.TH "la_gercond" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME la_gercond \- la_gercond: Skeel condition number estimate .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "real function \fBcla_gercond_c\fP (trans, n, a, lda, af, ldaf, ipiv, c, capply, info, work, rwork)" .br .RI "\fBCLA_GERCOND_C\fP computes the infinity norm condition number of op(A)*inv(diag(c)) for general matrices\&. " .ti -1c .RI "real function \fBcla_gercond_x\fP (trans, n, a, lda, af, ldaf, ipiv, x, info, work, rwork)" .br .RI "\fBCLA_GERCOND_X\fP computes the infinity norm condition number of op(A)*diag(x) for general matrices\&. " .ti -1c .RI "double precision function \fBdla_gercond\fP (trans, n, a, lda, af, ldaf, ipiv, cmode, c, info, work, iwork)" .br .RI "\fBDLA_GERCOND\fP estimates the Skeel condition number for a general matrix\&. " .ti -1c .RI "real function \fBsla_gercond\fP (trans, n, a, lda, af, ldaf, ipiv, cmode, c, info, work, iwork)" .br .RI "\fBSLA_GERCOND\fP estimates the Skeel condition number for a general matrix\&. " .ti -1c .RI "double precision function \fBzla_gercond_c\fP (trans, n, a, lda, af, ldaf, ipiv, c, capply, info, work, rwork)" .br .RI "\fBZLA_GERCOND_C\fP computes the infinity norm condition number of op(A)*inv(diag(c)) for general matrices\&. " .ti -1c .RI "double precision function \fBzla_gercond_x\fP (trans, n, a, lda, af, ldaf, ipiv, x, info, work, rwork)" .br .RI "\fBZLA_GERCOND_X\fP computes the infinity norm condition number of op(A)*diag(x) for general matrices\&. " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "real function cla_gercond_c (character trans, 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)" .PP \fBCLA_GERCOND_C\fP computes the infinity norm condition number of op(A)*inv(diag(c)) for general matrices\&. .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> !> CLA_GERCOND_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 \fITRANS\fP .PP .nf !> 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) !> .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 factors L and U from the factorization !> A = P*L*U as computed by CGETRF\&. !> .fi .PP .br \fILDAF\fP .PP .nf !> LDAF is INTEGER !> The leading dimension of the array AF\&. LDAF >= max(1,N)\&. !> .fi .PP .br \fIIPIV\fP .PP .nf !> IPIV is INTEGER array, dimension (N) !> The pivot indices from the factorization A = P*L*U !> as computed by CGETRF; row i of the matrix was interchanged !> with row IPIV(i)\&. !> .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 .PP Definition at line \fB140\fP of file \fBcla_gercond_c\&.f\fP\&. .SS "real function cla_gercond_x (character trans, 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)" .PP \fBCLA_GERCOND_X\fP computes the infinity norm condition number of op(A)*diag(x) for general matrices\&. .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> !> CLA_GERCOND_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 \fITRANS\fP .PP .nf !> 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) !> .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 factors L and U from the factorization !> A = P*L*U as computed by CGETRF\&. !> .fi .PP .br \fILDAF\fP .PP .nf !> LDAF is INTEGER !> The leading dimension of the array AF\&. LDAF >= max(1,N)\&. !> .fi .PP .br \fIIPIV\fP .PP .nf !> IPIV is INTEGER array, dimension (N) !> The pivot indices from the factorization A = P*L*U !> as computed by CGETRF; row i of the matrix was interchanged !> with row IPIV(i)\&. !> .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 .PP Definition at line \fB133\fP of file \fBcla_gercond_x\&.f\fP\&. .SS "double precision function dla_gercond (character trans, 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)" .PP \fBDLA_GERCOND\fP estimates the Skeel condition number for a general matrix\&. .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> DLA_GERCOND 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 \fITRANS\fP .PP .nf !> 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) !> .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 factors L and U from the factorization !> A = P*L*U as computed by DGETRF\&. !> .fi .PP .br \fILDAF\fP .PP .nf !> LDAF is INTEGER !> The leading dimension of the array AF\&. LDAF >= max(1,N)\&. !> .fi .PP .br \fIIPIV\fP .PP .nf !> IPIV is INTEGER array, dimension (N) !> The pivot indices from the factorization A = P*L*U !> as computed by DGETRF; row i of the matrix was interchanged !> with row IPIV(i)\&. !> .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 .PP Definition at line \fB149\fP of file \fBdla_gercond\&.f\fP\&. .SS "real function sla_gercond (character trans, 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)" .PP \fBSLA_GERCOND\fP estimates the Skeel condition number for a general matrix\&. .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> SLA_GERCOND 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 \fITRANS\fP .PP .nf !> 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) !> .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 factors L and U from the factorization !> A = P*L*U as computed by SGETRF\&. !> .fi .PP .br \fILDAF\fP .PP .nf !> LDAF is INTEGER !> The leading dimension of the array AF\&. LDAF >= max(1,N)\&. !> .fi .PP .br \fIIPIV\fP .PP .nf !> IPIV is INTEGER array, dimension (N) !> The pivot indices from the factorization A = P*L*U !> as computed by SGETRF; row i of the matrix was interchanged !> with row IPIV(i)\&. !> .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\&.2 !> .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 .PP Definition at line \fB148\fP of file \fBsla_gercond\&.f\fP\&. .SS "double precision function zla_gercond_c (character trans, 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)" .PP \fBZLA_GERCOND_C\fP computes the infinity norm condition number of op(A)*inv(diag(c)) for general matrices\&. .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> ZLA_GERCOND_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 \fITRANS\fP .PP .nf !> 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) !> .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 factors L and U from the factorization !> A = P*L*U as computed by ZGETRF\&. !> .fi .PP .br \fILDAF\fP .PP .nf !> LDAF is INTEGER !> The leading dimension of the array AF\&. LDAF >= max(1,N)\&. !> .fi .PP .br \fIIPIV\fP .PP .nf !> IPIV is INTEGER array, dimension (N) !> The pivot indices from the factorization A = P*L*U !> as computed by ZGETRF; row i of the matrix was interchanged !> with row IPIV(i)\&. !> .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 .PP Definition at line \fB140\fP of file \fBzla_gercond_c\&.f\fP\&. .SS "double precision function zla_gercond_x (character trans, 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)" .PP \fBZLA_GERCOND_X\fP computes the infinity norm condition number of op(A)*diag(x) for general matrices\&. .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> ZLA_GERCOND_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 \fITRANS\fP .PP .nf !> 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) !> .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 factors L and U from the factorization !> A = P*L*U as computed by ZGETRF\&. !> .fi .PP .br \fILDAF\fP .PP .nf !> LDAF is INTEGER !> The leading dimension of the array AF\&. LDAF >= max(1,N)\&. !> .fi .PP .br \fIIPIV\fP .PP .nf !> IPIV is INTEGER array, dimension (N) !> The pivot indices from the factorization A = P*L*U !> as computed by ZGETRF; row i of the matrix was interchanged !> with row IPIV(i)\&. !> .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 .PP Definition at line \fB133\fP of file \fBzla_gercond_x\&.f\fP\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.