.TH "lahef_rook" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME lahef_rook \- la{he,sy}f_rook: triangular factor step .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBclahef_rook\fP (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info)" .br .RI " " .ti -1c .RI "subroutine \fBclasyf_rook\fP (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info)" .br .RI "\fBCLASYF_ROOK\fP computes a partial factorization of a complex symmetric matrix using the bounded Bunch-Kaufman ('rook') diagonal pivoting method\&. " .ti -1c .RI "subroutine \fBdlasyf_rook\fP (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info)" .br .RI "\fBDLASYF_ROOK\fP *> DLASYF_ROOK computes a partial factorization of a real symmetric matrix using the bounded Bunch-Kaufman ('rook') diagonal pivoting method\&. " .ti -1c .RI "subroutine \fBslasyf_rook\fP (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info)" .br .RI "\fBSLASYF_ROOK\fP computes a partial factorization of a real symmetric matrix using the bounded Bunch-Kaufman ('rook') diagonal pivoting method\&. " .ti -1c .RI "subroutine \fBzlahef_rook\fP (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info)" .br .RI " " .ti -1c .RI "subroutine \fBzlasyf_rook\fP (uplo, n, nb, kb, a, lda, ipiv, w, ldw, info)" .br .RI "\fBZLASYF_ROOK\fP computes a partial factorization of a complex symmetric matrix using the bounded Bunch-Kaufman ('rook') diagonal pivoting method\&. " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine clahef_rook (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 .PP \fBPurpose:\fP .RS 4 .PP .nf CLAHEF_ROOK computes a partial factorization of a complex Hermitian matrix A using the bounded Bunch-Kaufman ('rook') 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_ROOK is an auxiliary routine called by CHETRF_ROOK\&. 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) < 0 and IPIV(k-1) < 0, then rows and columns k and -IPIV(k) were interchanged and rows and columns k-1 and -IPIV(k-1) were inerchaged, 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) < 0 and IPIV(k+1) < 0, then rows and columns k and -IPIV(k) were interchanged and rows and columns k+1 and -IPIV(k+1) were inerchaged, 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 September 2007, Sven Hammarling, Nicholas J\&. Higham, Craig Lucas, School of Mathematics, University of Manchester .fi .PP .RE .PP .SS "subroutine clasyf_rook (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_ROOK\fP computes a partial factorization of a complex symmetric matrix using the bounded Bunch-Kaufman ('rook') diagonal pivoting method\&. .PP \fBPurpose:\fP .RS 4 .PP .nf CLASYF_ROOK computes a partial factorization of a complex symmetric matrix A using the bounded Bunch-Kaufman ('rook') 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\&. CLASYF_ROOK is an auxiliary routine called by CSYTRF_ROOK\&. 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) < 0 and IPIV(k-1) < 0, then rows and columns k and -IPIV(k) were interchanged and rows and columns k-1 and -IPIV(k-1) were inerchaged, 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) < 0 and IPIV(k+1) < 0, then rows and columns k and -IPIV(k) were interchanged and rows and columns k+1 and -IPIV(k+1) were inerchaged, 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 September 2007, Sven Hammarling, Nicholas J\&. Higham, Craig Lucas, School of Mathematics, University of Manchester .fi .PP .RE .PP .SS "subroutine dlasyf_rook (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_ROOK\fP *> DLASYF_ROOK computes a partial factorization of a real symmetric matrix using the bounded Bunch-Kaufman ('rook') diagonal pivoting method\&. .PP \fBPurpose:\fP .RS 4 .PP .nf DLASYF_ROOK computes a partial factorization of a real symmetric matrix A using the bounded Bunch-Kaufman ('rook') 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_ROOK is an auxiliary routine called by DSYTRF_ROOK\&. 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) < 0 and IPIV(k-1) < 0, then rows and columns k and -IPIV(k) were interchanged and rows and columns k-1 and -IPIV(k-1) were inerchaged, 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) < 0 and IPIV(k+1) < 0, then rows and columns k and -IPIV(k) were interchanged and rows and columns k+1 and -IPIV(k+1) were inerchaged, 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 September 2007, Sven Hammarling, Nicholas J\&. Higham, Craig Lucas, School of Mathematics, University of Manchester .fi .PP .RE .PP .SS "subroutine slasyf_rook (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_ROOK\fP computes a partial factorization of a real symmetric matrix using the bounded Bunch-Kaufman ('rook') diagonal pivoting method\&. .PP \fBPurpose:\fP .RS 4 .PP .nf SLASYF_ROOK computes a partial factorization of a real symmetric matrix A using the bounded Bunch-Kaufman ('rook') 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_ROOK is an auxiliary routine called by SSYTRF_ROOK\&. 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) < 0 and IPIV(k-1) < 0, then rows and columns k and -IPIV(k) were interchanged and rows and columns k-1 and -IPIV(k-1) were inerchaged, 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) < 0 and IPIV(k+1) < 0, then rows and columns k and -IPIV(k) were interchanged and rows and columns k+1 and -IPIV(k+1) were inerchaged, 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 September 2007, Sven Hammarling, Nicholas J\&. Higham, Craig Lucas, School of Mathematics, University of Manchester .fi .PP .RE .PP .SS "subroutine zlahef_rook (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 .PP \fBPurpose:\fP .RS 4 .PP .nf ZLAHEF_ROOK computes a partial factorization of a complex Hermitian matrix A using the bounded Bunch-Kaufman ('rook') 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_ROOK is an auxiliary routine called by ZHETRF_ROOK\&. 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) < 0 and IPIV(k-1) < 0, then rows and columns k and -IPIV(k) were interchanged and rows and columns k-1 and -IPIV(k-1) were inerchaged, 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) < 0 and IPIV(k+1) < 0, then rows and columns k and -IPIV(k) were interchanged and rows and columns k+1 and -IPIV(k+1) were inerchaged, 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 September 2007, Sven Hammarling, Nicholas J\&. Higham, Craig Lucas, School of Mathematics, University of Manchester .fi .PP .RE .PP .SS "subroutine zlasyf_rook (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_ROOK\fP computes a partial factorization of a complex symmetric matrix using the bounded Bunch-Kaufman ('rook') diagonal pivoting method\&. .PP \fBPurpose:\fP .RS 4 .PP .nf ZLASYF_ROOK computes a partial factorization of a complex symmetric matrix A using the bounded Bunch-Kaufman ('rook') 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\&. ZLASYF_ROOK is an auxiliary routine called by ZSYTRF_ROOK\&. 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) < 0 and IPIV(k-1) < 0, then rows and columns k and -IPIV(k) were interchanged and rows and columns k-1 and -IPIV(k-1) were inerchaged, 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) < 0 and IPIV(k+1) < 0, then rows and columns k and -IPIV(k) were interchanged and rows and columns k+1 and -IPIV(k+1) were inerchaged, 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 September 2007, Sven Hammarling, Nicholas J\&. Higham, Craig Lucas, School of Mathematics, University of Manchester .fi .PP .RE .PP .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.