la_gbrcond(3)

📦
version 3.12.1 · 9 versions
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💅 la_gbrcond — Skeel condition number estimate ✨

okay so this is the la_gbrcond(3) page from the Library Functions Manual, and bestie, it's a whole family of functions, not just one. Buckle up 🎀

🌸 NAME 🌸

la_gbrcond — la_gbrcond: Skeel condition number estimate

✨ SYNOPSIS ✨

🦋 Functions 🦋

  • real function cla_gbrcond_c (trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, c, capply, info, work, rwork) — CLA_GBRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for general banded matrices.
  • real function cla_gbrcond_x (trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, x, info, work, rwork) — CLA_GBRCOND_X computes the infinity norm condition number of op(A)*diag(x) for general banded matrices.
  • double precision function dla_gbrcond (trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, cmode, c, info, work, iwork) — DLA_GBRCOND estimates the Skeel condition number for a general banded matrix.
  • real function sla_gbrcond (trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, cmode, c, info, work, iwork) — SLA_GBRCOND estimates the Skeel condition number for a general banded matrix.
  • double precision function zla_gbrcond_c (trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, c, capply, info, work, rwork) — ZLA_GBRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for general banded matrices.
  • double precision function zla_gbrcond_x (trans, n, kl, ku, ab, ldab, afb, ldafb, ipiv, x, info, work, rwork) — ZLA_GBRCOND_X computes the infinity norm condition number of op(A)*diag(x) for general banded matrices.

🔥 Detailed Description 🔥

No thoughts, just vibes and a big pile of function docs. Let's go function by function 👑

Function Documentation

🧚 real function cla_gbrcond_c (character trans, integer n, integer kl, integer ku, complex, dimension( ldab, * ) ab, integer ldab, complex, dimension( ldafb, * ) afb, integer ldafb, integer, dimension( * ) ipiv, real, dimension( * ) c, logical capply, integer info, complex, dimension( * ) work, real, dimension( * ) rwork)

CLA_GBRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for general banded matrices.

💖 Purpose:

CLA_GBRCOND_C Computes the infinity norm condition number of op(A) * inv(diag(C)) where C is a REAL vector. like, the whole point 💅

🌈 Parameters

  • TRANS — TRANS is CHARACTER*1. Specifies the form of the system of equations:
    • = 'N': A * X = B (No transpose)
    • = 'T': A**T * X = B (Transpose)
    • = 'C': A**H * X = B (Conjugate Transpose = Transpose)
  • N — N is INTEGER. The number of linear equations, i.e., the order of the matrix A. N >= 0.
  • KL — KL is INTEGER. The number of subdiagonals within the band of A. KL >= 0.
  • KU — KU is INTEGER. The number of superdiagonals within the band of A. KU >= 0.
  • AB — AB is COMPLEX array, dimension (LDAB,N). On entry, the matrix A in band storage, in rows 1 to KL+KU+1. The j-th column of A is stored in the j-th column of the array AB as follows:
AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)
  • LDAB — LDAB is INTEGER. The leading dimension of the array AB. LDAB >= KL+KU+1.
  • AFB — AFB is COMPLEX array, dimension (LDAFB,N). Details of the LU factorization of the band matrix A, as computed by CGBTRF. U is stored as an upper triangular band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and the multipliers used during the factorization are stored in rows KL+KU+2 to 2*KL+KU+1.
  • LDAFB — LDAFB is INTEGER. The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1.
  • IPIV — IPIV is INTEGER array, dimension (N). The pivot indices from the factorization A = P*L*U as computed by CGBTRF; row i of the matrix was interchanged with row IPIV(i).
  • C — C is REAL array, dimension (N). The vector C in the formula op(A) * inv(diag(C)).
  • CAPPLY — CAPPLY is LOGICAL. If .TRUE. then access the vector C in the formula above.
  • INFO — INFO is INTEGER:
    • = 0: Successful exit.
    • i > 0: The ith argument is invalid.
  • WORK — WORK is COMPLEX array, dimension (2*N). Workspace.
  • RWORK — RWORK is REAL array, dimension (N). Workspace.

👑 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 158 of file cla_gbrcond_c.f.

🦋 real function cla_gbrcond_x (character trans, integer n, integer kl, integer ku, complex, dimension( ldab, * ) ab, integer ldab, complex, dimension( ldafb, * ) afb, integer ldafb, integer, dimension( * ) ipiv, complex, dimension( * ) x, integer info, complex, dimension( * ) work, real, dimension( * ) rwork)

CLA_GBRCOND_X computes the infinity norm condition number of op(A)*diag(x) for general banded matrices.

💖 Purpose:

CLA_GBRCOND_X Computes the infinity norm condition number of op(A) * diag(X) where X is a COMPLEX vector. (yes, X this time, not C — they're different girlies 🙈)

🌈 Parameters

  • TRANS — TRANS is CHARACTER*1. Specifies the form of the system of equations:
    • = 'N': A * X = B (No transpose)
    • = 'T': A**T * X = B (Transpose)
    • = 'C': A**H * X = B (Conjugate Transpose = Transpose)
  • N — N is INTEGER. The number of linear equations, i.e., the order of the matrix A. N >= 0.
  • KL — KL is INTEGER. The number of subdiagonals within the band of A. KL >= 0.
  • KU — KU is INTEGER. The number of superdiagonals within the band of A. KU >= 0.
  • AB — AB is COMPLEX array, dimension (LDAB,N). On entry, the matrix A in band storage, in rows 1 to KL+KU+1. The j-th column of A is stored in the j-th column of the array AB as follows:
AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)
  • LDAB — LDAB is INTEGER. The leading dimension of the array AB. LDAB >= KL+KU+1.
  • AFB — AFB is COMPLEX array, dimension (LDAFB,N). Details of the LU factorization of the band matrix A, as computed by CGBTRF. U is stored as an upper triangular band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and the multipliers used during the factorization are stored in rows KL+KU+2 to 2*KL+KU+1.
  • LDAFB — LDAFB is INTEGER. The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1.
  • IPIV — IPIV is INTEGER array, dimension (N). The pivot indices from the factorization A = P*L*U as computed by CGBTRF; row i of the matrix was interchanged with row IPIV(i).
  • X — X is COMPLEX array, dimension (N). The vector X in the formula op(A) * diag(X).
  • INFO — INFO is INTEGER:
    • = 0: Successful exit.
    • i > 0: The ith argument is invalid.
  • WORK — WORK is COMPLEX array, dimension (2*N). Workspace.
  • RWORK — RWORK is REAL array, dimension (N). Workspace.

👑 Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 151 of file cla_gbrcond_x.f.

💜 double precision function dla_gbrcond (character trans, integer n, integer kl, integer ku, double precision, dimension( ldab, * ) ab, integer ldab, double precision, dimension( ldafb, * ) afb, integer ldafb, integer, dimension( * ) ipiv, integer cmode, double precision, dimension( * ) c, integer info, double precision, dimension( * ) work, integer, dimension( * ) iwork)

DLA_GBRCOND estimates the Skeel condition number for a general banded matrix.

💖 Purpose:

DLA_GBRCOND Estimates the Skeel condition number of op(A) * op2(C) where op2 is determined by CMODE as follows:

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

  • TRANS — TRANS is CHARACTER*1. Specifies the form of the system of equations:
    • = 'N': A * X = B (No transpose)
    • = 'T': A**T * X = B (Transpose)
    • = 'C': A**H * X = B (Conjugate Transpose = Transpose)
  • N — N is INTEGER. The number of linear equations, i.e., the order of the matrix A. N >= 0.
  • KL — KL is INTEGER. The number of subdiagonals within the band of A. KL >= 0.
  • KU — KU is INTEGER. The number of superdiagonals within the band of A. KU >= 0.
  • AB — AB is DOUBLE PRECISION array, dimension (LDAB,N). On entry, the matrix A in band storage, in rows 1 to KL+KU+1. The j-th column of A is stored in the j-th column of the array AB as follows:
AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)
  • LDAB — LDAB is INTEGER. The leading dimension of the array AB. LDAB >= KL+KU+1.
  • AFB — AFB is DOUBLE PRECISION array, dimension (LDAFB,N). Details of the LU factorization of the band matrix A, as computed by DGBTRF. U is stored as an upper triangular band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and the multipliers used during the factorization are stored in rows KL+KU+2 to 2*KL+KU+1.
  • LDAFB — INTEGER energy ✨ this is just the leading dimension of the array AFB, and bestie you must respect LDAFB >= 2*KL+KU+1 or it's giving chaos 💅
  • IPIV — INTEGER array, dimension (N). The pivot indices from the factorization A = P*L*U as computed by DGBTRF; row i of the matrix was interchanged with row IPIV(i). Basically the receipts of who swapped with who 🔥
  • CMODE — INTEGER, and it decides op2(C) in the formula op(A) * op2(C) like so:
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). She's the moment 🎀
  • INFO — INTEGER, the vibe report:
  = 0:  Successful exit.
i > 0:  The ith argument is invalid.
  • WORK — DOUBLE PRECISION array, dimension (5*N). Workspace. Scratch paper era ✨
  • IWORK — INTEGER array, dimension (N). Workspace. More scratch paper, but ints this time 🧚

Author 💖

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 167 of file dla_gbrcond.f.

🫶 sla_gbrcond

real function sla_gbrcond (character trans, integer n, integer kl, integer
    ku, real, dimension( ldab, * ) ab, integer ldab, real, dimension( ldafb,
    * ) afb, integer ldafb, integer, dimension( * ) ipiv, integer cmode,
    real, dimension( * ) c, integer info, real, dimension( * ) work,
    integer, dimension( * ) iwork)

SLA_GBRCOND estimates the Skeel condition number for a general banded matrix. Iconic behavior, no notes 👑

Purpose 🎯

!>
!>    SLA_GBRCOND Estimates the Skeel condition number of  op(A) * op2(C)
!>    where op2 is determined by CMODE as follows
!>    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 💅

  • TRANS — CHARACTER*1</character>. Tells you which form of the system of equations you're in:
  = 'N':  A * X = B     (No transpose)
  = 'T':  A**T * X = B  (Transpose)
  = 'C':  A**H * X = B  (Conjugate Transpose = Transpose)
  • N — INTEGER. The number of linear equations, i.e., the order of the matrix A. N >= 0. She's the size of the whole situation 🦋
  • KL — INTEGER. The number of subdiagonals within the band of A. KL >= 0.
  • KU — INTEGER. The number of superdiagonals within the band of A. KU >= 0.
  • AB — REAL array, dimension (LDAB,N). On entry, the matrix A in band storage, in rows 1 to KL+KU+1. The j-th column of A is stored in the j-th column of the array AB as follows:
AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)
  • LDAB — INTEGER. The leading dimension of the array AB. LDAB >= KL+KU+1.
  • AFB — REAL array, dimension (LDAFB,N). Details of the LU factorization of the band matrix A, as computed by SGBTRF. U is stored as an upper triangular band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and the multipliers used during the factorization are stored in rows KL+KU+2 to 2*KL+KU+1. Lowkey a whole archive of what happened 😭
  • LDAFB — INTEGER. The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1.
  • IPIV — INTEGER array, dimension (N). The pivot indices from the factorization A = P*L*U as computed by SGBTRF; row i of the matrix was interchanged with row IPIV(i).
  • 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 — REAL 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 — REAL array, dimension (5*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 166 of file sla_gbrcond.f.

🦋 zla_gbrcond_c

double precision function zla_gbrcond_c (character trans, integer n, integer
    kl, integer ku, complex*16, dimension( ldab, * ) ab, integer ldab,
    complex*16, dimension( ldafb, * ) afb, integer ldafb, integer,
    dimension( * ) ipiv, double precision, dimension( * ) c, logical capply,
    integer info, complex*16, dimension( * ) work, double precision,
    dimension( * ) rwork)

ZLA_GBRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for general banded matrices. Complex math but make it fashion 💜

Purpose 🎯

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

Parameters 💅

  • TRANS — CHARACTER*1. Specifies the form of the system of equations:
  = 'N':  A * X = B     (No transpose)
  = 'T':  A**T * X = B  (Transpose)
  = 'C':  A**H * X = B  (Conjugate Transpose = Transpose)
  • N — INTEGER. The number of linear equations, i.e., the order of the matrix A. N >= 0.
  • KL — INTEGER. The number of subdiagonals within the band of A. KL >= 0.
  • KU — INTEGER. The number of superdiagonals within the band of A. KU >= 0.
  • AB — COMPLEX*16 array, dimension (LDAB,N). On entry, the matrix A in band storage, in rows 1 to KL+KU+1. The j-th column of A is stored in the j-th column of the array AB as follows:
AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)
  • LDAB — INTEGER. The leading dimension of the array AB. LDAB >= KL+KU+1.
  • AFB — COMPLEX*16 array, dimension (LDAFB,N). Details of the LU factorization of the band matrix A, as computed by ZGBTRF. U is stored as an upper triangular band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and the multipliers used during the factorization are stored in rows KL+KU+2 to 2*KL+KU+1.
  • LDAFB — INTEGER. The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1.
  • IPIV — INTEGER array, dimension (N). The pivot indices from the factorization A = P*L*U as computed by ZGBTRF; row i of the matrix was interchanged with row IPIV(i).
  • 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. The switch of destiny ✨
  • 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 159 of file zla_gbrcond_c.f.

🌸 zla_gbrcond_x

double precision function zla_gbrcond_x (character trans, integer n, integer
    kl, integer ku, complex*16, dimension( ldab, * ) ab, integer ldab,
    complex*16, dimension( ldafb, * ) afb, integer ldafb, integer,
    dimension( * ) ipiv, complex*16, dimension( * ) x, integer info,
    complex*16, dimension( * ) work, double precision, dimension( * ) rwork)

ZLA_GBRCOND_X computes the infinity norm condition number of op(A)*diag(x) for general banded matrices. X marks the spot, bestie 🎯

Purpose 🎯

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

Parameters 💅

  • TRANS — CHARACTER*1. Specifies the form of the system of equations:
  = 'N':  A * X = B     (No transpose)
  = 'T':  A**T * X = B  (Transpose)
  = 'C':  A**H * X = B  (Conjugate Transpose = Transpose)
  • N — INTEGER. The number of linear equations, i.e., the order of the matrix A. N >= 0.
  • KL — INTEGER. The number of subdiagonals within the band of A. KL >= 0.
  • KU — INTEGER. The number of superdiagonals within the band of A. KU >= 0.
  • AB — COMPLEX*16 array, dimension (LDAB,N). On entry, the matrix A in band storage, in rows 1 to KL+KU+1. The j-th column of A is stored in the j-th column of the array AB as follows:
AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)
  • LDAB — INTEGER. The leading dimension of the array AB. LDAB >= KL+KU+1.
  • AFB
  • AFB 💅 — AFB is a COMPLEX*16 array, dimension (LDAFB,N). It’s holding the details of the LU factorization of the band matrix A, exactly as computed by ZGBTRF. U is stored as an upper triangular band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and the multipliers used during the factorization are stored in rows KL+KU+2 to 2*KL+KU+1. Obsessed with the row math, ngl. ✨
  • LDAFB — LDAFB is INTEGER. It’s the leading dimension of the array AFB, and bestie, LDAFB >= 2*KL+KU+1 — that’s the vibe check. 💖
  • IPIV — IPIV is an INTEGER array, dimension (N). These are the pivot indices from the factorization A = P*L*U, as computed by ZGBTRF; row i of the matrix was interchanged with row IPIV(i). Pivot queen behavior, lowkey. 👑
  • X — X is a COMPLEX*16 array, dimension (N). It’s the vector X in the formula op(A) * diag(X). Main character vector, fr fr. 🦋
  • INFO — INFO is INTEGER.
    • = 0: Successful exit.
    • i > 0: The ith argument is invalid.
  • WORK — WORK is a COMPLEX*16 array, dimension (2*N). Workspace. 💜
  • RWORK — RWORK is a DOUBLE PRECISION array, dimension (N). Workspace. 🌸

👑 Author

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

Definition at line 152 of file zla_gbrcond_x.f.

🤖 Author

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