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

NAME

       syconvf_rook - syconvf_rook: convert to/from hetrf_rook to hetrf_rk format

SYNOPSIS

   Functions
       subroutine csyconvf_rook (uplo, way, n, a, lda, e, ipiv, info)
           CSYCONVF_ROOK
       subroutine dsyconvf_rook (uplo, way, n, a, lda, e, ipiv, info)
           DSYCONVF_ROOK
       subroutine ssyconvf_rook (uplo, way, n, a, lda, e, ipiv, info)
           SSYCONVF_ROOK
       subroutine zsyconvf_rook (uplo, way, n, a, lda, e, ipiv, info)
           ZSYCONVF_ROOK

Detailed Description

Function Documentation

   subroutine csyconvf_rook (character uplo, character way, integer n, complex, dimension( lda, *
       ) a, integer lda, complex, dimension( * ) e, integer, dimension( * ) ipiv, integer info)
       CSYCONVF_ROOK

       Purpose:

            If parameter WAY = 'C':
            CSYCONVF_ROOK converts the factorization output format used in
            CSYTRF_ROOK provided on entry in parameter A into the factorization
            output format used in CSYTRF_RK (or CSYTRF_BK) that is stored
            on exit in parameters A and E. IPIV format for CSYTRF_ROOK and
            CSYTRF_RK (or CSYTRF_BK) is the same and is not converted.

            If parameter WAY = 'R':
            CSYCONVF_ROOK performs the conversion in reverse direction, i.e.
            converts the factorization output format used in CSYTRF_RK
            (or CSYTRF_BK) provided on entry in parameters A and E into
            the factorization output format used in CSYTRF_ROOK that is stored
            on exit in parameter A. IPIV format for CSYTRF_ROOK and
            CSYTRF_RK (or CSYTRF_BK) is the same and is not converted.

            CSYCONVF_ROOK can also convert in Hermitian matrix case, i.e. between
            formats used in CHETRF_ROOK and CHETRF_RK (or CHETRF_BK).

       Parameters
           UPLO

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

           WAY

                     WAY is CHARACTER*1
                     = 'C': Convert
                     = 'R': Revert

           N

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

           A

                     A is COMPLEX array, dimension (LDA,N)

                     1) If WAY ='C':

                     On entry, contains factorization details in format used in
                     CSYTRF_ROOK:
                       a) all elements of the symmetric block diagonal
                          matrix D on the diagonal of A and on superdiagonal
                          (or subdiagonal) of A, and
                       b) If UPLO = 'U': multipliers used to obtain factor U
                          in the superdiagonal part of A.
                          If UPLO = 'L': multipliers used to obtain factor L
                          in the superdiagonal part of A.

                     On exit, contains factorization details in format used in
                     CSYTRF_RK or 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
                           are stored on exit 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.

                     2) If WAY = 'R':

                     On entry, contains factorization details in format used in
                     CSYTRF_RK or 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
                           are stored on exit 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, contains factorization details in format used in
                     CSYTRF_ROOK:
                       a) all elements of the symmetric block diagonal
                          matrix D on the diagonal of A and on superdiagonal
                          (or subdiagonal) of A, and
                       b) If UPLO = 'U': multipliers used to obtain factor U
                          in the superdiagonal part of A.
                          If UPLO = 'L': multipliers used to obtain factor L
                          in the superdiagonal 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)

                     1) If WAY ='C':

                     On entry, just a workspace.

                     On exit, 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) is set to 0;
                     If UPLO = 'L': E(i) = D(i+1,i), i=1:N-1, E(N) is set to 0.

                     2) If WAY = 'R':

                     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.

                     On exit, is not changed

           IPIV

                     IPIV is INTEGER array, dimension (N)
                     On entry, details of the interchanges and the block
                     structure of D as determined:
                     1) by CSYTRF_ROOK, if WAY ='C';
                     2) by CSYTRF_RK (or CSYTRF_BK), if WAY ='R'.
                     The IPIV format is the same for all these routines.

                     On exit, is not changed.

           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:

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

   subroutine dsyconvf_rook (character uplo, character way, integer n, double precision,
       dimension( lda, * ) a, integer lda, double precision, dimension( * ) e, integer,
       dimension( * ) ipiv, integer info)
       DSYCONVF_ROOK

       Purpose:

            If parameter WAY = 'C':
            DSYCONVF_ROOK converts the factorization output format used in
            DSYTRF_ROOK provided on entry in parameter A into the factorization
            output format used in DSYTRF_RK (or DSYTRF_BK) that is stored
            on exit in parameters A and E. IPIV format for DSYTRF_ROOK and
            DSYTRF_RK (or DSYTRF_BK) is the same and is not converted.

            If parameter WAY = 'R':
            DSYCONVF_ROOK performs the conversion in reverse direction, i.e.
            converts the factorization output format used in DSYTRF_RK
            (or DSYTRF_BK) provided on entry in parameters A and E into
            the factorization output format used in DSYTRF_ROOK that is stored
            on exit in parameter A. IPIV format for DSYTRF_ROOK and
            DSYTRF_RK (or DSYTRF_BK) is the same and is not converted.

       Parameters
           UPLO

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

           WAY

                     WAY is CHARACTER*1
                     = 'C': Convert
                     = 'R': Revert

           N

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

           A

                     A is DOUBLE PRECISION array, dimension (LDA,N)

                     1) If WAY ='C':

                     On entry, contains factorization details in format used in
                     DSYTRF_ROOK:
                       a) all elements of the symmetric block diagonal
                          matrix D on the diagonal of A and on superdiagonal
                          (or subdiagonal) of A, and
                       b) If UPLO = 'U': multipliers used to obtain factor U
                          in the superdiagonal part of A.
                          If UPLO = 'L': multipliers used to obtain factor L
                          in the superdiagonal part of A.

                     On exit, contains factorization details in format used in
                     DSYTRF_RK or 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
                           are stored on exit 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.

                     2) If WAY = 'R':

                     On entry, contains factorization details in format used in
                     DSYTRF_RK or 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
                           are stored on exit 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, contains factorization details in format used in
                     DSYTRF_ROOK:
                       a) all elements of the symmetric block diagonal
                          matrix D on the diagonal of A and on superdiagonal
                          (or subdiagonal) of A, and
                       b) If UPLO = 'U': multipliers used to obtain factor U
                          in the superdiagonal part of A.
                          If UPLO = 'L': multipliers used to obtain factor L
                          in the superdiagonal 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)

                     1) If WAY ='C':

                     On entry, just a workspace.

                     On exit, 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) is set to 0;
                     If UPLO = 'L': E(i) = D(i+1,i), i=1:N-1, E(N) is set to 0.

                     2) If WAY = 'R':

                     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.

                     On exit, is not changed

           IPIV

                     IPIV is INTEGER array, dimension (N)
                     On entry, details of the interchanges and the block
                     structure of D as determined:
                     1) by DSYTRF_ROOK, if WAY ='C';
                     2) by DSYTRF_RK (or DSYTRF_BK), if WAY ='R'.
                     The IPIV format is the same for all these routines.

                     On exit, is not changed.

           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:

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

   subroutine ssyconvf_rook (character uplo, character way, integer n, real, dimension( lda, * )
       a, integer lda, real, dimension( * ) e, integer, dimension( * ) ipiv, integer info)
       SSYCONVF_ROOK

       Purpose:

            If parameter WAY = 'C':
            SSYCONVF_ROOK converts the factorization output format used in
            SSYTRF_ROOK provided on entry in parameter A into the factorization
            output format used in SSYTRF_RK (or SSYTRF_BK) that is stored
            on exit in parameters A and E. IPIV format for SSYTRF_ROOK and
            SSYTRF_RK (or SSYTRF_BK) is the same and is not converted.

            If parameter WAY = 'R':
            SSYCONVF_ROOK performs the conversion in reverse direction, i.e.
            converts the factorization output format used in SSYTRF_RK
            (or SSYTRF_BK) provided on entry in parameters A and E into
            the factorization output format used in SSYTRF_ROOK that is stored
            on exit in parameter A. IPIV format for SSYTRF_ROOK and
            SSYTRF_RK (or SSYTRF_BK) is the same and is not converted.

       Parameters
           UPLO

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

           WAY

                     WAY is CHARACTER*1
                     = 'C': Convert
                     = 'R': Revert

           N

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

           A

                     A is REAL array, dimension (LDA,N)

                     1) If WAY ='C':

                     On entry, contains factorization details in format used in
                     SSYTRF_ROOK:
                       a) all elements of the symmetric block diagonal
                          matrix D on the diagonal of A and on superdiagonal
                          (or subdiagonal) of A, and
                       b) If UPLO = 'U': multipliers used to obtain factor U
                          in the superdiagonal part of A.
                          If UPLO = 'L': multipliers used to obtain factor L
                          in the superdiagonal part of A.

                     On exit, contains factorization details in format used in
                     SSYTRF_RK or 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
                           are stored on exit 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.

                     2) If WAY = 'R':

                     On entry, contains factorization details in format used in
                     SSYTRF_RK or 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
                           are stored on exit 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, contains factorization details in format used in
                     SSYTRF_ROOK:
                       a) all elements of the symmetric block diagonal
                          matrix D on the diagonal of A and on superdiagonal
                          (or subdiagonal) of A, and
                       b) If UPLO = 'U': multipliers used to obtain factor U
                          in the superdiagonal part of A.
                          If UPLO = 'L': multipliers used to obtain factor L
                          in the superdiagonal 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)

                     1) If WAY ='C':

                     On entry, just a workspace.

                     On exit, 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) is set to 0;
                     If UPLO = 'L': E(i) = D(i+1,i), i=1:N-1, E(N) is set to 0.

                     2) If WAY = 'R':

                     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.

                     On exit, is not changed

           IPIV

                     IPIV is INTEGER array, dimension (N)
                     On entry, details of the interchanges and the block
                     structure of D as determined:
                     1) by SSYTRF_ROOK, if WAY ='C';
                     2) by SSYTRF_RK (or SSYTRF_BK), if WAY ='R'.
                     The IPIV format is the same for all these routines.

                     On exit, is not changed.

           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:

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

   subroutine zsyconvf_rook (character uplo, character way, integer n, complex*16, dimension(
       lda, * ) a, integer lda, complex*16, dimension( * ) e, integer, dimension( * ) ipiv,
       integer info)
       ZSYCONVF_ROOK

       Purpose:

            If parameter WAY = 'C':
            ZSYCONVF_ROOK converts the factorization output format used in
            ZSYTRF_ROOK provided on entry in parameter A into the factorization
            output format used in ZSYTRF_RK (or ZSYTRF_BK) that is stored
            on exit in parameters A and E. IPIV format for ZSYTRF_ROOK and
            ZSYTRF_RK (or ZSYTRF_BK) is the same and is not converted.

            If parameter WAY = 'R':
            ZSYCONVF_ROOK performs the conversion in reverse direction, i.e.
            converts the factorization output format used in ZSYTRF_RK
            (or ZSYTRF_BK) provided on entry in parameters A and E into
            the factorization output format used in ZSYTRF_ROOK that is stored
            on exit in parameter A. IPIV format for ZSYTRF_ROOK and
            ZSYTRF_RK (or ZSYTRF_BK) is the same and is not converted.

            ZSYCONVF_ROOK can also convert in Hermitian matrix case, i.e. between
            formats used in ZHETRF_ROOK and ZHETRF_RK (or ZHETRF_BK).

       Parameters
           UPLO

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

           WAY

                     WAY is CHARACTER*1
                     = 'C': Convert
                     = 'R': Revert

           N

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

           A

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

                     1) If WAY ='C':

                     On entry, contains factorization details in format used in
                     ZSYTRF_ROOK:
                       a) all elements of the symmetric block diagonal
                          matrix D on the diagonal of A and on superdiagonal
                          (or subdiagonal) of A, and
                       b) If UPLO = 'U': multipliers used to obtain factor U
                          in the superdiagonal part of A.
                          If UPLO = 'L': multipliers used to obtain factor L
                          in the superdiagonal part of A.

                     On exit, contains factorization details in format used in
                     ZSYTRF_RK or 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
                           are stored on exit 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.

                     2) If WAY = 'R':

                     On entry, contains factorization details in format used in
                     ZSYTRF_RK or 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
                           are stored on exit 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, contains factorization details in format used in
                     ZSYTRF_ROOK:
                       a) all elements of the symmetric block diagonal
                          matrix D on the diagonal of A and on superdiagonal
                          (or subdiagonal) of A, and
                       b) If UPLO = 'U': multipliers used to obtain factor U
                          in the superdiagonal part of A.
                          If UPLO = 'L': multipliers used to obtain factor L
                          in the superdiagonal 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)

                     1) If WAY ='C':

                     On entry, just a workspace.

                     On exit, 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) is set to 0;
                     If UPLO = 'L': E(i) = D(i+1,i), i=1:N-1, E(N) is set to 0.

                     2) If WAY = 'R':

                     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.

                     On exit, is not changed

           IPIV

                     IPIV is INTEGER array, dimension (N)
                     On entry, details of the interchanges and the block
                     structure of D as determined:
                     1) by ZSYTRF_ROOK, if WAY ='C';
                     2) by ZSYTRF_RK (or ZSYTRF_BK), if WAY ='R'.
                     The IPIV format is the same for all these routines.

                     On exit, is not changed.

           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:

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

Author

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