la_hercond(3)
๐
la_hercond(3) โ Skeel condition number estimate
okay bestie, welcome to la_hercond(3) from the Library Functions Manual. This page is the Skeel condition number estimate moment, and it is lowkey stacked with LAPACK routines. Let's get into it ๐
โจ NAME
la_hercondโla_hercond: Skeel condition number estimate
๐ฆ SYNOPSIS
๐ง Functions
real function cla_hercond_c (uplo, n, a, lda, af, ldaf, ipiv, c, capply, info, work, rwork)โCLA_HERCOND_Ccomputes the infinity norm condition number ofop(A)*inv(diag(c))for Hermitian indefinite matrices.real function cla_hercond_x (uplo, n, a, lda, af, ldaf, ipiv, x, info, work, rwork)โCLA_HERCOND_Xcomputes the infinity norm condition number ofop(A)*diag(x)for Hermitian indefinite matrices.real function cla_syrcond_c (uplo, n, a, lda, af, ldaf, ipiv, c, capply, info, work, rwork)โCLA_SYRCOND_Ccomputes the infinity norm condition number ofop(A)*inv(diag(c))for symmetric indefinite matrices.real function cla_syrcond_x (uplo, n, a, lda, af, ldaf, ipiv, x, info, work, rwork)โCLA_SYRCOND_Xcomputes the infinity norm condition number ofop(A)*diag(x)for symmetric indefinite matrices.double precision function dla_syrcond (uplo, n, a, lda, af, ldaf, ipiv, cmode, c, info, work, iwork)โDLA_SYRCONDestimates the Skeel condition number for a symmetric indefinite matrix.real function sla_syrcond (uplo, n, a, lda, af, ldaf, ipiv, cmode, c, info, work, iwork)โSLA_SYRCONDestimates the Skeel condition number for a symmetric indefinite matrix.double precision function zla_hercond_c (uplo, n, a, lda, af, ldaf, ipiv, c, capply, info, work, rwork)โZLA_HERCOND_Ccomputes the infinity norm condition number ofop(A)*inv(diag(c))for Hermitian indefinite matrices.double precision function zla_hercond_x (uplo, n, a, lda, af, ldaf, ipiv, x, info, work, rwork)โZLA_HERCOND_Xcomputes the infinity norm condition number ofop(A)*diag(x)for Hermitian indefinite matrices.double precision function zla_syrcond_c (uplo, n, a, lda, af, ldaf, ipiv, c, capply, info, work, rwork)โZLA_SYRCOND_Ccomputes the infinity norm condition number ofop(A)*inv(diag(c))for symmetric indefinite matrices.double precision function zla_syrcond_x (uplo, n, a, lda, af, ldaf, ipiv, x, info, work, rwork)โZLA_SYRCOND_Xcomputes the infinity norm condition number ofop(A)*diag(x)for symmetric indefinite matrices.
๐ธ DETAILED DESCRIPTION
This is the part where the page rolls straight into the function docs, bestie. No extra prose here in this part โ just the receipts below ๐
๐ฅ FUNCTION DOCUMENTATION
๐ cla_hercond_c
real function cla_hercond_c (character uplo, integer n, complex, dimension(
lda, * ) a, integer lda, complex, dimension( ldaf, * ) af, integer ldaf,
integer, dimension( * ) ipiv, real, dimension ( * ) c, logical capply,
integer info, complex, dimension( * ) work, real, dimension( * ) rwork)
CLA_HERCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian indefinite matrices.
Purpose: CLA_HERCOND_C computes the infinity norm condition number of op(A) * inv(diag(C)) where C is a REAL vector.
Parameters:
UPLOโCHARACTER*1= 'U': Upper triangle of A is stored;= 'L': Lower triangle of A is stored.
NโINTEGERThe number of linear equations, i.e., the order of the matrixA.N >= 0.AโCOMPLEXarray, dimension(LDA,N)On entry, theN-by-NmatrixALDAโINTEGERThe leading dimension of the arrayA.LDA >= max(1,N).AFโCOMPLEXarray, dimension(LDAF,N)The block diagonal matrixDand the multipliers used to obtain the factorUorLas computed byCHETRF.LDAFโINTEGERThe leading dimension of the arrayAF.LDAF >= max(1,N).IPIVโINTEGERarray, dimension(N)Details of the interchanges and the block structure ofDas determined byCHETRF.CโREALarray, dimension(N)The vectorCin the formulaop(A) * inv(diag(C)).CAPPLYโLOGICALIf.TRUE.then access the vectorCin the formula above.INFOโINTEGER= 0: Successful exit.i > 0: The ith argument is invalid.
WORKโCOMPLEXarray, dimension(2*N). Workspace.RWORKโREALarray, dimension(N). Workspace.
Author: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd.
Definition: at line 136 of file cla_hercond_c.f.
๐ฆ cla_hercond_x
real function cla_hercond_x (character uplo, integer n, complex, dimension(
lda, * ) a, integer lda, complex, dimension( ldaf, * ) af, integer ldaf,
integer, dimension( * ) ipiv, complex, dimension( * ) x, integer info,
complex, dimension( * ) work, real, dimension( * ) rwork)
CLA_HERCOND_X computes the infinity norm condition number of op(A)*diag(x) for Hermitian indefinite matrices.
Purpose: CLA_HERCOND_X computes the infinity norm condition number of op(A) * diag(X) where X is a COMPLEX vector.
Parameters:
UPLOโCHARACTER*1= 'U': Upper triangle of A is stored;= 'L': Lower triangle of A is stored.
NโINTEGERThe number of linear equations, i.e., the order of the matrixA.N >= 0.AโCOMPLEXarray, dimension(LDA,N)On entry, theN-by-NmatrixA.LDAโINTEGERThe leading dimension of the arrayA.LDA >= max(1,N).AFโCOMPLEXarray, dimension(LDAF,N)The block diagonal matrixDand the multipliers used to obtain the factorUorLas computed byCHETRF.LDAFโINTEGERThe leading dimension of the arrayAF.LDAF >= max(1,N).IPIVโINTEGERarray, dimension(N)Details of the interchanges and the block structure ofDas determined byCHETRF.XโCOMPLEXarray, dimension(N)The vectorXin the formulaop(A) * diag(X).INFOโINTEGER= 0: Successful exit.i > 0: The ith argument is invalid.
WORKโCOMPLEXarray, dimension(2*N). Workspace.RWORKโREALarray, dimension(N). Workspace.
Author: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd.
Definition: at line 129 of file cla_hercond_x.f.
๐ cla_syrcond_c
real function cla_syrcond_c (character uplo, integer n, complex, dimension(
lda, * ) a, integer lda, complex, dimension( ldaf, * ) af, integer ldaf,
integer, dimension( * ) ipiv, real, dimension( * ) c, logical capply,
integer info, complex, dimension( * ) work, real, dimension( * ) rwork)
CLA_SYRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for symmetric indefinite matrices.
Purpose: CLA_SYRCOND_C computes the infinity norm condition number of op(A) * inv(diag(C)) where C is a REAL vector.
Parameters:
UPLOโCHARACTER*1= 'U': Upper triangle of A is stored;= 'L': Lower triangle of A is stored.
NโINTEGERThe number of linear equations, i.e., the order of the matrixA.N >= 0.AโCOMPLEXarray, dimension(LDA,N)On entry, theN-by-NmatrixALDAโINTEGERThe leading dimension of the arrayA.LDA >= max(1,N).AFโCOMPLEXarray, dimension(LDAF,N)The block diagonal matrixDand the multipliers used to obtain the factorUorLas computed byCSYTRF.LDAFโINTEGERThe leading dimension of the arrayAF.LDAF >= max(1,N).IPIVโINTEGERarray, dimension(N)Details of the interchanges and the block structure ofDas determined byCSYTRF.CโREALarray, dimension(N)The vectorCin the formulaop(A) * inv(diag(C)).CAPPLYโLOGICALIf.TRUE.then access the vectorCin the formula above.INFOโINTEGER= 0: Successful exit.i > 0: The ith argument is invalid.
WORKโCOMPLEXarray, dimension(2*N). Workspace.RWORKโREALarray, dimension(N). Workspace.
Author: Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver, NAG Ltd.
Definition: at line 136 of file cla_syrcond_c.f.
๐ cla_syrcond_x
real function cla_syrcond_x (character uplo, integer n, complex, dimension(
lda, * ) a, integer lda, complex, dimension( ldaf, * ) af, integer ldaf,
integer, dimension( * ) ipiv, complex, dimension( * ) x, integer info,
complex, dimension( * ) work, real, dimension( * ) rwork)
CLA_SYRCOND_X computes the infinity norm condition number of op(A)*diag(x) for symmetric indefinite matrices.
Purpose: CLA_SYRCOND_X computes the infinity norm condition number of op(A) * diag(X) where X is a COMPLEX vector.
Parameters:
UPLOโCHARACTER*1= 'U': Upper triangle of A is stored;= 'L': Lower triangle of A is stored.
NโINTEGERThe number of linear equations, i.e., the order of the matrixA.N >= 0.AAโCOMPLEX array, dimension (LDA,N). On entry, this is theN-by-NmatrixA. main character matrix behavior, honestly ๐LDAโINTEGER. The leading dimension of the arrayA, and the rule isLDA >= max(1,N). respect the leading dimension, bestie โจAFโCOMPLEX array, dimension (LDAF,N). This is the block diagonal matrixDplus the multipliers used to obtain the factorUorL, exactly as computed byCSYTRF. ๐ฆLDAFโINTEGER. The leading dimension of the arrayAF;LDAF >= max(1,N). ๐IPIVโINTEGER array, dimension (N). All the deets on the interchanges and the block structure ofD, as determined byCSYTRF. ๐XโCOMPLEX array, dimension (N). The vectorXin the formulaop(A) * diag(X). ๐ธINFOโINTEGER.= 0:Successful exit.i > 0:theith argument is invalid. if this comes back nonzero, somebody handed over a bad argument, fr ๐WORKโCOMPLEX array, dimension (2*N). Workspace. ๐งRWORKโREAL array, dimension (N). Workspace. ๐
๐ Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Definition at line 129 of file cla_syrcond_x.f.
๐งฎ dla_syrcond
double precision function dla_syrcond (character uplo, integer n, double
precision, dimension( lda, * ) a, integer lda, double precision,
dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv,
integer cmode, double precision, dimension( * ) c, integer info, double
precision, dimension( * ) work, integer, dimension( * ) iwork)
DLA_SYRCOND estimates the Skeel condition number for a symmetric indefinite matrix โ itโs giving โI can absolutely handle this symmetric indefinite situationโ ๐
โจ Purpose
DLA_SYRCONDestimates the Skeel condition number ofop(A) * op2(C)whereop2is determined byCMODElike this: -CMODE = 1โop2(C) = C-CMODE = 0โop2(C) = I-CMODE = -1โop2(C) = inv(C)The Skeel condition numbercond(A) = norminf( |inv(A)||A| )is computed by computing scaling factorsRsuch thatdiag(R)*A*op2(C)is row equilibrated and computing the standard infinity-norm condition number.
๐ธ Parameters
UPLOโCHARACTER*1.= 'U':Upper triangle ofAis stored;= 'L':Lower triangle ofAis stored. pick your triangle, bestie ๐ฅNโINTEGER. The number of linear equations, aka the order of the matrixA.N >= 0. โญAโDOUBLE PRECISION array, dimension (LDA,N). On entry, theN-by-NmatrixA. ๐LDAโINTEGER. The leading dimension of the arrayA;LDA >= max(1,N). โจAFโDOUBLE PRECISION array, dimension (LDAF,N). The block diagonal matrixDand the multipliers used to obtain the factorUorLas computed byDSYTRF. ๐ฆLDAFโINTEGER. The leading dimension of the arrayAF;LDAF >= max(1,N). ๐IPIVโINTEGER array, dimension (N). Details of the interchanges and the block structure ofDas determined byDSYTRF. ๐CMODEโINTEGER. Determinesop2(C)in the formulaop(A) * op2(C)like this:CMODE = 1โop2(C) = C;CMODE = 0โop2(C) = I;CMODE = -1โop2(C) = inv(C). ๐CโDOUBLE PRECISION array, dimension (N). The vectorCin the formulaop(A) * op2(C). ๐INFOโINTEGER.= 0:Successful exit.i > 0:theith argument is invalid. bad argument alert, no cap ๐WORKโDOUBLE PRECISION array, dimension (3*N). Workspace. ๐งIWORKโINTEGER array, dimension (N). Workspace. ๐
๐ Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Definition at line 145 of file dla_syrcond.f.
๐งฎ sla_syrcond
real function sla_syrcond (character uplo, integer n, real, dimension( lda,
* ) a, integer lda, real, dimension( ldaf, * ) af, integer ldaf,
integer, dimension( * ) ipiv, integer cmode, real, dimension( * ) c,
integer info, real, dimension( * ) work, integer, dimension( * ) iwork)
SLA_SYRCOND estimates the Skeel condition number for a symmetric indefinite matrix โ same energy as the double-precision version, but make it REAL โจ
โจ Purpose
SLA_SYRCONDestimates the Skeel condition number ofop(A) * op2(C)whereop2is determined byCMODElike this: -CMODE = 1โop2(C) = C-CMODE = 0โop2(C) = I-CMODE = -1โop2(C) = inv(C)The Skeel condition numbercond(A) = norminf( |inv(A)||A| )is computed by computing scaling factorsRsuch thatdiag(R)*A*op2(C)is row equilibrated and computing the standard infinity-norm condition number.
๐ธ Parameters
UPLOโCHARACTER*1.= 'U':Upper triangle ofAis stored;= 'L':Lower triangle ofAis stored. triangle choice is literally your moment ๐ฅNโINTEGER. The number of linear equations, aka the order of the matrixA.N >= 0. โญAโREAL array, dimension (LDA,N). On entry, theN-by-NmatrixA. ๐LDAโINTEGER. The leading dimension of the arrayA;LDA >= max(1,N). โจAFโREAL array, dimension (LDAF,N). The block diagonal matrixDand the multipliers used to obtain the factorUorLas computed bySSYTRF. ๐ฆLDAFโINTEGER. The leading dimension of the arrayAF;LDAF >= max(1,N). ๐IPIVโINTEGER array, dimension (N). Details of the interchanges and the block structure ofDas determined bySSYTRF. ๐CMODEโINTEGER. Determinesop2(C)in the formulaop(A) * op2(C)like this:CMODE = 1โop2(C) = C;CMODE = 0โop2(C) = I;CMODE = -1โop2(C) = inv(C). ๐CโREAL array, dimension (N). The vectorCin the formulaop(A) * op2(C). ๐INFOโINTEGER.= 0:Successful exit.i > 0:theith argument is invalid. if this is nonzero, an argument said โnot todayโ ๐WORKโREAL array, dimension (3*N). Workspace. ๐งIWORKโINTEGER array, dimension (N). Workspace. ๐
๐ Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Definition at line 144 of file sla_syrcond.f.
๐งฎ zla_hercond_c
double precision function zla_hercond_c (character uplo, integer n,
complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension(
ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv, double
precision, dimension ( * ) c, logical capply, integer info, complex*16,
dimension( * ) work, double precision, dimension( * ) rwork)
ZLA_HERCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian indefinite matrices โ Hermitian indefinite representation, we love to see it ๐
โจ Purpose
ZLA_HERCOND_Ccomputes the infinity norm condition number ofop(A) * inv(diag(C))whereCis aDOUBLE PRECISIONvector.
๐ธ Parameters
UPLOโCHARACTER*1.= 'U':Upper triangle ofAis stored;= 'L':Lower triangle ofAis stored. choose your triangle era ๐ฅNโINTEGER. The number of linear equations, aka the order of the matrixA.N >= 0. โญAโCOMPLEX*16 array, dimension (LDA,N). On entry, theN-by-NmatrixA. ๐LDAโINTEGER. The leading dimension of the arrayA;LDA >= max(1,N). โจAFโCOMPLEX*16 array, dimension (LDAF,N). The block diagonal matrixDand the multipliers used to obtain the factorUorLas computed byZHETRF. ๐ฆLDAFโINTEGER. The leading dimension of the arrayAF;LDAF >= max(1,N). ๐IPIVโINTEGER array, dimension (N). Details of the interchanges and the block structure ofDas determined byCHETRF. ๐CโDOUBLE PRECISION array, dimension (N). The vectorCin the formulaop(A) * inv(diag(C)). ๐CAPPLYโLOGICAL. If.TRUE.then access the vectorCin the formula above. only if the vibe check says.TRUE.๐ซถINFOโINTEGER.= 0:Successful exit.i > 0:theith argument is invalid. invalid argument detected, not iconic ๐WORKโCOMPLEX*16 array, dimension (2*N). Workspace. ๐งRWORKโDOUBLE PRECISION array, dimension (N). Workspace. ๐
๐ Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Definition at line 137 of file zla_hercond_c.f.
๐งฎ zla_hercond_x
double precision function zla_hercond_x (character uplo, integer n,
complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension(
ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv, complex*16,
dimension( * ) x, integer info, complex*16, dimension( * ) work, double
precision, dimension( * ) rwork)
ZLA_HERCOND_X computes the infinity norm condition number of op(A)*diag(x) for Hermitian indefinite matrices โ the x is lowercase here and weโre not gonna question the font choices ๐
โจ Purpose
ZLA_HERCOND_Xcomputes the infinity norm condition number ofop(A) * diag(X)whereXis aCOMPLEX*16vector.
๐ธ Parameters
UPLOโ
Still in the previous functionโs parameter list (definition file: zla_hercond_x.f, if youโre keeping receipts) โ hereโs the rest of the tea โ๐
UPLOโCHARACTER*1= 'U': Upper triangle ofAis stored;= 'L': Lower triangle ofAis stored.
NโINTEGER. The number of linear equations, i.e., the order of the matrixA.N >= 0.AโCOMPLEX*16 array, dimension (LDA,N). On entry, the N-by-N matrixA.LDAโINTEGER. The leading dimension of the arrayA.LDA >= max(1,N).AFโCOMPLEX*16 array, dimension (LDAF,N). The block diagonal matrixDand the multipliers used to obtain the factorUorLas computed byZHETRF.LDAFโINTEGER. The leading dimension of the arrayAF.LDAF >= max(1,N).IPIVโINTEGER array, dimension (N). Details of the interchanges and the block structure ofDas determined byCHETRF.XโCOMPLEX*16 array, dimension (N). The vectorXin the formulaop(A) * diag(X).INFOโINTEGER= 0: Successful exit.i > 0: The ith argument is invalid.
WORKโCOMPLEX*16 array, dimension (2*N). Workspace.RWORKโDOUBLE PRECISION array, dimension (N). Workspace.
Author ๐ซถ
- Univ. of Tennessee
- Univ. of California Berkeley
- Univ. of Colorado Denver
- NAG Ltd.
Definition at line 130 of file zla_hercond_x.f.
๐ zla_syrcond_c
double precision function zla_syrcond_c (character uplo, integer n,
complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension(
ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv, double
precision, dimension( * ) c, logical capply, integer info, complex*16,
dimension( * ) work, double precision, dimension( * ) rwork)
ZLA_SYRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for symmetric indefinite matrices. No cap, thatโs literally the whole assignment โจ
Purpose:
ZLA_SYRCOND_C Computes the infinity norm condition number of op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector.
Parameters
UPLOโCHARACTER*1= 'U': Upper triangle ofAis stored;= 'L': Lower triangle ofAis stored.
NโINTEGER. The number of linear equations, i.e., the order of the matrixA.N >= 0.AโCOMPLEX*16 array, dimension (LDA,N). On entry, the N-by-N matrixA.LDAโINTEGER. The leading dimension of the arrayA.LDA >= max(1,N).AFโCOMPLEX*16 array, dimension (LDAF,N). The block diagonal matrixDand the multipliers used to obtain the factorUorLas computed byZSYTRF.LDAFโINTEGER. The leading dimension of the arrayAF.LDAF >= max(1,N).IPIVโINTEGER array, dimension (N). Details of the interchanges and the block structure ofDas determined byZSYTRF.CโDOUBLE PRECISION array, dimension (N). The vectorCin the formulaop(A) * inv(diag(C)).CAPPLYโLOGICAL. If.TRUE.then access the vectorCin the formula above.INFOโINTEGER= 0: Successful exit.i > 0: The ith argument is invalid.
WORKโCOMPLEX*16 array, dimension (2*N). Workspace.RWORKโDOUBLE PRECISION array, dimension (N). Workspace.
Author ๐ธ
- Univ. of Tennessee
- Univ. of California Berkeley
- Univ. of Colorado Denver
- NAG Ltd.
Definition at line 137 of file zla_syrcond_c.f.
๐ฆ zla_syrcond_x
double precision function zla_syrcond_x (character uplo, integer n,
complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension(
ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv, complex*16,
dimension( * ) x, integer info, complex*16, dimension( * ) work, double
precision, dimension( * ) rwork)
ZLA_SYRCOND_X computes the infinity norm condition number of op(A)*diag(x) for symmetric indefinite matrices. Iconic behavior, honestly ๐
Purpose:
ZLA_SYRCOND_X Computes the infinity norm condition number of op(A) * diag(X) where X is a COMPLEX*16 vector.
Parameters
UPLOโCHARACTER*1= 'U': Upper triangle ofAis stored;= 'L': Lower triangle ofAis stored.
NโINTEGER. The number of linear equations, i.e., the order of the matrixA.N >= 0.AโCOMPLEX*16 array, dimension (LDA,N). On entry, the N-by-N matrixA.LDAโINTEGER. The leading dimension of the arrayA.LDA >= max(1,N).AFโCOMPLEX*16 array, dimension (LDAF,N). The block diagonal matrixDand the multipliers used to obtain the factorUorLas computed byZSYTRF.LDAFโINTEGER. The leading dimension of the arrayAF.LDAF >= max(1,N).IPIVโINTEGER array, dimension (N). Details of the interchanges and the block structure ofDas determined byZSYTRF.XโCOMPLEX*16 array, dimension (N). The vectorXin the formulaop(A) * diag(X).INFOโINTEGER= 0: Successful exit.i > 0: The ith argument is invalid.
WORKโCOMPLEX*16 array, dimension (2*N). Workspace.RWORKโDOUBLE PRECISION array, dimension (N). Workspace.
Author ๐
- Univ. of Tennessee
- Univ. of California Berkeley
- Univ. of Colorado Denver
- NAG Ltd.
Definition at line 130 of file zla_syrcond_x.f.
Author ๐
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