.TH "la_porcond" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
la_porcond \- la_porcond: Skeel condition number estimate
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "real function \fBcla_porcond_c\fP (uplo, n, a, lda, af, ldaf, c, capply, info, work, rwork)"
.br
.RI "\fBCLA_PORCOND_C\fP computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian positive-definite matrices\&. "
.ti -1c
.RI "real function \fBcla_porcond_x\fP (uplo, n, a, lda, af, ldaf, x, info, work, rwork)"
.br
.RI "\fBCLA_PORCOND_X\fP computes the infinity norm condition number of op(A)*diag(x) for Hermitian positive-definite matrices\&. "
.ti -1c
.RI "double precision function \fBdla_porcond\fP (uplo, n, a, lda, af, ldaf, cmode, c, info, work, iwork)"
.br
.RI "\fBDLA_PORCOND\fP estimates the Skeel condition number for a symmetric positive-definite matrix\&. "
.ti -1c
.RI "real function \fBsla_porcond\fP (uplo, n, a, lda, af, ldaf, cmode, c, info, work, iwork)"
.br
.RI "\fBSLA_PORCOND\fP estimates the Skeel condition number for a symmetric positive-definite matrix\&. "
.ti -1c
.RI "double precision function \fBzla_porcond_c\fP (uplo, n, a, lda, af, ldaf, c, capply, info, work, rwork)"
.br
.RI "\fBZLA_PORCOND_C\fP computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian positive-definite matrices\&. "
.ti -1c
.RI "double precision function \fBzla_porcond_x\fP (uplo, n, a, lda, af, ldaf, x, info, work, rwork)"
.br
.RI "\fBZLA_PORCOND_X\fP computes the infinity norm condition number of op(A)*diag(x) for Hermitian positive-definite matrices\&. "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "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)"

.PP
\fBCLA_PORCOND_C\fP computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian positive-definite matrices\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
    CLA_PORCOND_C Computes the infinity norm condition number of
    op(A) * inv(diag(C)) where C is a REAL vector
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
       = 'U':  Upper triangle of A is stored;
       = 'L':  Lower triangle of A is stored\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
     The number of linear equations, i\&.e\&., the order of the
     matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is COMPLEX array, dimension (LDA,N)
     On entry, the N-by-N matrix A
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
     The leading dimension of the array A\&.  LDA >= max(1,N)\&.
.fi
.PP
.br
\fIAF\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fILDAF\fP 
.PP
.nf
          LDAF is INTEGER
     The leading dimension of the array AF\&.  LDAF >= max(1,N)\&.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is REAL array, dimension (N)
     The vector C in the formula op(A) * inv(diag(C))\&.
.fi
.PP
.br
\fICAPPLY\fP 
.PP
.nf
          CAPPLY is LOGICAL
     If \&.TRUE\&. then access the vector C in the formula above\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
       = 0:  Successful exit\&.
     i > 0:  The ith argument is invalid\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is COMPLEX array, dimension (2*N)\&.
     Workspace\&.
.fi
.PP
.br
\fIRWORK\fP 
.PP
.nf
          RWORK is REAL array, dimension (N)\&.
     Workspace\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP

.SS "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)"

.PP
\fBCLA_PORCOND_X\fP computes the infinity norm condition number of op(A)*diag(x) for Hermitian positive-definite matrices\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
    CLA_PORCOND_X Computes the infinity norm condition number of
    op(A) * diag(X) where X is a COMPLEX vector\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
       = 'U':  Upper triangle of A is stored;
       = 'L':  Lower triangle of A is stored\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
     The number of linear equations, i\&.e\&., the order of the
     matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is COMPLEX array, dimension (LDA,N)
     On entry, the N-by-N matrix A\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
     The leading dimension of the array A\&.  LDA >= max(1,N)\&.
.fi
.PP
.br
\fIAF\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fILDAF\fP 
.PP
.nf
          LDAF is INTEGER
     The leading dimension of the array AF\&.  LDAF >= max(1,N)\&.
.fi
.PP
.br
\fIX\fP 
.PP
.nf
          X is COMPLEX array, dimension (N)
     The vector X in the formula op(A) * diag(X)\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
       = 0:  Successful exit\&.
     i > 0:  The ith argument is invalid\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is COMPLEX array, dimension (2*N)\&.
     Workspace\&.
.fi
.PP
.br
\fIRWORK\fP 
.PP
.nf
          RWORK is REAL array, dimension (N)\&.
     Workspace\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP

.SS "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)"

.PP
\fBDLA_PORCOND\fP estimates the Skeel condition number for a symmetric positive-definite matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
    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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
       = 'U':  Upper triangle of A is stored;
       = 'L':  Lower triangle of A is stored\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
     The number of linear equations, i\&.e\&., the order of the
     matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is DOUBLE PRECISION array, dimension (LDA,N)
     On entry, the N-by-N matrix A\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
     The leading dimension of the array A\&.  LDA >= max(1,N)\&.
.fi
.PP
.br
\fIAF\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fILDAF\fP 
.PP
.nf
          LDAF is INTEGER
     The leading dimension of the array AF\&.  LDAF >= max(1,N)\&.
.fi
.PP
.br
\fICMODE\fP 
.PP
.nf
          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)
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is DOUBLE PRECISION array, dimension (N)
     The vector C in the formula op(A) * op2(C)\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
       = 0:  Successful exit\&.
     i > 0:  The ith argument is invalid\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is DOUBLE PRECISION array, dimension (3*N)\&.
     Workspace\&.
.fi
.PP
.br
\fIIWORK\fP 
.PP
.nf
          IWORK is INTEGER array, dimension (N)\&.
     Workspace\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP

.SS "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)"

.PP
\fBSLA_PORCOND\fP estimates the Skeel condition number for a symmetric positive-definite matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
    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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
       = 'U':  Upper triangle of A is stored;
       = 'L':  Lower triangle of A is stored\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
     The number of linear equations, i\&.e\&., the order of the
     matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is REAL array, dimension (LDA,N)
     On entry, the N-by-N matrix A\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
     The leading dimension of the array A\&.  LDA >= max(1,N)\&.
.fi
.PP
.br
\fIAF\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fILDAF\fP 
.PP
.nf
          LDAF is INTEGER
     The leading dimension of the array AF\&.  LDAF >= max(1,N)\&.
.fi
.PP
.br
\fICMODE\fP 
.PP
.nf
          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)
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is REAL array, dimension (N)
     The vector C in the formula op(A) * op2(C)\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
       = 0:  Successful exit\&.
     i > 0:  The ith argument is invalid\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is REAL array, dimension (3*N)\&.
     Workspace\&.
.fi
.PP
.br
\fIIWORK\fP 
.PP
.nf
          IWORK is INTEGER array, dimension (N)\&.
     Workspace\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP

.SS "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)"

.PP
\fBZLA_PORCOND_C\fP computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian positive-definite matrices\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
    ZLA_PORCOND_C Computes the infinity norm condition number of
    op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
       = 'U':  Upper triangle of A is stored;
       = 'L':  Lower triangle of A is stored\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
     The number of linear equations, i\&.e\&., the order of the
     matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is COMPLEX*16 array, dimension (LDA,N)
     On entry, the N-by-N matrix A
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
     The leading dimension of the array A\&.  LDA >= max(1,N)\&.
.fi
.PP
.br
\fIAF\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fILDAF\fP 
.PP
.nf
          LDAF is INTEGER
     The leading dimension of the array AF\&.  LDAF >= max(1,N)\&.
.fi
.PP
.br
\fIC\fP 
.PP
.nf
          C is DOUBLE PRECISION array, dimension (N)
     The vector C in the formula op(A) * inv(diag(C))\&.
.fi
.PP
.br
\fICAPPLY\fP 
.PP
.nf
          CAPPLY is LOGICAL
     If \&.TRUE\&. then access the vector C in the formula above\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
       = 0:  Successful exit\&.
     i > 0:  The ith argument is invalid\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is COMPLEX*16 array, dimension (2*N)\&.
     Workspace\&.
.fi
.PP
.br
\fIRWORK\fP 
.PP
.nf
          RWORK is DOUBLE PRECISION array, dimension (N)\&.
     Workspace\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP

.SS "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)"

.PP
\fBZLA_PORCOND_X\fP computes the infinity norm condition number of op(A)*diag(x) for Hermitian positive-definite matrices\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
    ZLA_PORCOND_X Computes the infinity norm condition number of
    op(A) * diag(X) where X is a COMPLEX*16 vector\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
       = 'U':  Upper triangle of A is stored;
       = 'L':  Lower triangle of A is stored\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
     The number of linear equations, i\&.e\&., the order of the
     matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is COMPLEX*16 array, dimension (LDA,N)
     On entry, the N-by-N matrix A\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
     The leading dimension of the array A\&.  LDA >= max(1,N)\&.
.fi
.PP
.br
\fIAF\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fILDAF\fP 
.PP
.nf
          LDAF is INTEGER
     The leading dimension of the array AF\&.  LDAF >= max(1,N)\&.
.fi
.PP
.br
\fIX\fP 
.PP
.nf
          X is COMPLEX*16 array, dimension (N)
     The vector X in the formula op(A) * diag(X)\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
       = 0:  Successful exit\&.
     i > 0:  The ith argument is invalid\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is COMPLEX*16 array, dimension (2*N)\&.
     Workspace\&.
.fi
.PP
.br
\fIRWORK\fP 
.PP
.nf
          RWORK is DOUBLE PRECISION array, dimension (N)\&.
     Workspace\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP

.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.