hecon_3(3)

NAME
hecon_3 - {he,sy}con_3: condition number estimate

SYNOPSIS

  Functions

subroutine checon_3 (uplo, n, a, lda, e, ipiv, anorm, rcond, work, info)
CHECON_3
subroutine csycon_3 (uplo, n, a, lda, e, ipiv, anorm, rcond, work, info)
CSYCON_3
subroutine dsycon_3 (uplo, n, a, lda, e, ipiv, anorm, rcond, work, iwork, info)
DSYCON_3
subroutine ssycon_3 (uplo, n, a, lda, e, ipiv, anorm, rcond, work, iwork, info)
SSYCON_3
subroutine zhecon_3 (uplo, n, a, lda, e, ipiv, anorm, rcond, work, info)
ZHECON_3
subroutine zsycon_3 (uplo, n, a, lda, e, ipiv, anorm, rcond, work, info)
ZSYCON_3

Detailed Description

Function Documentation

  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)

CHECON_3

Purpose:

    !> 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.
    !>

Parameters
    UPLO

    !>          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).
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.
    !>

    A

    !>          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.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= max(1,N).
    !>

    E

    !>          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.
    !>

    IPIV

    !>          IPIV is INTEGER array, dimension (N)
    !>          Details of the interchanges and the block structure of D
    !>          as determined by CHETRF_RK or CHETRF_BK.
    !>

    ANORM

    !>          ANORM is REAL
    !>          The 1-norm of the original matrix A.
    !>

    RCOND

    !>          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.
    !>

    WORK

    !>          WORK is COMPLEX array, dimension (2*N)
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Contributors:

    !>
    !>  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
    !>
    !>

  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)

CSYCON_3

Purpose:

    !> 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.
    !>

Parameters
    UPLO

    !>          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).
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.
    !>

    A

    !>          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.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= max(1,N).
    !>

    E

    !>          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.
    !>

    IPIV

    !>          IPIV is INTEGER array, dimension (N)
    !>          Details of the interchanges and the block structure of D
    !>          as determined by CSYTRF_RK or CSYTRF_BK.
    !>

    ANORM

    !>          ANORM is REAL
    !>          The 1-norm of the original matrix A.
    !>

    RCOND

    !>          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.
    !>

    WORK

    !>          WORK is COMPLEX array, dimension (2*N)
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Contributors:

    !>
    !>  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
    !>
    !>

  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)

DSYCON_3

Purpose:

    !> 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.
    !>

Parameters
    UPLO

    !>          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).
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.
    !>

    A

    !>          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.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= max(1,N).
    !>

    E

    !>          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.
    !>

    IPIV

    !>          IPIV is INTEGER array, dimension (N)
    !>          Details of the interchanges and the block structure of D
    !>          as determined by DSYTRF_RK or DSYTRF_BK.
    !>

    ANORM

    !>          ANORM is DOUBLE PRECISION
    !>          The 1-norm of the original matrix A.
    !>

    RCOND

    !>          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.
    !>

    WORK

    !>          WORK is DOUBLE PRECISION array, dimension (2*N)
    !>

    IWORK

    !>          IWORK is INTEGER array, dimension (N)
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Contributors:

    !>
    !>  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
    !>
    !>

  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)

SSYCON_3

Purpose:

    !> 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.
    !>

Parameters
    UPLO

    !>          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).
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.
    !>

    A

    !>          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.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= max(1,N).
    !>

    E

    !>          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.
    !>

    IPIV

    !>          IPIV is INTEGER array, dimension (N)
    !>          Details of the interchanges and the block structure of D
    !>          as determined by SSYTRF_RK or SSYTRF_BK.
    !>

    ANORM

    !>          ANORM is REAL
    !>          The 1-norm of the original matrix A.
    !>

    RCOND

    !>          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.
    !>

    WORK

    !>          WORK is REAL array, dimension (2*N)
    !>

    IWORK

    !>          IWORK is INTEGER array, dimension (N)
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Contributors:

    !>
    !>  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
    !>
    !>

  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)

ZHECON_3

Purpose:

    !> 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.
    !>

Parameters
    UPLO

    !>          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).
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.
    !>

    A

    !>          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.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= max(1,N).
    !>

    E

    !>          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.
    !>

    IPIV

    !>          IPIV is INTEGER array, dimension (N)
    !>          Details of the interchanges and the block structure of D
    !>          as determined by ZHETRF_RK or ZHETRF_BK.
    !>

    ANORM

    !>          ANORM is DOUBLE PRECISION
    !>          The 1-norm of the original matrix A.
    !>

    RCOND

    !>          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.
    !>

    WORK

    !>          WORK is COMPLEX*16 array, dimension (2*N)
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Contributors:

    !>
    !>  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
    !>
    !>

  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)

ZSYCON_3

Purpose:

    !> 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.
    !>

Parameters
    UPLO

    !>          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).
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.
    !>

    A

    !>          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.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= max(1,N).
    !>

    E

    !>          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.
    !>

    IPIV

    !>          IPIV is INTEGER array, dimension (N)
    !>          Details of the interchanges and the block structure of D
    !>          as determined by ZSYTRF_RK or ZSYTRF_BK.
    !>

    ANORM

    !>          ANORM is DOUBLE PRECISION
    !>          The 1-norm of the original matrix A.
    !>

    RCOND

    !>          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.
    !>

    WORK

    !>          WORK is COMPLEX*16 array, dimension (2*N)
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Contributors:

    !>
    !>  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
    !>
    !>

Author

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