Provided by: liblapack-doc_3.12.0-3build1.1_all bug

NAME

       hetri_3 - {he,sy}tri_3: inverse

SYNOPSIS

   Functions
       subroutine chetri_3 (uplo, n, a, lda, e, ipiv, work, lwork, info)
           CHETRI_3
       subroutine csytri_3 (uplo, n, a, lda, e, ipiv, work, lwork, info)
           CSYTRI_3
       subroutine dsytri_3 (uplo, n, a, lda, e, ipiv, work, lwork, info)
           DSYTRI_3
       subroutine ssytri_3 (uplo, n, a, lda, e, ipiv, work, lwork, info)
           SSYTRI_3
       subroutine zhetri_3 (uplo, n, a, lda, e, ipiv, work, lwork, info)
           ZHETRI_3
       subroutine zsytri_3 (uplo, n, a, lda, e, ipiv, work, lwork, info)
           ZSYTRI_3

Detailed Description

Function Documentation

   subroutine chetri_3 (character uplo, integer n, complex, dimension( lda, * ) a, integer lda,
       complex, dimension( * ) e, integer, dimension( * ) ipiv, complex, dimension( * ) work,
       integer lwork, integer info)
       CHETRI_3

       Purpose:

            CHETRI_3 computes the inverse of a complex Hermitian indefinite
            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.

            CHETRI_3 sets the leading dimension of the workspace  before calling
            CHETRI_3X that actually computes the inverse.  This is the blocked
            version of the algorithm, calling Level 3 BLAS.

       Parameters
           UPLO

                     UPLO is CHARACTER*1
                     Specifies whether the details of the factorization are
                     stored as an upper or lower triangular matrix.
                     = 'U':  Upper triangle of A is stored;
                     = 'L':  Lower triangle of A is stored.

           N

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

           A

                     A is COMPLEX array, dimension (LDA,N)
                     On entry, 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.

                     On exit, if INFO = 0, the Hermitian inverse of the original
                     matrix.
                        If UPLO = 'U': the upper triangular part of the inverse
                        is formed and the part of A below the diagonal is not
                        referenced;
                        If UPLO = 'L': the lower triangular part of the inverse
                        is formed and the part of A above the diagonal is not
                        referenced.

           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.

           WORK

                     WORK is COMPLEX array, dimension (N+NB+1)*(NB+3).
                     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

           LWORK

                     LWORK is INTEGER
                     The length of WORK. LWORK >= (N+NB+1)*(NB+3).

                     If LDWORK = -1, then a workspace query is assumed;
                     the routine only calculates the optimal size of the optimal
                     size of the WORK array, returns this value as the first
                     entry of the WORK array, and no error message related to
                     LWORK is issued by XERBLA.

           INFO

                     INFO is INTEGER
                     = 0: successful exit
                     < 0: if INFO = -i, the i-th argument had an illegal value
                     > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
                          inverse could not be computed.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Contributors:

             November 2017,  Igor Kozachenko,
                             Computer Science Division,
                             University of California, Berkeley

   subroutine csytri_3 (character uplo, integer n, complex, dimension( lda, * ) a, integer lda,
       complex, dimension( * ) e, integer, dimension( * ) ipiv, complex, dimension( * ) work,
       integer lwork, integer info)
       CSYTRI_3

       Purpose:

            CSYTRI_3 computes the inverse of a complex symmetric indefinite
            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.

            CSYTRI_3 sets the leading dimension of the workspace  before calling
            CSYTRI_3X that actually computes the inverse.  This is the blocked
            version of the algorithm, calling Level 3 BLAS.

       Parameters
           UPLO

                     UPLO is CHARACTER*1
                     Specifies whether the details of the factorization are
                     stored as an upper or lower triangular matrix.
                     = 'U':  Upper triangle of A is stored;
                     = 'L':  Lower triangle of A is stored.

           N

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

           A

                     A is COMPLEX array, dimension (LDA,N)
                     On entry, 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.

                     On exit, if INFO = 0, the symmetric inverse of the original
                     matrix.
                        If UPLO = 'U': the upper triangular part of the inverse
                        is formed and the part of A below the diagonal is not
                        referenced;
                        If UPLO = 'L': the lower triangular part of the inverse
                        is formed and the part of A above the diagonal is not
                        referenced.

           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.

           WORK

                     WORK is COMPLEX array, dimension (N+NB+1)*(NB+3).
                     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

           LWORK

                     LWORK is INTEGER
                     The length of WORK. LWORK >= (N+NB+1)*(NB+3).

                     If LDWORK = -1, then a workspace query is assumed;
                     the routine only calculates the optimal size of the optimal
                     size of the WORK array, returns this value as the first
                     entry of the WORK array, and no error message related to
                     LWORK is issued by XERBLA.

           INFO

                     INFO is INTEGER
                     = 0: successful exit
                     < 0: if INFO = -i, the i-th argument had an illegal value
                     > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
                          inverse could not be computed.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Contributors:

             November 2017,  Igor Kozachenko,
                             Computer Science Division,
                             University of California, Berkeley

   subroutine dsytri_3 (character uplo, integer n, double precision, dimension( lda, * ) a,
       integer lda, double precision, dimension( * ) e, integer, dimension( * ) ipiv, double
       precision, dimension( * ) work, integer lwork, integer info)
       DSYTRI_3

       Purpose:

            DSYTRI_3 computes the inverse of a real symmetric indefinite
            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.

            DSYTRI_3 sets the leading dimension of the workspace  before calling
            DSYTRI_3X that actually computes the inverse.  This is the blocked
            version of the algorithm, calling Level 3 BLAS.

       Parameters
           UPLO

                     UPLO is CHARACTER*1
                     Specifies whether the details of the factorization are
                     stored as an upper or lower triangular matrix.
                     = 'U':  Upper triangle of A is stored;
                     = 'L':  Lower triangle of A is stored.

           N

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

           A

                     A is DOUBLE PRECISION array, dimension (LDA,N)
                     On entry, 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.

                     On exit, if INFO = 0, the symmetric inverse of the original
                     matrix.
                        If UPLO = 'U': the upper triangular part of the inverse
                        is formed and the part of A below the diagonal is not
                        referenced;
                        If UPLO = 'L': the lower triangular part of the inverse
                        is formed and the part of A above the diagonal is not
                        referenced.

           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.

           WORK

                     WORK is DOUBLE PRECISION array, dimension (N+NB+1)*(NB+3).
                     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

           LWORK

                     LWORK is INTEGER
                     The length of WORK. LWORK >= (N+NB+1)*(NB+3).

                     If LDWORK = -1, then a workspace query is assumed;
                     the routine only calculates the optimal size of the optimal
                     size of the WORK array, returns this value as the first
                     entry of the WORK array, and no error message related to
                     LWORK is issued by XERBLA.

           INFO

                     INFO is INTEGER
                     = 0: successful exit
                     < 0: if INFO = -i, the i-th argument had an illegal value
                     > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
                          inverse could not be computed.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Contributors:

             November 2017,  Igor Kozachenko,
                             Computer Science Division,
                             University of California, Berkeley

   subroutine ssytri_3 (character uplo, integer n, real, dimension( lda, * ) a, integer lda,
       real, dimension( * ) e, integer, dimension( * ) ipiv, real, dimension( * ) work, integer
       lwork, integer info)
       SSYTRI_3

       Purpose:

            SSYTRI_3 computes the inverse of a real symmetric indefinite
            matrix A using the factorization computed by SSYTRF_RK or SSYTRF_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.

            SSYTRI_3 sets the leading dimension of the workspace  before calling
            SSYTRI_3X that actually computes the inverse.  This is the blocked
            version of the algorithm, calling Level 3 BLAS.

       Parameters
           UPLO

                     UPLO is CHARACTER*1
                     Specifies whether the details of the factorization are
                     stored as an upper or lower triangular matrix.
                     = 'U':  Upper triangle of A is stored;
                     = 'L':  Lower triangle of A is stored.

           N

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

           A

                     A is REAL array, dimension (LDA,N)
                     On entry, 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.

                     On exit, if INFO = 0, the symmetric inverse of the original
                     matrix.
                        If UPLO = 'U': the upper triangular part of the inverse
                        is formed and the part of A below the diagonal is not
                        referenced;
                        If UPLO = 'L': the lower triangular part of the inverse
                        is formed and the part of A above the diagonal is not
                        referenced.

           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.

           WORK

                     WORK is REAL array, dimension (N+NB+1)*(NB+3).
                     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

           LWORK

                     LWORK is INTEGER
                     The length of WORK. LWORK >= (N+NB+1)*(NB+3).

                     If LDWORK = -1, then a workspace query is assumed;
                     the routine only calculates the optimal size of the optimal
                     size of the WORK array, returns this value as the first
                     entry of the WORK array, and no error message related to
                     LWORK is issued by XERBLA.

           INFO

                     INFO is INTEGER
                     = 0: successful exit
                     < 0: if INFO = -i, the i-th argument had an illegal value
                     > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
                          inverse could not be computed.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Contributors:

             November 2017,  Igor Kozachenko,
                             Computer Science Division,
                             University of California, Berkeley

   subroutine zhetri_3 (character uplo, integer n, complex*16, dimension( lda, * ) a, integer
       lda, complex*16, dimension( * ) e, integer, dimension( * ) ipiv, complex*16, dimension( *
       ) work, integer lwork, integer info)
       ZHETRI_3

       Purpose:

            ZHETRI_3 computes the inverse of a complex Hermitian indefinite
            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.

            ZHETRI_3 sets the leading dimension of the workspace  before calling
            ZHETRI_3X that actually computes the inverse.  This is the blocked
            version of the algorithm, calling Level 3 BLAS.

       Parameters
           UPLO

                     UPLO is CHARACTER*1
                     Specifies whether the details of the factorization are
                     stored as an upper or lower triangular matrix.
                     = 'U':  Upper triangle of A is stored;
                     = 'L':  Lower triangle of A is stored.

           N

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

           A

                     A is COMPLEX*16 array, dimension (LDA,N)
                     On entry, 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.

                     On exit, if INFO = 0, the Hermitian inverse of the original
                     matrix.
                        If UPLO = 'U': the upper triangular part of the inverse
                        is formed and the part of A below the diagonal is not
                        referenced;
                        If UPLO = 'L': the lower triangular part of the inverse
                        is formed and the part of A above the diagonal is not
                        referenced.

           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.

           WORK

                     WORK is COMPLEX*16 array, dimension (N+NB+1)*(NB+3).
                     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

           LWORK

                     LWORK is INTEGER
                     The length of WORK. LWORK >= (N+NB+1)*(NB+3).

                     If LDWORK = -1, then a workspace query is assumed;
                     the routine only calculates the optimal size of the optimal
                     size of the WORK array, returns this value as the first
                     entry of the WORK array, and no error message related to
                     LWORK is issued by XERBLA.

           INFO

                     INFO is INTEGER
                     = 0: successful exit
                     < 0: if INFO = -i, the i-th argument had an illegal value
                     > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
                          inverse could not be computed.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Contributors:

             November 2017,  Igor Kozachenko,
                             Computer Science Division,
                             University of California, Berkeley

   subroutine zsytri_3 (character uplo, integer n, complex*16, dimension( lda, * ) a, integer
       lda, complex*16, dimension( * ) e, integer, dimension( * ) ipiv, complex*16, dimension( *
       ) work, integer lwork, integer info)
       ZSYTRI_3

       Purpose:

            ZSYTRI_3 computes the inverse of a complex symmetric indefinite
            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.

            ZSYTRI_3 sets the leading dimension of the workspace  before calling
            ZSYTRI_3X that actually computes the inverse.  This is the blocked
            version of the algorithm, calling Level 3 BLAS.

       Parameters
           UPLO

                     UPLO is CHARACTER*1
                     Specifies whether the details of the factorization are
                     stored as an upper or lower triangular matrix.
                     = 'U':  Upper triangle of A is stored;
                     = 'L':  Lower triangle of A is stored.

           N

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

           A

                     A is COMPLEX*16 array, dimension (LDA,N)
                     On entry, 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.

                     On exit, if INFO = 0, the symmetric inverse of the original
                     matrix.
                        If UPLO = 'U': the upper triangular part of the inverse
                        is formed and the part of A below the diagonal is not
                        referenced;
                        If UPLO = 'L': the lower triangular part of the inverse
                        is formed and the part of A above the diagonal is not
                        referenced.

           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.

           WORK

                     WORK is COMPLEX*16 array, dimension (N+NB+1)*(NB+3).
                     On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

           LWORK

                     LWORK is INTEGER
                     The length of WORK. LWORK >= (N+NB+1)*(NB+3).

                     If LDWORK = -1, then a workspace query is assumed;
                     the routine only calculates the optimal size of the optimal
                     size of the WORK array, returns this value as the first
                     entry of the WORK array, and no error message related to
                     LWORK is issued by XERBLA.

           INFO

                     INFO is INTEGER
                     = 0: successful exit
                     < 0: if INFO = -i, the i-th argument had an illegal value
                     > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
                          inverse could not be computed.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Contributors:

             November 2017,  Igor Kozachenko,
                             Computer Science Division,
                             University of California, Berkeley

Author

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