.TH "hecon_3" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME hecon_3 \- {he,sy}con_3: condition number estimate .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBchecon_3\fP (uplo, n, a, lda, e, ipiv, anorm, rcond, work, info)" .br .RI "\fBCHECON_3\fP " .ti -1c .RI "subroutine \fBcsycon_3\fP (uplo, n, a, lda, e, ipiv, anorm, rcond, work, info)" .br .RI "\fBCSYCON_3\fP " .ti -1c .RI "subroutine \fBdsycon_3\fP (uplo, n, a, lda, e, ipiv, anorm, rcond, work, iwork, info)" .br .RI "\fBDSYCON_3\fP " .ti -1c .RI "subroutine \fBssycon_3\fP (uplo, n, a, lda, e, ipiv, anorm, rcond, work, iwork, info)" .br .RI "\fBSSYCON_3\fP " .ti -1c .RI "subroutine \fBzhecon_3\fP (uplo, n, a, lda, e, ipiv, anorm, rcond, work, info)" .br .RI "\fBZHECON_3\fP " .ti -1c .RI "subroutine \fBzsycon_3\fP (uplo, n, a, lda, e, ipiv, anorm, rcond, work, info)" .br .RI "\fBZSYCON_3\fP " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine checon_3 (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) e, integer, dimension( * ) ipiv, real anorm, real rcond, complex, dimension( * ) work, integer info)" .PP \fBCHECON_3\fP .PP \fBPurpose:\fP .RS 4 .PP .nf CHECON_3 estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian matrix A using the factorization computed by CHETRF_RK or CHETRF_BK: A = P*U*D*(U**H)*(P**T) or A = P*L*D*(L**H)*(P**T), where U (or L) is unit upper (or lower) triangular matrix, U**H (or L**H) is the conjugate of U (or L), P is a permutation matrix, P**T is the transpose of P, and D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks\&. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A)))\&. This routine uses BLAS3 solver CHETRS_3\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf UPLO is CHARACTER*1 Specifies whether the details of the factorization are stored as an upper or lower triangular matrix: = 'U': Upper triangular, form is A = P*U*D*(U**H)*(P**T); = 'L': Lower triangular, form is A = P*L*D*(L**H)*(P**T)\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. N >= 0\&. .fi .PP .br \fIA\fP .PP .nf A is COMPLEX array, dimension (LDA,N) Diagonal of the block diagonal matrix D and factors U or L as computed by CHETRF_RK and CHETRF_BK: a) ONLY diagonal elements of the Hermitian block diagonal matrix D on the diagonal of A, i\&.e\&. D(k,k) = A(k,k); (superdiagonal (or subdiagonal) elements of D should be provided on entry in array E), and b) If UPLO = 'U': factor U in the superdiagonal part of A\&. If UPLO = 'L': factor L in the subdiagonal part of 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 \fIE\fP .PP .nf E is COMPLEX array, dimension (N) On entry, contains the superdiagonal (or subdiagonal) elements of the Hermitian block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks, where If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced; If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced\&. NOTE: For 1-by-1 diagonal block D(k), where 1 <= k <= N, the element E(k) is not referenced in both UPLO = 'U' or UPLO = 'L' cases\&. .fi .PP .br \fIIPIV\fP .PP .nf IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by CHETRF_RK or CHETRF_BK\&. .fi .PP .br \fIANORM\fP .PP .nf ANORM is REAL The 1-norm of the original matrix A\&. .fi .PP .br \fIRCOND\fP .PP .nf RCOND is REAL The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is COMPLEX array, dimension (2*N) .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value .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 \fBContributors:\fP .RS 4 .PP .nf June 2017, Igor Kozachenko, Computer Science Division, University of California, Berkeley September 2007, Sven Hammarling, Nicholas J\&. Higham, Craig Lucas, School of Mathematics, University of Manchester .fi .PP .RE .PP .SS "subroutine csycon_3 (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) e, integer, dimension( * ) ipiv, real anorm, real rcond, complex, dimension( * ) work, integer info)" .PP \fBCSYCON_3\fP .PP \fBPurpose:\fP .RS 4 .PP .nf CSYCON_3 estimates the reciprocal of the condition number (in the 1-norm) of a complex symmetric matrix A using the factorization computed by CSYTRF_RK or CSYTRF_BK: A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T), where U (or L) is unit upper (or lower) triangular matrix, U**T (or L**T) is the transpose of U (or L), P is a permutation matrix, P**T is the transpose of P, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks\&. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A)))\&. This routine uses BLAS3 solver CSYTRS_3\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf UPLO is CHARACTER*1 Specifies whether the details of the factorization are stored as an upper or lower triangular matrix: = 'U': Upper triangular, form is A = P*U*D*(U**T)*(P**T); = 'L': Lower triangular, form is A = P*L*D*(L**T)*(P**T)\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. N >= 0\&. .fi .PP .br \fIA\fP .PP .nf A is COMPLEX array, dimension (LDA,N) Diagonal of the block diagonal matrix D and factors U or L as computed by CSYTRF_RK and CSYTRF_BK: a) ONLY diagonal elements of the symmetric block diagonal matrix D on the diagonal of A, i\&.e\&. D(k,k) = A(k,k); (superdiagonal (or subdiagonal) elements of D should be provided on entry in array E), and b) If UPLO = 'U': factor U in the superdiagonal part of A\&. If UPLO = 'L': factor L in the subdiagonal part of 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 \fIE\fP .PP .nf E is COMPLEX array, dimension (N) On entry, contains the superdiagonal (or subdiagonal) elements of the symmetric block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks, where If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced; If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced\&. NOTE: For 1-by-1 diagonal block D(k), where 1 <= k <= N, the element E(k) is not referenced in both UPLO = 'U' or UPLO = 'L' cases\&. .fi .PP .br \fIIPIV\fP .PP .nf IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by CSYTRF_RK or CSYTRF_BK\&. .fi .PP .br \fIANORM\fP .PP .nf ANORM is REAL The 1-norm of the original matrix A\&. .fi .PP .br \fIRCOND\fP .PP .nf RCOND is REAL The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is COMPLEX array, dimension (2*N) .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value .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 \fBContributors:\fP .RS 4 .PP .nf June 2017, Igor Kozachenko, Computer Science Division, University of California, Berkeley September 2007, Sven Hammarling, Nicholas J\&. Higham, Craig Lucas, School of Mathematics, University of Manchester .fi .PP .RE .PP .SS "subroutine dsycon_3 (character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) e, integer, dimension( * ) ipiv, double precision anorm, double precision rcond, double precision, dimension( * ) work, integer, dimension( * ) iwork, integer info)" .PP \fBDSYCON_3\fP .PP \fBPurpose:\fP .RS 4 .PP .nf DSYCON_3 estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric matrix A using the factorization computed by DSYTRF_RK or DSYTRF_BK: A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T), where U (or L) is unit upper (or lower) triangular matrix, U**T (or L**T) is the transpose of U (or L), P is a permutation matrix, P**T is the transpose of P, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks\&. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A)))\&. This routine uses BLAS3 solver DSYTRS_3\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf UPLO is CHARACTER*1 Specifies whether the details of the factorization are stored as an upper or lower triangular matrix: = 'U': Upper triangular, form is A = P*U*D*(U**T)*(P**T); = 'L': Lower triangular, form is A = P*L*D*(L**T)*(P**T)\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. N >= 0\&. .fi .PP .br \fIA\fP .PP .nf A is DOUBLE PRECISION array, dimension (LDA,N) Diagonal of the block diagonal matrix D and factors U or L as computed by DSYTRF_RK and DSYTRF_BK: a) ONLY diagonal elements of the symmetric block diagonal matrix D on the diagonal of A, i\&.e\&. D(k,k) = A(k,k); (superdiagonal (or subdiagonal) elements of D should be provided on entry in array E), and b) If UPLO = 'U': factor U in the superdiagonal part of A\&. If UPLO = 'L': factor L in the subdiagonal part of 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 \fIE\fP .PP .nf E is DOUBLE PRECISION array, dimension (N) On entry, contains the superdiagonal (or subdiagonal) elements of the symmetric block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks, where If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced; If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced\&. NOTE: For 1-by-1 diagonal block D(k), where 1 <= k <= N, the element E(k) is not referenced in both UPLO = 'U' or UPLO = 'L' cases\&. .fi .PP .br \fIIPIV\fP .PP .nf IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by DSYTRF_RK or DSYTRF_BK\&. .fi .PP .br \fIANORM\fP .PP .nf ANORM is DOUBLE PRECISION The 1-norm of the original matrix A\&. .fi .PP .br \fIRCOND\fP .PP .nf RCOND is DOUBLE PRECISION The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is DOUBLE PRECISION array, dimension (2*N) .fi .PP .br \fIIWORK\fP .PP .nf IWORK is INTEGER array, dimension (N) .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value .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 \fBContributors:\fP .RS 4 .PP .nf June 2017, Igor Kozachenko, Computer Science Division, University of California, Berkeley September 2007, Sven Hammarling, Nicholas J\&. Higham, Craig Lucas, School of Mathematics, University of Manchester .fi .PP .RE .PP .SS "subroutine ssycon_3 (character uplo, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) e, integer, dimension( * ) ipiv, real anorm, real rcond, real, dimension( * ) work, integer, dimension( * ) iwork, integer info)" .PP \fBSSYCON_3\fP .PP \fBPurpose:\fP .RS 4 .PP .nf SSYCON_3 estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric matrix A using the factorization computed by DSYTRF_RK or DSYTRF_BK: A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T), where U (or L) is unit upper (or lower) triangular matrix, U**T (or L**T) is the transpose of U (or L), P is a permutation matrix, P**T is the transpose of P, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks\&. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A)))\&. This routine uses BLAS3 solver SSYTRS_3\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf UPLO is CHARACTER*1 Specifies whether the details of the factorization are stored as an upper or lower triangular matrix: = 'U': Upper triangular, form is A = P*U*D*(U**T)*(P**T); = 'L': Lower triangular, form is A = P*L*D*(L**T)*(P**T)\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. N >= 0\&. .fi .PP .br \fIA\fP .PP .nf A is REAL array, dimension (LDA,N) Diagonal of the block diagonal matrix D and factors U or L as computed by SSYTRF_RK and SSYTRF_BK: a) ONLY diagonal elements of the symmetric block diagonal matrix D on the diagonal of A, i\&.e\&. D(k,k) = A(k,k); (superdiagonal (or subdiagonal) elements of D should be provided on entry in array E), and b) If UPLO = 'U': factor U in the superdiagonal part of A\&. If UPLO = 'L': factor L in the subdiagonal part of 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 \fIE\fP .PP .nf E is REAL array, dimension (N) On entry, contains the superdiagonal (or subdiagonal) elements of the symmetric block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks, where If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced; If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced\&. NOTE: For 1-by-1 diagonal block D(k), where 1 <= k <= N, the element E(k) is not referenced in both UPLO = 'U' or UPLO = 'L' cases\&. .fi .PP .br \fIIPIV\fP .PP .nf IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by SSYTRF_RK or SSYTRF_BK\&. .fi .PP .br \fIANORM\fP .PP .nf ANORM is REAL The 1-norm of the original matrix A\&. .fi .PP .br \fIRCOND\fP .PP .nf RCOND is REAL The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is REAL array, dimension (2*N) .fi .PP .br \fIIWORK\fP .PP .nf IWORK is INTEGER array, dimension (N) .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value .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 \fBContributors:\fP .RS 4 .PP .nf June 2017, Igor Kozachenko, Computer Science Division, University of California, Berkeley September 2007, Sven Hammarling, Nicholas J\&. Higham, Craig Lucas, School of Mathematics, University of Manchester .fi .PP .RE .PP .SS "subroutine zhecon_3 (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) e, integer, dimension( * ) ipiv, double precision anorm, double precision rcond, complex*16, dimension( * ) work, integer info)" .PP \fBZHECON_3\fP .PP \fBPurpose:\fP .RS 4 .PP .nf ZHECON_3 estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian matrix A using the factorization computed by ZHETRF_RK or ZHETRF_BK: A = P*U*D*(U**H)*(P**T) or A = P*L*D*(L**H)*(P**T), where U (or L) is unit upper (or lower) triangular matrix, U**H (or L**H) is the conjugate of U (or L), P is a permutation matrix, P**T is the transpose of P, and D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks\&. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A)))\&. This routine uses BLAS3 solver ZHETRS_3\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf UPLO is CHARACTER*1 Specifies whether the details of the factorization are stored as an upper or lower triangular matrix: = 'U': Upper triangular, form is A = P*U*D*(U**H)*(P**T); = 'L': Lower triangular, form is A = P*L*D*(L**H)*(P**T)\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. N >= 0\&. .fi .PP .br \fIA\fP .PP .nf A is COMPLEX*16 array, dimension (LDA,N) Diagonal of the block diagonal matrix D and factors U or L as computed by ZHETRF_RK and ZHETRF_BK: a) ONLY diagonal elements of the Hermitian block diagonal matrix D on the diagonal of A, i\&.e\&. D(k,k) = A(k,k); (superdiagonal (or subdiagonal) elements of D should be provided on entry in array E), and b) If UPLO = 'U': factor U in the superdiagonal part of A\&. If UPLO = 'L': factor L in the subdiagonal part of 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 \fIE\fP .PP .nf E is COMPLEX*16 array, dimension (N) On entry, contains the superdiagonal (or subdiagonal) elements of the Hermitian block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks, where If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced; If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced\&. NOTE: For 1-by-1 diagonal block D(k), where 1 <= k <= N, the element E(k) is not referenced in both UPLO = 'U' or UPLO = 'L' cases\&. .fi .PP .br \fIIPIV\fP .PP .nf IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by ZHETRF_RK or ZHETRF_BK\&. .fi .PP .br \fIANORM\fP .PP .nf ANORM is DOUBLE PRECISION The 1-norm of the original matrix A\&. .fi .PP .br \fIRCOND\fP .PP .nf RCOND is DOUBLE PRECISION The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is COMPLEX*16 array, dimension (2*N) .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value .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 \fBContributors:\fP .RS 4 .PP .nf June 2017, Igor Kozachenko, Computer Science Division, University of California, Berkeley September 2007, Sven Hammarling, Nicholas J\&. Higham, Craig Lucas, School of Mathematics, University of Manchester .fi .PP .RE .PP .SS "subroutine zsycon_3 (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) e, integer, dimension( * ) ipiv, double precision anorm, double precision rcond, complex*16, dimension( * ) work, integer info)" .PP \fBZSYCON_3\fP .PP \fBPurpose:\fP .RS 4 .PP .nf ZSYCON_3 estimates the reciprocal of the condition number (in the 1-norm) of a complex symmetric matrix A using the factorization computed by ZSYTRF_RK or ZSYTRF_BK: A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T), where U (or L) is unit upper (or lower) triangular matrix, U**T (or L**T) is the transpose of U (or L), P is a permutation matrix, P**T is the transpose of P, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks\&. An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM * norm(inv(A)))\&. This routine uses BLAS3 solver ZSYTRS_3\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf UPLO is CHARACTER*1 Specifies whether the details of the factorization are stored as an upper or lower triangular matrix: = 'U': Upper triangular, form is A = P*U*D*(U**T)*(P**T); = 'L': Lower triangular, form is A = P*L*D*(L**T)*(P**T)\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. N >= 0\&. .fi .PP .br \fIA\fP .PP .nf A is COMPLEX*16 array, dimension (LDA,N) Diagonal of the block diagonal matrix D and factors U or L as computed by ZSYTRF_RK and ZSYTRF_BK: a) ONLY diagonal elements of the symmetric block diagonal matrix D on the diagonal of A, i\&.e\&. D(k,k) = A(k,k); (superdiagonal (or subdiagonal) elements of D should be provided on entry in array E), and b) If UPLO = 'U': factor U in the superdiagonal part of A\&. If UPLO = 'L': factor L in the subdiagonal part of 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 \fIE\fP .PP .nf E is COMPLEX*16 array, dimension (N) On entry, contains the superdiagonal (or subdiagonal) elements of the symmetric block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks, where If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced; If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced\&. NOTE: For 1-by-1 diagonal block D(k), where 1 <= k <= N, the element E(k) is not referenced in both UPLO = 'U' or UPLO = 'L' cases\&. .fi .PP .br \fIIPIV\fP .PP .nf IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by ZSYTRF_RK or ZSYTRF_BK\&. .fi .PP .br \fIANORM\fP .PP .nf ANORM is DOUBLE PRECISION The 1-norm of the original matrix A\&. .fi .PP .br \fIRCOND\fP .PP .nf RCOND is DOUBLE PRECISION The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is COMPLEX*16 array, dimension (2*N) .fi .PP .br \fIINFO\fP .PP .nf INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value .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 \fBContributors:\fP .RS 4 .PP .nf June 2017, Igor Kozachenko, Computer Science Division, University of California, Berkeley September 2007, Sven Hammarling, Nicholas J\&. Higham, Craig Lucas, School of Mathematics, University of Manchester .fi .PP .RE .PP .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.