syconvf(3)

NAME
syconvf - syconvf: convert to/from hetrf to hetrf_rk format

SYNOPSIS

  Functions
subroutine csyconvf (uplo, way, n, a, lda, e, ipiv, info)
CSYCONVF
subroutine dsyconvf (uplo, way, n, a, lda, e, ipiv, info)
DSYCONVF
subroutine ssyconvf (uplo, way, n, a, lda, e, ipiv, info)
SSYCONVF
subroutine zsyconvf (uplo, way, n, a, lda, e, ipiv, info)
ZSYCONVF

Detailed Description

Function Documentation

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

CSYCONVF

Purpose:

     If parameter WAY = 'C':
     CSYCONVF converts the factorization output format used in
     CSYTRF 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. It also converts in place details of
     the interchanges stored in IPIV from the format used in CSYTRF into
     the format used in CSYTRF_RK (or CSYTRF_BK).
     If parameter WAY = 'R':
     CSYCONVF 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 that is stored
     on exit in parameter A. It also converts in place details of
     the interchanges stored in IPIV from the format used in CSYTRF_RK
     (or CSYTRF_BK) into the format used in CSYTRF.
     CSYCONVF can also convert in Hermitian matrix case, i.e. between
     formats used in CHETRF 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:
                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:
                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)
              1) If WAY ='C':
              On entry, details of the interchanges and the block
              structure of D in the format used in CSYTRF.
              On exit, details of the interchanges and the block
              structure of D in the format used in CSYTRF_RK
              ( or CSYTRF_BK).
              1) If WAY ='R':
              On entry, details of the interchanges and the block
              structure of D in the format used in CSYTRF_RK
              ( or CSYTRF_BK).
              On exit, details of the interchanges and the block
              structure of D in the format used in CSYTRF.

    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

Definition at line 208 of file csyconvf.f.

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

DSYCONVF

Purpose:

     If parameter WAY = 'C':
     DSYCONVF converts the factorization output format used in
     DSYTRF 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. It also converts in place details of
     the interchanges stored in IPIV from the format used in DSYTRF into
     the format used in DSYTRF_RK (or DSYTRF_BK).
     If parameter WAY = 'R':
     DSYCONVF 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 that is stored
     on exit in parameter A. It also converts in place details of
     the interchanges stored in IPIV from the format used in DSYTRF_RK
     (or DSYTRF_BK) into the format used in DSYTRF.

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:
                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:
                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)
              1) If WAY ='C':
              On entry, details of the interchanges and the block
              structure of D in the format used in DSYTRF.
              On exit, details of the interchanges and the block
              structure of D in the format used in DSYTRF_RK
              ( or DSYTRF_BK).
              1) If WAY ='R':
              On entry, details of the interchanges and the block
              structure of D in the format used in DSYTRF_RK
              ( or DSYTRF_BK).
              On exit, details of the interchanges and the block
              structure of D in the format used in DSYTRF.

    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

Definition at line 205 of file dsyconvf.f.

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

SSYCONVF

Purpose:

     If parameter WAY = 'C':
     SSYCONVF converts the factorization output format used in
     SSYTRF 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. It also converts in place details of
     the interchanges stored in IPIV from the format used in SSYTRF into
     the format used in SSYTRF_RK (or SSYTRF_BK).
     If parameter WAY = 'R':
     SSYCONVF 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 that is stored
     on exit in parameter A. It also converts in place details of
     the interchanges stored in IPIV from the format used in SSYTRF_RK
     (or SSYTRF_BK) into the format used in SSYTRF.

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:
                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:
                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)
              1) If WAY ='C':
              On entry, details of the interchanges and the block
              structure of D in the format used in SSYTRF.
              On exit, details of the interchanges and the block
              structure of D in the format used in SSYTRF_RK
              ( or SSYTRF_BK).
              1) If WAY ='R':
              On entry, details of the interchanges and the block
              structure of D in the format used in SSYTRF_RK
              ( or SSYTRF_BK).
              On exit, details of the interchanges and the block
              structure of D in the format used in SSYTRF.

    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

Definition at line 205 of file ssyconvf.f.

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

ZSYCONVF

Purpose:

     If parameter WAY = 'C':
     ZSYCONVF converts the factorization output format used in
     ZSYTRF 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. It also converts in place details of
     the interchanges stored in IPIV from the format used in ZSYTRF into
     the format used in ZSYTRF_RK (or ZSYTRF_BK).
     If parameter WAY = 'R':
     ZSYCONVF 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 that is stored
     on exit in parameter A. It also converts in place details of
     the interchanges stored in IPIV from the format used in ZSYTRF_RK
     (or ZSYTRF_BK) into the format used in ZSYTRF.
     ZSYCONVF can also convert in Hermitian matrix case, i.e. between
     formats used in ZHETRF 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:
                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:
                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)
              1) If WAY ='C':
              On entry, details of the interchanges and the block
              structure of D in the format used in ZSYTRF.
              On exit, details of the interchanges and the block
              structure of D in the format used in ZSYTRF_RK
              ( or ZSYTRF_BK).
              1) If WAY ='R':
              On entry, details of the interchanges and the block
              structure of D in the format used in ZSYTRF_RK
              ( or ZSYTRF_BK).
              On exit, details of the interchanges and the block
              structure of D in the format used in ZSYTRF.

    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

Definition at line 208 of file zsyconvf.f.

Author

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