la_gercond - la_gercond: Skeel condition number estimate

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realfunctioncla_gercond_c(charactertrans,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_GERCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for general matrices. Purpose: CLA_GERCOND_C computes the infinity norm condition number of op(A) * inv(diag(C)) where C is a REAL vector. ParametersTRANS 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) 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 factors L and U from the factorization A = P*L*U as computed by CGETRF. LDAF LDAF is INTEGER The leading dimension of the array AF. LDAF >= max(1,N). IPIV 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). 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_gercond_x(charactertrans,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_GERCOND_X computes the infinity norm condition number of op(A)*diag(x) for general matrices. Purpose: CLA_GERCOND_X computes the infinity norm condition number of op(A) * diag(X) where X is a COMPLEX vector. ParametersTRANS 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) 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 factors L and U from the factorization A = P*L*U as computed by CGETRF. LDAF LDAF is INTEGER The leading dimension of the array AF. LDAF >= max(1,N). IPIV 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). 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_gercond(charactertrans,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_GERCOND estimates the Skeel condition number for a general matrix. Purpose: 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. ParametersTRANS 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) 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 factors L and U from the factorization A = P*L*U as computed by DGETRF. LDAF LDAF is INTEGER The leading dimension of the array AF. LDAF >= max(1,N). IPIV 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). 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_gercond(charactertrans,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_GERCOND estimates the Skeel condition number for a general matrix. Purpose: 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. ParametersTRANS 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) 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 factors L and U from the factorization A = P*L*U as computed by SGETRF. LDAF LDAF is INTEGER The leading dimension of the array AF. LDAF >= max(1,N). IPIV 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). 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.2 Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. doubleprecisionfunctionzla_gercond_c(charactertrans,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_GERCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for general matrices. Purpose: ZLA_GERCOND_C computes the infinity norm condition number of op(A) * inv(diag(C)) where C is a DOUBLE PRECISION vector. ParametersTRANS 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) 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 factors L and U from the factorization A = P*L*U as computed by ZGETRF. LDAF LDAF is INTEGER The leading dimension of the array AF. LDAF >= max(1,N). IPIV 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). 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_gercond_x(charactertrans,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_GERCOND_X computes the infinity norm condition number of op(A)*diag(x) for general matrices. Purpose: ZLA_GERCOND_X computes the infinity norm condition number of op(A) * diag(X) where X is a COMPLEX*16 vector. ParametersTRANS 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) 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 factors L and U from the factorization A = P*L*U as computed by ZGETRF. LDAF LDAF is INTEGER The leading dimension of the array AF. LDAF >= max(1,N). IPIV 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). 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_gercond - la_gercond: Skeel condition number estimate

Functions real function cla_gercond_c (trans, n, a, lda, af, ldaf, ipiv, c, capply, info, work, rwork) CLA_GERCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for general matrices. real function cla_gercond_x (trans, n, a, lda, af, ldaf, ipiv, x, info, work, rwork) CLA_GERCOND_X computes the infinity norm condition number of op(A)*diag(x) for general matrices. double precision function dla_gercond (trans, n, a, lda, af, ldaf, ipiv, cmode, c, info, work, iwork) DLA_GERCOND estimates the Skeel condition number for a general matrix. real function sla_gercond (trans, n, a, lda, af, ldaf, ipiv, cmode, c, info, work, iwork) SLA_GERCOND estimates the Skeel condition number for a general matrix. double precision function zla_gercond_c (trans, n, a, lda, af, ldaf, ipiv, c, capply, info, work, rwork) ZLA_GERCOND_C computes the infinity norm condition number of op(A)*inv(diag(c)) for general matrices. double precision function zla_gercond_x (trans, n, a, lda, af, ldaf, ipiv, x, info, work, rwork) ZLA_GERCOND_X computes the infinity norm condition number of op(A)*diag(x) for general matrices.