DOKK / manpages / debian 13 / liblapack-doc / la_porcond.3.en
la_porcond(3) LAPACK la_porcond(3)

la_porcond - la_porcond: Skeel condition number estimate


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.

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 



          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.

A



          A is COMPLEX array, dimension (LDA,N)


     On entry, the N-by-N matrix A

LDA



          LDA is INTEGER


     The leading dimension of the array A.  LDA >= max(1,N).

AF



          AF is 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



          LDAF is INTEGER


     The leading dimension of the array AF.  LDAF >= max(1,N).

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.

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 



          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.

A



          A is COMPLEX array, dimension (LDA,N)


     On entry, the N-by-N matrix A.

LDA



          LDA is INTEGER


     The leading dimension of the array A.  LDA >= max(1,N).

AF



          AF is 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



          LDAF is INTEGER


     The leading dimension of the array AF.  LDAF >= max(1,N).

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.

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 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

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.

A



          A is DOUBLE PRECISION array, dimension (LDA,N)


     On entry, the N-by-N matrix A.

LDA



          LDA is INTEGER


     The leading dimension of the array A.  LDA >= max(1,N).

AF



          AF is 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



          LDAF is INTEGER


     The leading dimension of the array AF.  LDAF >= max(1,N).

CMODE



          CMODE is 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



          C is DOUBLE PRECISION array, dimension (N)


     The vector C in the formula op(A) * op2(C).

INFO



          INFO is INTEGER


       = 0:  Successful exit.


     i > 0:  The ith argument is invalid.

WORK



          WORK is DOUBLE PRECISION array, dimension (3*N).


     Workspace.

IWORK



          IWORK is INTEGER array, dimension (N).


     Workspace.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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 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

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.

A



          A is REAL array, dimension (LDA,N)


     On entry, the N-by-N matrix A.

LDA



          LDA is INTEGER


     The leading dimension of the array A.  LDA >= max(1,N).

AF



          AF is 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



          LDAF is INTEGER


     The leading dimension of the array AF.  LDAF >= max(1,N).

CMODE



          CMODE is 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



          C is REAL array, dimension (N)


     The vector C in the formula op(A) * op2(C).

INFO



          INFO is INTEGER


       = 0:  Successful exit.


     i > 0:  The ith argument is invalid.

WORK



          WORK is REAL array, dimension (3*N).


     Workspace.

IWORK



          IWORK is INTEGER array, dimension (N).


     Workspace.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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

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 



          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.

A



          A is COMPLEX*16 array, dimension (LDA,N)


     On entry, the N-by-N matrix A

LDA



          LDA is INTEGER


     The leading dimension of the array A.  LDA >= max(1,N).

AF



          AF is 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



          LDAF is INTEGER


     The leading dimension of the array AF.  LDAF >= max(1,N).

C



          C is DOUBLE PRECISION 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*16 array, dimension (2*N).


     Workspace.

RWORK



          RWORK is DOUBLE PRECISION array, dimension (N).


     Workspace.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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

Purpose:



    ZLA_PORCOND_X Computes the infinity norm condition number of


    op(A) * diag(X) where X is a COMPLEX*16 vector.

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.

A



          A is COMPLEX*16 array, dimension (LDA,N)


     On entry, the N-by-N matrix A.

LDA



          LDA is INTEGER


     The leading dimension of the array A.  LDA >= max(1,N).

AF



          AF is 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



          LDAF is INTEGER


     The leading dimension of the array AF.  LDAF >= max(1,N).

X



          X is COMPLEX*16 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*16 array, dimension (2*N).


     Workspace.

RWORK



          RWORK is DOUBLE PRECISION array, dimension (N).


     Workspace.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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