroutine zppcon (character uplo, integer n, complex*16, dimension( * ) ap,
    double precision anorm, double precision rcond, complex*16, dimension( *
    ) work, double precision, dimension( * ) rwork, integer info)

ZPPCON

Purpose

ZPPCON estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian positive definite packed matrix using the Cholesky factorization A = U**H*U or A = L*L**H computed by ZPPTRF 🔥

An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as:

RCOND = 1 / (ANORM * norm(inv(A)))

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 order of the matrix A. N >= 0 ✨
  • AP — AP is COMPLEX*16 array, dimension (N*(N+1)/2). The triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, packed columnwise in a linear array. The j-th column of U or L is stored in the array AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
  • ANORM — ANORM is DOUBLE PRECISION; the 1-norm (or infinity-norm) of the Hermitian matrix A 🦋
  • RCOND — RCOND is DOUBLE PRECISION; the reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine 💖
  • WORK — WORK is COMPLEX*16 array, dimension (2*N) 🌸
  • RWORK — RWORK is DOUBLE PRECISION array, dimension (N) 🎀
  • INFO — INFO is INTEGER; = 0: successful exit; < 0: if INFO = -i, the i-th argument had an illegal value 👑

Author

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

Definition: at line 117 of file zppcon.f.

👑 Author

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