# syconvf - Man Page

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**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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