.TH "lahef" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME lahef \- la{he,sy}f: step in hetrf .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBclahef\fP (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info)" .br .RI "\fBCLAHEF\fP computes a partial factorization of a complex Hermitian indefinite matrix using the Bunch-Kaufman diagonal pivoting method (blocked algorithm, calling Level 3 BLAS)\&. " .ti -1c .RI "subroutine \fBclasyf\fP (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info)" .br .RI "\fBCLASYF\fP computes a partial factorization of a complex symmetric matrix using the Bunch-Kaufman diagonal pivoting method\&. " .ti -1c .RI "subroutine \fBdlasyf\fP (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info)" .br .RI "\fBDLASYF\fP computes a partial factorization of a real symmetric matrix using the Bunch-Kaufman diagonal pivoting method\&. " .ti -1c .RI "subroutine \fBslasyf\fP (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info)" .br .RI "\fBSLASYF\fP computes a partial factorization of a real symmetric matrix using the Bunch-Kaufman diagonal pivoting method\&. " .ti -1c .RI "subroutine \fBzlahef\fP (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info)" .br .RI "\fBZLAHEF\fP computes a partial factorization of a complex Hermitian indefinite matrix using the Bunch-Kaufman diagonal pivoting method (blocked algorithm, calling Level 3 BLAS)\&. " .ti -1c .RI "subroutine \fBzlasyf\fP (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info)" .br .RI "\fBZLASYF\fP computes a partial factorization of a complex symmetric matrix using the Bunch-Kaufman diagonal pivoting method\&. " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine clahef (character uplo, integer n, integer nb, integer kb, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( ldw, * ) w, integer ldw, integer info)" .PP \fBCLAHEF\fP computes a partial factorization of a complex Hermitian indefinite matrix using the Bunch-Kaufman diagonal pivoting method (blocked algorithm, calling Level 3 BLAS)\&. .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> CLAHEF computes a partial factorization of a complex Hermitian !> matrix A using the Bunch-Kaufman diagonal pivoting method\&. The !> partial factorization has the form: !> !> A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = 'U', or: !> ( 0 U22 ) ( 0 D ) ( U12**H U22**H ) !> !> A = ( L11 0 ) ( D 0 ) ( L11**H L21**H ) if UPLO = 'L' !> ( L21 I ) ( 0 A22 ) ( 0 I ) !> !> where the order of D is at most NB\&. The actual order is returned in !> the argument KB, and is either NB or NB-1, or N if N <= NB\&. !> Note that U**H denotes the conjugate transpose of U\&. !> !> CLAHEF is an auxiliary routine called by CHETRF\&. It uses blocked code !> (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or !> A22 (if UPLO = 'L')\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf !> UPLO is CHARACTER*1 !> Specifies whether the upper or lower triangular part of the !> Hermitian matrix A is stored: !> = 'U': Upper triangular !> = 'L': Lower triangular !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrix A\&. N >= 0\&. !> .fi .PP .br \fINB\fP .PP .nf !> NB is INTEGER !> The maximum number of columns of the matrix A that should be !> factored\&. NB should be at least 2 to allow for 2-by-2 pivot !> blocks\&. !> .fi .PP .br \fIKB\fP .PP .nf !> KB is INTEGER !> The number of columns of A that were actually factored\&. !> KB is either NB-1 or NB, or N if N <= NB\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is COMPLEX array, dimension (LDA,N) !> On entry, the Hermitian matrix A\&. If UPLO = 'U', the leading !> n-by-n upper triangular part of A contains the upper !> triangular part of the matrix A, and the strictly lower !> triangular part of A is not referenced\&. If UPLO = 'L', the !> leading n-by-n lower triangular part of A contains the lower !> triangular part of the matrix A, and the strictly upper !> triangular part of A is not referenced\&. !> On exit, A contains details of the partial factorization\&. !> .fi .PP .br \fILDA\fP .PP .nf !> LDA is INTEGER !> The leading dimension of the array A\&. LDA >= max(1,N)\&. !> .fi .PP .br \fIIPIV\fP .PP .nf !> IPIV is INTEGER array, dimension (N) !> Details of the interchanges and the block structure of D\&. !> !> If UPLO = 'U': !> Only the last KB elements of IPIV are set\&. !> !> If IPIV(k) > 0, then rows and columns k and IPIV(k) were !> interchanged and D(k,k) is a 1-by-1 diagonal block\&. !> !> If IPIV(k) = IPIV(k-1) < 0, then rows and columns !> k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) !> is a 2-by-2 diagonal block\&. !> !> If UPLO = 'L': !> Only the first KB elements of IPIV are set\&. !> !> If IPIV(k) > 0, then rows and columns k and IPIV(k) were !> interchanged and D(k,k) is a 1-by-1 diagonal block\&. !> !> If IPIV(k) = IPIV(k+1) < 0, then rows and columns !> k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1) !> is a 2-by-2 diagonal block\&. !> .fi .PP .br \fIW\fP .PP .nf !> W is COMPLEX array, dimension (LDW,NB) !> .fi .PP .br \fILDW\fP .PP .nf !> LDW is INTEGER !> The leading dimension of the array W\&. LDW >= max(1,N)\&. !> .fi .PP .br \fIINFO\fP .PP .nf !> INFO is INTEGER !> = 0: successful exit !> > 0: if INFO = k, D(k,k) is exactly zero\&. The factorization !> has been completed, but the block diagonal matrix D is !> exactly singular\&. !> .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBContributors:\fP .RS 4 .PP .nf !> !> November 2013, Igor Kozachenko, !> Computer Science Division, !> University of California, Berkeley !> .fi .PP .RE .PP .PP Definition at line \fB176\fP of file \fBclahef\&.f\fP\&. .SS "subroutine clasyf (character uplo, integer n, integer nb, integer kb, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( ldw, * ) w, integer ldw, integer info)" .PP \fBCLASYF\fP computes a partial factorization of a complex symmetric matrix using the Bunch-Kaufman diagonal pivoting method\&. .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> CLASYF computes a partial factorization of a complex symmetric matrix !> A using the Bunch-Kaufman diagonal pivoting method\&. The partial !> factorization has the form: !> !> A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = 'U', or: !> ( 0 U22 ) ( 0 D ) ( U12**T U22**T ) !> !> A = ( L11 0 ) ( D 0 ) ( L11**T L21**T ) if UPLO = 'L' !> ( L21 I ) ( 0 A22 ) ( 0 I ) !> !> where the order of D is at most NB\&. The actual order is returned in !> the argument KB, and is either NB or NB-1, or N if N <= NB\&. !> Note that U**T denotes the transpose of U\&. !> !> CLASYF is an auxiliary routine called by CSYTRF\&. It uses blocked code !> (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or !> A22 (if UPLO = 'L')\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf !> UPLO is CHARACTER*1 !> Specifies whether the upper or lower triangular part of the !> symmetric matrix A is stored: !> = 'U': Upper triangular !> = 'L': Lower triangular !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrix A\&. N >= 0\&. !> .fi .PP .br \fINB\fP .PP .nf !> NB is INTEGER !> The maximum number of columns of the matrix A that should be !> factored\&. NB should be at least 2 to allow for 2-by-2 pivot !> blocks\&. !> .fi .PP .br \fIKB\fP .PP .nf !> KB is INTEGER !> The number of columns of A that were actually factored\&. !> KB is either NB-1 or NB, or N if N <= NB\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is COMPLEX array, dimension (LDA,N) !> On entry, the symmetric matrix A\&. If UPLO = 'U', the leading !> n-by-n upper triangular part of A contains the upper !> triangular part of the matrix A, and the strictly lower !> triangular part of A is not referenced\&. If UPLO = 'L', the !> leading n-by-n lower triangular part of A contains the lower !> triangular part of the matrix A, and the strictly upper !> triangular part of A is not referenced\&. !> On exit, A contains details of the partial factorization\&. !> .fi .PP .br \fILDA\fP .PP .nf !> LDA is INTEGER !> The leading dimension of the array A\&. LDA >= max(1,N)\&. !> .fi .PP .br \fIIPIV\fP .PP .nf !> IPIV is INTEGER array, dimension (N) !> Details of the interchanges and the block structure of D\&. !> !> If UPLO = 'U': !> Only the last KB elements of IPIV are set\&. !> !> If IPIV(k) > 0, then rows and columns k and IPIV(k) were !> interchanged and D(k,k) is a 1-by-1 diagonal block\&. !> !> If IPIV(k) = IPIV(k-1) < 0, then rows and columns !> k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) !> is a 2-by-2 diagonal block\&. !> !> If UPLO = 'L': !> Only the first KB elements of IPIV are set\&. !> !> If IPIV(k) > 0, then rows and columns k and IPIV(k) were !> interchanged and D(k,k) is a 1-by-1 diagonal block\&. !> !> If IPIV(k) = IPIV(k+1) < 0, then rows and columns !> k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1) !> is a 2-by-2 diagonal block\&. !> .fi .PP .br \fIW\fP .PP .nf !> W is COMPLEX array, dimension (LDW,NB) !> .fi .PP .br \fILDW\fP .PP .nf !> LDW is INTEGER !> The leading dimension of the array W\&. LDW >= max(1,N)\&. !> .fi .PP .br \fIINFO\fP .PP .nf !> INFO is INTEGER !> = 0: successful exit !> > 0: if INFO = k, D(k,k) is exactly zero\&. The factorization !> has been completed, but the block diagonal matrix D is !> exactly singular\&. !> .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBContributors:\fP .RS 4 .PP .nf !> !> November 2013, Igor Kozachenko, !> Computer Science Division, !> University of California, Berkeley !> .fi .PP .RE .PP .PP Definition at line \fB176\fP of file \fBclasyf\&.f\fP\&. .SS "subroutine dlasyf (character uplo, integer n, integer nb, integer kb, double precision, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precision, dimension( ldw, * ) w, integer ldw, integer info)" .PP \fBDLASYF\fP computes a partial factorization of a real symmetric matrix using the Bunch-Kaufman diagonal pivoting method\&. .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> DLASYF computes a partial factorization of a real symmetric matrix A !> using the Bunch-Kaufman diagonal pivoting method\&. The partial !> factorization has the form: !> !> A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = 'U', or: !> ( 0 U22 ) ( 0 D ) ( U12**T U22**T ) !> !> A = ( L11 0 ) ( D 0 ) ( L11**T L21**T ) if UPLO = 'L' !> ( L21 I ) ( 0 A22 ) ( 0 I ) !> !> where the order of D is at most NB\&. The actual order is returned in !> the argument KB, and is either NB or NB-1, or N if N <= NB\&. !> !> DLASYF is an auxiliary routine called by DSYTRF\&. It uses blocked code !> (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or !> A22 (if UPLO = 'L')\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf !> UPLO is CHARACTER*1 !> Specifies whether the upper or lower triangular part of the !> symmetric matrix A is stored: !> = 'U': Upper triangular !> = 'L': Lower triangular !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrix A\&. N >= 0\&. !> .fi .PP .br \fINB\fP .PP .nf !> NB is INTEGER !> The maximum number of columns of the matrix A that should be !> factored\&. NB should be at least 2 to allow for 2-by-2 pivot !> blocks\&. !> .fi .PP .br \fIKB\fP .PP .nf !> KB is INTEGER !> The number of columns of A that were actually factored\&. !> KB is either NB-1 or NB, or N if N <= NB\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is DOUBLE PRECISION array, dimension (LDA,N) !> On entry, the symmetric matrix A\&. If UPLO = 'U', the leading !> n-by-n upper triangular part of A contains the upper !> triangular part of the matrix A, and the strictly lower !> triangular part of A is not referenced\&. If UPLO = 'L', the !> leading n-by-n lower triangular part of A contains the lower !> triangular part of the matrix A, and the strictly upper !> triangular part of A is not referenced\&. !> On exit, A contains details of the partial factorization\&. !> .fi .PP .br \fILDA\fP .PP .nf !> LDA is INTEGER !> The leading dimension of the array A\&. LDA >= max(1,N)\&. !> .fi .PP .br \fIIPIV\fP .PP .nf !> IPIV is INTEGER array, dimension (N) !> Details of the interchanges and the block structure of D\&. !> !> If UPLO = 'U': !> Only the last KB elements of IPIV are set\&. !> !> If IPIV(k) > 0, then rows and columns k and IPIV(k) were !> interchanged and D(k,k) is a 1-by-1 diagonal block\&. !> !> If IPIV(k) = IPIV(k-1) < 0, then rows and columns !> k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) !> is a 2-by-2 diagonal block\&. !> !> If UPLO = 'L': !> Only the first KB elements of IPIV are set\&. !> !> If IPIV(k) > 0, then rows and columns k and IPIV(k) were !> interchanged and D(k,k) is a 1-by-1 diagonal block\&. !> !> If IPIV(k) = IPIV(k+1) < 0, then rows and columns !> k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1) !> is a 2-by-2 diagonal block\&. !> .fi .PP .br \fIW\fP .PP .nf !> W is DOUBLE PRECISION array, dimension (LDW,NB) !> .fi .PP .br \fILDW\fP .PP .nf !> LDW is INTEGER !> The leading dimension of the array W\&. LDW >= max(1,N)\&. !> .fi .PP .br \fIINFO\fP .PP .nf !> INFO is INTEGER !> = 0: successful exit !> > 0: if INFO = k, D(k,k) is exactly zero\&. The factorization !> has been completed, but the block diagonal matrix D is !> exactly singular\&. !> .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBContributors:\fP .RS 4 .PP .nf !> !> November 2013, Igor Kozachenko, !> Computer Science Division, !> University of California, Berkeley !> .fi .PP .RE .PP .PP Definition at line \fB175\fP of file \fBdlasyf\&.f\fP\&. .SS "subroutine slasyf (character uplo, integer n, integer nb, integer kb, real, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, real, dimension( ldw, * ) w, integer ldw, integer info)" .PP \fBSLASYF\fP computes a partial factorization of a real symmetric matrix using the Bunch-Kaufman diagonal pivoting method\&. .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> SLASYF computes a partial factorization of a real symmetric matrix A !> using the Bunch-Kaufman diagonal pivoting method\&. The partial !> factorization has the form: !> !> A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = 'U', or: !> ( 0 U22 ) ( 0 D ) ( U12**T U22**T ) !> !> A = ( L11 0 ) ( D 0 ) ( L11**T L21**T ) if UPLO = 'L' !> ( L21 I ) ( 0 A22 ) ( 0 I ) !> !> where the order of D is at most NB\&. The actual order is returned in !> the argument KB, and is either NB or NB-1, or N if N <= NB\&. !> !> SLASYF is an auxiliary routine called by SSYTRF\&. It uses blocked code !> (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or !> A22 (if UPLO = 'L')\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf !> UPLO is CHARACTER*1 !> Specifies whether the upper or lower triangular part of the !> symmetric matrix A is stored: !> = 'U': Upper triangular !> = 'L': Lower triangular !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrix A\&. N >= 0\&. !> .fi .PP .br \fINB\fP .PP .nf !> NB is INTEGER !> The maximum number of columns of the matrix A that should be !> factored\&. NB should be at least 2 to allow for 2-by-2 pivot !> blocks\&. !> .fi .PP .br \fIKB\fP .PP .nf !> KB is INTEGER !> The number of columns of A that were actually factored\&. !> KB is either NB-1 or NB, or N if N <= NB\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is REAL array, dimension (LDA,N) !> On entry, the symmetric matrix A\&. If UPLO = 'U', the leading !> n-by-n upper triangular part of A contains the upper !> triangular part of the matrix A, and the strictly lower !> triangular part of A is not referenced\&. If UPLO = 'L', the !> leading n-by-n lower triangular part of A contains the lower !> triangular part of the matrix A, and the strictly upper !> triangular part of A is not referenced\&. !> On exit, A contains details of the partial factorization\&. !> .fi .PP .br \fILDA\fP .PP .nf !> LDA is INTEGER !> The leading dimension of the array A\&. LDA >= max(1,N)\&. !> .fi .PP .br \fIIPIV\fP .PP .nf !> IPIV is INTEGER array, dimension (N) !> Details of the interchanges and the block structure of D\&. !> !> If UPLO = 'U': !> Only the last KB elements of IPIV are set\&. !> !> If IPIV(k) > 0, then rows and columns k and IPIV(k) were !> interchanged and D(k,k) is a 1-by-1 diagonal block\&. !> !> If IPIV(k) = IPIV(k-1) < 0, then rows and columns !> k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) !> is a 2-by-2 diagonal block\&. !> !> If UPLO = 'L': !> Only the first KB elements of IPIV are set\&. !> !> If IPIV(k) > 0, then rows and columns k and IPIV(k) were !> interchanged and D(k,k) is a 1-by-1 diagonal block\&. !> !> If IPIV(k) = IPIV(k+1) < 0, then rows and columns !> k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1) !> is a 2-by-2 diagonal block\&. !> .fi .PP .br \fIW\fP .PP .nf !> W is REAL array, dimension (LDW,NB) !> .fi .PP .br \fILDW\fP .PP .nf !> LDW is INTEGER !> The leading dimension of the array W\&. LDW >= max(1,N)\&. !> .fi .PP .br \fIINFO\fP .PP .nf !> INFO is INTEGER !> = 0: successful exit !> > 0: if INFO = k, D(k,k) is exactly zero\&. The factorization !> has been completed, but the block diagonal matrix D is !> exactly singular\&. !> .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBContributors:\fP .RS 4 .PP .nf !> !> November 2013, Igor Kozachenko, !> Computer Science Division, !> University of California, Berkeley !> .fi .PP .RE .PP .PP Definition at line \fB175\fP of file \fBslasyf\&.f\fP\&. .SS "subroutine zlahef (character uplo, integer n, integer nb, integer kb, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( ldw, * ) w, integer ldw, integer info)" .PP \fBZLAHEF\fP computes a partial factorization of a complex Hermitian indefinite matrix using the Bunch-Kaufman diagonal pivoting method (blocked algorithm, calling Level 3 BLAS)\&. .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> ZLAHEF computes a partial factorization of a complex Hermitian !> matrix A using the Bunch-Kaufman diagonal pivoting method\&. The !> partial factorization has the form: !> !> A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = 'U', or: !> ( 0 U22 ) ( 0 D ) ( U12**H U22**H ) !> !> A = ( L11 0 ) ( D 0 ) ( L11**H L21**H ) if UPLO = 'L' !> ( L21 I ) ( 0 A22 ) ( 0 I ) !> !> where the order of D is at most NB\&. The actual order is returned in !> the argument KB, and is either NB or NB-1, or N if N <= NB\&. !> Note that U**H denotes the conjugate transpose of U\&. !> !> ZLAHEF is an auxiliary routine called by ZHETRF\&. It uses blocked code !> (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or !> A22 (if UPLO = 'L')\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf !> UPLO is CHARACTER*1 !> Specifies whether the upper or lower triangular part of the !> Hermitian matrix A is stored: !> = 'U': Upper triangular !> = 'L': Lower triangular !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrix A\&. N >= 0\&. !> .fi .PP .br \fINB\fP .PP .nf !> NB is INTEGER !> The maximum number of columns of the matrix A that should be !> factored\&. NB should be at least 2 to allow for 2-by-2 pivot !> blocks\&. !> .fi .PP .br \fIKB\fP .PP .nf !> KB is INTEGER !> The number of columns of A that were actually factored\&. !> KB is either NB-1 or NB, or N if N <= NB\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is COMPLEX*16 array, dimension (LDA,N) !> On entry, the Hermitian matrix A\&. If UPLO = 'U', the leading !> n-by-n upper triangular part of A contains the upper !> triangular part of the matrix A, and the strictly lower !> triangular part of A is not referenced\&. If UPLO = 'L', the !> leading n-by-n lower triangular part of A contains the lower !> triangular part of the matrix A, and the strictly upper !> triangular part of A is not referenced\&. !> On exit, A contains details of the partial factorization\&. !> .fi .PP .br \fILDA\fP .PP .nf !> LDA is INTEGER !> The leading dimension of the array A\&. LDA >= max(1,N)\&. !> .fi .PP .br \fIIPIV\fP .PP .nf !> IPIV is INTEGER array, dimension (N) !> Details of the interchanges and the block structure of D\&. !> !> If UPLO = 'U': !> Only the last KB elements of IPIV are set\&. !> !> If IPIV(k) > 0, then rows and columns k and IPIV(k) were !> interchanged and D(k,k) is a 1-by-1 diagonal block\&. !> !> If IPIV(k) = IPIV(k-1) < 0, then rows and columns !> k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) !> is a 2-by-2 diagonal block\&. !> !> If UPLO = 'L': !> Only the first KB elements of IPIV are set\&. !> !> If IPIV(k) > 0, then rows and columns k and IPIV(k) were !> interchanged and D(k,k) is a 1-by-1 diagonal block\&. !> !> If IPIV(k) = IPIV(k+1) < 0, then rows and columns !> k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1) !> is a 2-by-2 diagonal block\&. !> .fi .PP .br \fIW\fP .PP .nf !> W is COMPLEX*16 array, dimension (LDW,NB) !> .fi .PP .br \fILDW\fP .PP .nf !> LDW is INTEGER !> The leading dimension of the array W\&. LDW >= max(1,N)\&. !> .fi .PP .br \fIINFO\fP .PP .nf !> INFO is INTEGER !> = 0: successful exit !> > 0: if INFO = k, D(k,k) is exactly zero\&. The factorization !> has been completed, but the block diagonal matrix D is !> exactly singular\&. !> .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBContributors:\fP .RS 4 .PP .nf !> !> December 2016, Igor Kozachenko, !> Computer Science Division, !> University of California, Berkeley !> .fi .PP .RE .PP .PP Definition at line \fB176\fP of file \fBzlahef\&.f\fP\&. .SS "subroutine zlasyf (character uplo, integer n, integer nb, integer kb, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( ldw, * ) w, integer ldw, integer info)" .PP \fBZLASYF\fP computes a partial factorization of a complex symmetric matrix using the Bunch-Kaufman diagonal pivoting method\&. .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> ZLASYF computes a partial factorization of a complex symmetric matrix !> A using the Bunch-Kaufman diagonal pivoting method\&. The partial !> factorization has the form: !> !> A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = 'U', or: !> ( 0 U22 ) ( 0 D ) ( U12**T U22**T ) !> !> A = ( L11 0 ) ( D 0 ) ( L11**T L21**T ) if UPLO = 'L' !> ( L21 I ) ( 0 A22 ) ( 0 I ) !> !> where the order of D is at most NB\&. The actual order is returned in !> the argument KB, and is either NB or NB-1, or N if N <= NB\&. !> Note that U**T denotes the transpose of U\&. !> !> ZLASYF is an auxiliary routine called by ZSYTRF\&. It uses blocked code !> (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or !> A22 (if UPLO = 'L')\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf !> UPLO is CHARACTER*1 !> Specifies whether the upper or lower triangular part of the !> symmetric matrix A is stored: !> = 'U': Upper triangular !> = 'L': Lower triangular !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrix A\&. N >= 0\&. !> .fi .PP .br \fINB\fP .PP .nf !> NB is INTEGER !> The maximum number of columns of the matrix A that should be !> factored\&. NB should be at least 2 to allow for 2-by-2 pivot !> blocks\&. !> .fi .PP .br \fIKB\fP .PP .nf !> KB is INTEGER !> The number of columns of A that were actually factored\&. !> KB is either NB-1 or NB, or N if N <= NB\&. !> .fi .PP .br \fIA\fP .PP .nf !> A is COMPLEX*16 array, dimension (LDA,N) !> On entry, the symmetric matrix A\&. If UPLO = 'U', the leading !> n-by-n upper triangular part of A contains the upper !> triangular part of the matrix A, and the strictly lower !> triangular part of A is not referenced\&. If UPLO = 'L', the !> leading n-by-n lower triangular part of A contains the lower !> triangular part of the matrix A, and the strictly upper !> triangular part of A is not referenced\&. !> On exit, A contains details of the partial factorization\&. !> .fi .PP .br \fILDA\fP .PP .nf !> LDA is INTEGER !> The leading dimension of the array A\&. LDA >= max(1,N)\&. !> .fi .PP .br \fIIPIV\fP .PP .nf !> IPIV is INTEGER array, dimension (N) !> Details of the interchanges and the block structure of D\&. !> !> If UPLO = 'U': !> Only the last KB elements of IPIV are set\&. !> !> If IPIV(k) > 0, then rows and columns k and IPIV(k) were !> interchanged and D(k,k) is a 1-by-1 diagonal block\&. !> !> If IPIV(k) = IPIV(k-1) < 0, then rows and columns !> k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) !> is a 2-by-2 diagonal block\&. !> !> If UPLO = 'L': !> Only the first KB elements of IPIV are set\&. !> !> If IPIV(k) > 0, then rows and columns k and IPIV(k) were !> interchanged and D(k,k) is a 1-by-1 diagonal block\&. !> !> If IPIV(k) = IPIV(k+1) < 0, then rows and columns !> k+1 and -IPIV(k) were interchanged and D(k:k+1,k:k+1) !> is a 2-by-2 diagonal block\&. !> .fi .PP .br \fIW\fP .PP .nf !> W is COMPLEX*16 array, dimension (LDW,NB) !> .fi .PP .br \fILDW\fP .PP .nf !> LDW is INTEGER !> The leading dimension of the array W\&. LDW >= max(1,N)\&. !> .fi .PP .br \fIINFO\fP .PP .nf !> INFO is INTEGER !> = 0: successful exit !> > 0: if INFO = k, D(k,k) is exactly zero\&. The factorization !> has been completed, but the block diagonal matrix D is !> exactly singular\&. !> .fi .PP .RE .PP \fBAuthor\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBContributors:\fP .RS 4 .PP .nf !> !> November 2013, Igor Kozachenko, !> Computer Science Division, !> University of California, Berkeley !> .fi .PP .RE .PP .PP Definition at line \fB176\fP of file \fBzlasyf\&.f\fP\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.