la_hercond - la_hercond: Skeel condition number estimate

Generated automatically by Doxygen for LAPACK from the source code. Version 3.12.0 Thu Aug 7 2025 17:26:25 la_hercond(3)

realfunctioncla_hercond_c(characteruplo,integern,complex,dimension(lda,*)a,integerlda,complex,dimension(ldaf,*)af,integerldaf,integer,dimension(*)ipiv,real,dimension(*)c,logicalcapply,integerinfo,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. ParametersUPLO 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 block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by CHETRF. LDAF LDAF is INTEGER The leading dimension of the array AF. LDAF >= max(1,N). IPIV IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by CHETRF. 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. realfunctioncla_hercond_x(characteruplo,integern,complex,dimension(lda,*)a,integerlda,complex,dimension(ldaf,*)af,integerldaf,integer,dimension(*)ipiv,complex,dimension(*)x,integerinfo,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. ParametersUPLO 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 block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by CHETRF. LDAF LDAF is INTEGER The leading dimension of the array AF. LDAF >= max(1,N). IPIV IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by CHETRF. 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. realfunctioncla_syrcond_c(characteruplo,integern,complex,dimension(lda,*)a,integerlda,complex,dimension(ldaf,*)af,integerldaf,integer,dimension(*)ipiv,real,dimension(*)c,logicalcapply,integerinfo,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. ParametersUPLO 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 block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by CSYTRF. LDAF LDAF is INTEGER The leading dimension of the array AF. LDAF >= max(1,N). IPIV IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by CSYTRF. 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. realfunctioncla_syrcond_x(characteruplo,integern,complex,dimension(lda,*)a,integerlda,complex,dimension(ldaf,*)af,integerldaf,integer,dimension(*)ipiv,complex,dimension(*)x,integerinfo,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. ParametersUPLO 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 block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by CSYTRF. LDAF LDAF is INTEGER The leading dimension of the array AF. LDAF >= max(1,N). IPIV IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by CSYTRF. 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. doubleprecisionfunctiondla_syrcond(characteruplo,integern,doubleprecision,dimension(lda,*)a,integerlda,doubleprecision,dimension(ldaf,*)af,integerldaf,integer,dimension(*)ipiv,integercmode,doubleprecision,dimension(*)c,integerinfo,doubleprecision,dimension(*)work,integer,dimension(*)iwork)DLA_SYRCOND estimates the Skeel condition number for a symmetric indefinite matrix. Purpose: DLA_SYRCOND 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. ParametersUPLO 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 block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by DSYTRF. LDAF LDAF is INTEGER The leading dimension of the array AF. LDAF >= max(1,N). IPIV IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by DSYTRF. 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. realfunctionsla_syrcond(characteruplo,integern,real,dimension(lda,*)a,integerlda,real,dimension(ldaf,*)af,integerldaf,integer,dimension(*)ipiv,integercmode,real,dimension(*)c,integerinfo,real,dimension(*)work,integer,dimension(*)iwork)SLA_SYRCOND estimates the Skeel condition number for a symmetric indefinite matrix. Purpose: SLA_SYRCOND 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. ParametersUPLO 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 block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by SSYTRF. LDAF LDAF is INTEGER The leading dimension of the array AF. LDAF >= max(1,N). IPIV IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by SSYTRF. 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. doubleprecisionfunctionzla_hercond_c(characteruplo,integern,complex*16,dimension(lda,*)a,integerlda,complex*16,dimension(ldaf,*)af,integerldaf,integer,dimension(*)ipiv,doubleprecision,dimension(*)c,logicalcapply,integerinfo,complex*16,dimension(*)work,doubleprecision,dimension(*)rwork)ZLA_HERCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian indefinite matrices. Purpose: ZLA_HERCOND_C computes the infinity norm condition number of op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector. ParametersUPLO 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 block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by ZHETRF. LDAF LDAF is INTEGER The leading dimension of the array AF. LDAF >= max(1,N). IPIV IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by CHETRF. 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. doubleprecisionfunctionzla_hercond_x(characteruplo,integern,complex*16,dimension(lda,*)a,integerlda,complex*16,dimension(ldaf,*)af,integerldaf,integer,dimension(*)ipiv,complex*16,dimension(*)x,integerinfo,complex*16,dimension(*)work,doubleprecision,dimension(*)rwork)ZLA_HERCOND_X computes the infinity norm condition number of op(A)*diag(x) for Hermitian indefinite matrices. Purpose: ZLA_HERCOND_X computes the infinity norm condition number of op(A) * diag(X) where X is a COMPLEX*16 vector. ParametersUPLO 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 block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by ZHETRF. LDAF LDAF is INTEGER The leading dimension of the array AF. LDAF >= max(1,N). IPIV IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by CHETRF. 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. doubleprecisionfunctionzla_syrcond_c(characteruplo,integern,complex*16,dimension(lda,*)a,integerlda,complex*16,dimension(ldaf,*)af,integerldaf,integer,dimension(*)ipiv,doubleprecision,dimension(*)c,logicalcapply,integerinfo,complex*16,dimension(*)work,doubleprecision,dimension(*)rwork)ZLA_SYRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for symmetric indefinite matrices. Purpose: ZLA_SYRCOND_C Computes the infinity norm condition number of op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector. ParametersUPLO 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 block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by ZSYTRF. LDAF LDAF is INTEGER The leading dimension of the array AF. LDAF >= max(1,N). IPIV IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by ZSYTRF. 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. doubleprecisionfunctionzla_syrcond_x(characteruplo,integern,complex*16,dimension(lda,*)a,integerlda,complex*16,dimension(ldaf,*)af,integerldaf,integer,dimension(*)ipiv,complex*16,dimension(*)x,integerinfo,complex*16,dimension(*)work,doubleprecision,dimension(*)rwork)ZLA_SYRCOND_X computes the infinity norm condition number of op(A)*diag(x) for symmetric indefinite matrices. Purpose: ZLA_SYRCOND_X Computes the infinity norm condition number of op(A) * diag(X) where X is a COMPLEX*16 vector. ParametersUPLO 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 block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by ZSYTRF. LDAF LDAF is INTEGER The leading dimension of the array AF. LDAF >= max(1,N). IPIV IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by ZSYTRF. 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.

la_hercond - la_hercond: Skeel condition number estimate

Functions real function cla_hercond_c (uplo, n, a, lda, af, ldaf, ipiv, c, capply, info, work, rwork) CLA_HERCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for Hermitian indefinite matrices. real function cla_hercond_x (uplo, n, a, lda, af, ldaf, ipiv, x, info, work, rwork) CLA_HERCOND_X computes the infinity norm condition number of op(A)*diag(x) for Hermitian indefinite matrices. real function cla_syrcond_c (uplo, n, a, lda, af, ldaf, ipiv, c, capply, info, work, rwork) CLA_SYRCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for symmetric indefinite matrices. real function cla_syrcond_x (uplo, n, a, lda, af, ldaf, ipiv, x, info, work, rwork) CLA_SYRCOND_X computes the infinity norm condition number of op(A)*diag(x) for symmetric indefinite matrices. double precision function dla_syrcond (uplo, n, a, lda, af, ldaf, ipiv, cmode, c, info, work, iwork) DLA_SYRCOND estimates 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) SLA_SYRCOND estimates 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) ZLA_HERCOND_C computes the infinity norm condition number of op(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) ZLA_HERCOND_X computes the infinity norm condition number of op(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) ZLA_SYRCOND_C computes the infinity norm condition number of op(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) ZLA_SYRCOND_X computes the infinity norm condition number of op(A)*diag(x) for symmetric indefinite matrices.