la_porcond(3)

📦

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💅 `la_porcond(3)` — Skeel condition number estimate 💅

Okay bestie, welcome to la_porcond(3) from the Library Functions Manual. This page is the whole la_porcond situation: Skeel condition number estimate energy. It's a family of routines, and we're about to go through them one by one. 🫶

💖 NAME 💖

la_porcond — la_porcond: Skeel condition number estimate

✨ SYNOPSIS ✨

Functions

real function cla_porcond_c (uplo, n, a, lda, af, ldaf, c, capply, info, work, rwork) — CLA_PORCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian positive-definite matrices.
real function cla_porcond_x (uplo, n, a, lda, af, ldaf, x, info, work, rwork) — CLA_PORCOND_X computes the infinity norm condition number of op(A)*diag(x) for Hermitian positive-definite matrices.
double precision function dla_porcond (uplo, n, a, lda, af, ldaf, cmode, c, info, work, iwork) — DLA_PORCOND estimates the Skeel condition number for a symmetric positive-definite matrix.
real function sla_porcond (uplo, n, a, lda, af, ldaf, cmode, c, info, work, iwork) — SLA_PORCOND estimates the Skeel condition number for a symmetric positive-definite matrix.
double precision function zla_porcond_c (uplo, n, a, lda, af, ldaf, c, capply, info, work, rwork) — ZLA_PORCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian positive-definite matrices.
double precision function zla_porcond_x (uplo, n, a, lda, af, ldaf, x, info, work, rwork) — ZLA_PORCOND_X computes the infinity norm condition number of op(A)*diag(x) for Hermitian positive-definite matrices.

🌸 Detailed Description 🌸

This is the detailed docs zone, bestie. The function-by-function breakdown starts right below. 💖

🦋 Function Documentation 🦋

`cla_porcond_c` — `real function`

real function cla_porcond_c (character uplo, integer n, complex, dimension(
     lda, * ) a, integer lda, complex, dimension( ldaf, * ) af, integer ldaf,
     real, dimension( * ) c, logical capply, integer info, complex,
     dimension( * ) work, real, dimension( * ) rwork)

CLA_PORCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian positive-definite matrices.

Purpose

CLA_PORCOND_C computes the infinity norm condition number of op(A) * inv(diag(C)) where C is a REAL vector.

Parameters

UPLO — CHARACTER*1; = 'U': upper triangle of A is stored; = 'L': lower triangle of A is stored.
N — INTEGER; the number of linear equations, i.e., the order of the matrix A. N >= 0.
A — COMPLEX array, dimension (LDA,N); on entry, the N-by-N matrix A.
LDA — INTEGER; the leading dimension of the array A. LDA >= max(1,N).
AF — COMPLEX array, dimension (LDAF,N); the triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, as computed by CPOTRF.
LDAF — INTEGER; the leading dimension of the array AF. LDAF >= max(1,N).
C — REAL array, dimension (N); the vector C in the formula op(A) * inv(diag(C)).
CAPPLY — LOGICAL; if .TRUE. then access the vector C in the formula above.
INFO — INTEGER; = 0: successful exit; i > 0: the ith argument is invalid.
WORK — COMPLEX array, dimension (2*N); workspace.
RWORK — REAL array, dimension (N); workspace.

Author

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

Definition at line 128 of file cla_porcond_c.f.

`cla_porcond_x` — `real function`

real function cla_porcond_x (character uplo, integer n, complex, dimension(
     lda, * ) a, integer lda, complex, dimension( ldaf, * ) af, integer ldaf,
     complex, dimension( * ) x, integer info, complex, dimension( * ) work,
     real, dimension( * ) rwork)

CLA_PORCOND_X computes the infinity norm condition number of op(A)*diag(x) for Hermitian positive-definite matrices.

Purpose

CLA_PORCOND_X computes the infinity norm condition number of op(A) * diag(X) where X is a COMPLEX vector.

Parameters

UPLO — CHARACTER*1; = 'U': upper triangle of A is stored; = 'L': lower triangle of A is stored.
N — INTEGER; the number of linear equations, i.e., the order of the matrix A. N >= 0.
A — COMPLEX array, dimension (LDA,N); on entry, the N-by-N matrix A.
LDA — INTEGER; the leading dimension of the array A. LDA >= max(1,N).
AF — COMPLEX array, dimension (LDAF,N); the triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, as computed by CPOTRF.
LDAF — INTEGER; the leading dimension of the array AF. LDAF >= max(1,N).
X — COMPLEX array, dimension (N); the vector X in the formula op(A) * diag(X).
INFO — INTEGER; = 0: successful exit; i > 0: the ith argument is invalid.
WORK — COMPLEX array, dimension (2*N); workspace.
RWORK — REAL array, dimension (N); workspace.

Author

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

Definition at line 121 of file cla_porcond_x.f.

`dla_porcond` — `double precision function`

double precision function dla_porcond (character uplo, integer n, double
     precision, dimension( lda, * ) a, integer lda, double precision,
     dimension( ldaf, * ) af, integer ldaf, integer cmode, double precision,
     dimension( * ) c, integer info, double precision, dimension( * ) work,
     integer, dimension( * ) iwork)

DLA_PORCOND estimates the Skeel condition number for a symmetric positive-definite matrix.

Purpose

DLA_PORCOND estimates the Skeel condition number of op(A) * op2(C) where op2 is determined by CMODE like this:

CMODE =  1    op2(C) = C
CMODE =  0    op2(C) = I
CMODE = -1    op2(C) = inv(C)

The Skeel condition number cond(A) = norminf( |inv(A)||A| ) is computed by computing scaling factors R such that diag(R)*A*op2(C) is row equilibrated and computing the standard infinity-norm condition number.

Parameters

UPLO — CHARACTER*1; = 'U': upper triangle of A is stored; = 'L': lower triangle of A is stored.
N — INTEGER; the number of linear equations, i.e., the order of the matrix A. N >= 0.
A — DOUBLE PRECISION array, dimension (LDA,N); on entry, the N-by-N matrix A.
LDA — INTEGER; the leading dimension of the array A. LDA >= max(1,N).
AF — DOUBLE PRECISION array, dimension (LDAF,N); the triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, as computed by DPOTRF.
LDAF — INTEGER; the leading dimension of the array AF. LDAF >= max(1,N).
CMODE — INTEGER; determines op2(C) in the formula op(A) * op2(C) as follows:

CMODE =  1    op2(C) = C
CMODE =  0    op2(C) = I
CMODE = -1    op2(C) = inv(C)

C — DOUBLE PRECISION array, dimension (N); the vector C in the formula op(A) * op2(C).
INFO — INTEGER; = 0: successful exit; i > 0: the ith argument is invalid.
WORK — DOUBLE PRECISION array, dimension (3*N); workspace.
IWORK — INTEGER array, dimension (N); workspace.

Author

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

Definition at line 139 of file dla_porcond.f.

`sla_porcond` — `real function`

real function sla_porcond (character uplo, integer n, real, dimension( lda,
     * ) a, integer lda, real, dimension( ldaf, * ) af, integer ldaf, integer
     cmode, real, dimension( * ) c, integer info, real, dimension( * ) work,
     integer, dimension( * ) iwork)

SLA_PORCOND estimates the Skeel condition number for a symmetric positive-definite matrix.

Purpose

SLA_PORCOND estimates the Skeel condition number of op(A) * op2(C) where op2 is determined by CMODE like this:

CMODE =  1    op2(C) = C
CMODE =  0    op2(C) = I
CMODE = -1    op2(C) = inv(C)

Parameters

UPLO — CHARACTER*1; = 'U': upper triangle of A is stored; = 'L': lower triangle of A is stored.
N — INTEGER; the number of linear equations, i.e., the order of the matrix A. N >= 0.
A — REAL array, dimension (LDA,N); on entry, the N-by-N matrix A.
LDA — INTEGER; the leading dimension of the array A. LDA >= max(1,N).
AF — REAL array, dimension (LDAF,N); the triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, as computed by SPOTRF.
LDAF — INTEGER; the leading dimension of the array AF. LDAF >= max(1,N).

`CMODE`

…

CMODE is INTEGER — it determines op2(C) in the formula op(A) * op2(C), like this:

CMODE = 1 → op2(C) = C
CMODE = 0 → op2(C) = I
CMODE = -1 → op2(C) = inv(C)

🍓 `C`

C is REAL array, dimension (N) — literally the vector C in the formula op(A) * op2(C). That's the whole assignment, bestie.

🚨 `INFO`

INFO is INTEGER:

= 0: successful exit ✨
i > 0: the ith argument is invalid — not iconic, but important to know.

🧰 `WORK`

WORK is REAL array, dimension (3*N) — workspace. It's giving "behind the scenes" energy.

🗂️ `IWORK`

IWORK is INTEGER array, dimension (N) — also workspace. Periodt.

👑 Author

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

Definition: at line 138 of file sla_porcond.f.

💖 `zla_porcond_c`

double precision function zla_porcond_c (character uplo, integer n,
     complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension(
     ldaf, * ) af, integer ldaf, double precision, dimension( * ) c, logical
     capply, integer info, complex*16, dimension( * ) work, double precision,
     dimension( * ) rwork)

ZLA_PORCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian positive-definite matrices. It's giving "condition number but make it Cholesky-coded" ✨

🎯 Purpose

ZLA_PORCOND_C Computes the infinity norm condition number of op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector

🧚 Parameters

UPLO — CHARACTER*1: = 'U': upper triangle of A is stored; = 'L': lower triangle of A is stored.
N — INTEGER: the number of linear equations, i.e., the order of the matrix A. N >= 0.
A — COMPLEX*16 array, dimension (LDA,N): on entry, the N-by-N matrix A.
LDA — INTEGER: the leading dimension of the array A. LDA >= max(1,N).
AF — COMPLEX*16 array, dimension (LDAF,N): the triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, as computed by ZPOTRF.
LDAF — INTEGER: the leading dimension of the array AF. LDAF >= max(1,N).
C — DOUBLE PRECISION array, dimension (N): the vector C in the formula op(A) * inv(diag(C)).
CAPPLY — LOGICAL: if .TRUE. then access the vector C in the formula above.
INFO — INTEGER: = 0: successful exit. i > 0: the ith argument is invalid.
WORK — COMPLEX*16 array, dimension (2*N): workspace.
RWORK — DOUBLE PRECISION array, dimension (N): workspace.

👑 Author

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

Definition: at line 129 of file zla_porcond_c.f.

🦋 `zla_porcond_x`

double precision function zla_porcond_x (character uplo, integer n,
     complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension(
     ldaf, * ) af, integer ldaf, complex*16, dimension( * ) x, integer info,
     complex*16, dimension( * ) work, double precision, dimension( * ) rwork)

ZLA_PORCOND_X computes the infinity norm condition number of op(A)*diag(x) for Hermitian positive-definite matrices. Different flavor, same condition-number obsession 💅

🎯 Purpose

ZLA_PORCOND_X Computes the infinity norm condition number of op(A) * diag(X) where X is a COMPLEX*16 vector.

🧚 Parameters

UPLO — CHARACTER*1: = 'U': upper triangle of A is stored; = 'L': lower triangle of A is stored.
N — INTEGER: the number of linear equations, i.e., the order of the matrix A. N >= 0.
A — COMPLEX*16 array, dimension (LDA,N): on entry, the N-by-N matrix A.
LDA — INTEGER: the leading dimension of the array A. LDA >= max(1,N).
AF — COMPLEX*16 array, dimension (LDAF,N): the triangular factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H, as computed by ZPOTRF.
LDAF — INTEGER: the leading dimension of the array AF. LDAF >= max(1,N).
X — COMPLEX*16 array, dimension (N): the vector X in the formula op(A) * diag(X).
INFO — INTEGER: = 0: successful exit. i > 0: the ith argument is invalid.
WORK — COMPLEX*16 array, dimension (2*N): workspace.
RWORK — DOUBLE PRECISION array, dimension (N): workspace.

👑 Author

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

Definition: at line 122 of file zla_porcond_x.f.

👑 Author

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📦 where this page comes from

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la_porcond(3)

💅 la_porcond(3) — Skeel condition number estimate 💅

💖 NAME 💖

✨ SYNOPSIS ✨

Functions

🌸 Detailed Description 🌸

🦋 Function Documentation 🦋

cla_porcond_c — real function

Purpose

Parameters

Author

cla_porcond_x — real function

Purpose

Parameters

Author

dla_porcond — double precision function

Purpose

Parameters

Author

sla_porcond — real function

Purpose

Parameters

CMODE

🍓 C

🚨 INFO

🧰 WORK

🗂️ IWORK

👑 Author

💖 zla_porcond_c

🎯 Purpose

🧚 Parameters

👑 Author

🦋 zla_porcond_x

🎯 Purpose

🧚 Parameters

👑 Author

👑 Author

💅 `la_porcond(3)` — Skeel condition number estimate 💅

`cla_porcond_c` — `real function`

`cla_porcond_x` — `real function`

`dla_porcond` — `double precision function`

`sla_porcond` — `real function`

`CMODE`

🍓 `C`

🚨 `INFO`

🧰 `WORK`

🗂️ `IWORK`

💖 `zla_porcond_c`

🦋 `zla_porcond_x`