.TH "hetrf_rook" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME hetrf_rook \- {he,sy}trf_rook: triangular factor .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBchetrf_rook\fP (uplo, n, a, lda, ipiv, work, lwork, info)" .br .RI "\fBCHETRF_ROOK\fP computes the factorization of a complex Hermitian indefinite matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method (blocked algorithm, calling Level 3 BLAS)\&. " .ti -1c .RI "subroutine \fBcsytrf_rook\fP (uplo, n, a, lda, ipiv, work, lwork, info)" .br .RI "\fBCSYTRF_ROOK\fP " .ti -1c .RI "subroutine \fBdsytrf_rook\fP (uplo, n, a, lda, ipiv, work, lwork, info)" .br .RI "\fBDSYTRF_ROOK\fP " .ti -1c .RI "subroutine \fBssytrf_rook\fP (uplo, n, a, lda, ipiv, work, lwork, info)" .br .RI "\fBSSYTRF_ROOK\fP " .ti -1c .RI "subroutine \fBzhetrf_rook\fP (uplo, n, a, lda, ipiv, work, lwork, info)" .br .RI "\fBZHETRF_ROOK\fP computes the factorization of a complex Hermitian indefinite matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method (blocked algorithm, calling Level 3 BLAS)\&. " .ti -1c .RI "subroutine \fBzsytrf_rook\fP (uplo, n, a, lda, ipiv, work, lwork, info)" .br .RI "\fBZSYTRF_ROOK\fP " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine chetrf_rook (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( * ) work, integer lwork, integer info)" .PP \fBCHETRF_ROOK\fP computes the factorization of a complex Hermitian indefinite matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method (blocked algorithm, calling Level 3 BLAS)\&. .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> CHETRF_ROOK computes the factorization of a complex Hermitian matrix A !> using the bounded Bunch-Kaufman () diagonal pivoting method\&. !> The form of the factorization is !> !> A = U*D*U**T or A = L*D*L**T !> !> where U (or L) is a product of permutation and unit upper (lower) !> triangular matrices, and D is Hermitian and block diagonal with !> 1-by-1 and 2-by-2 diagonal blocks\&. !> !> This is the blocked version of the algorithm, calling Level 3 BLAS\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrix A\&. N >= 0\&. !> .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, the block diagonal matrix D and the multipliers used !> to obtain the factor U or L (see below for further details)\&. !> .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 \fIWORK\fP .PP .nf !> WORK is COMPLEX array, dimension (MAX(1,LWORK))\&. !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&. !> .fi .PP .br \fILWORK\fP .PP .nf !> LWORK is INTEGER !> The length of WORK\&. LWORK >= 1\&. For best performance !> LWORK >= N*NB, where NB is the block size returned by ILAENV\&. !> !> If LWORK = -1, then a workspace query is assumed; the routine !> only calculates the optimal size of the WORK array, returns !> this value as the first entry of the WORK array, and no error !> message related to LWORK is issued by XERBLA\&. !> .fi .PP .br \fIINFO\fP .PP .nf !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> > 0: if INFO = i, D(i,i) is exactly zero\&. The factorization !> has been completed, but the block diagonal matrix D is !> exactly singular, and division by zero will occur if it !> is used to solve a system of equations\&. !> .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 \fBFurther Details:\fP .RS 4 .PP .nf !> !> If UPLO = 'U', then A = U*D*U**T, where !> U = P(n)*U(n)* \&.\&.\&. *P(k)U(k)* \&.\&.\&., !> i\&.e\&., U is a product of terms P(k)*U(k), where k decreases from n to !> 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 !> and 2-by-2 diagonal blocks D(k)\&. P(k) is a permutation matrix as !> defined by IPIV(k), and U(k) is a unit upper triangular matrix, such !> that if the diagonal block D(k) is of order s (s = 1 or 2), then !> !> ( I v 0 ) k-s !> U(k) = ( 0 I 0 ) s !> ( 0 0 I ) n-k !> k-s s n-k !> !> If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k)\&. !> If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), !> and A(k,k), and v overwrites A(1:k-2,k-1:k)\&. !> !> If UPLO = 'L', then A = L*D*L**T, where !> L = P(1)*L(1)* \&.\&.\&. *P(k)*L(k)* \&.\&.\&., !> i\&.e\&., L is a product of terms P(k)*L(k), where k increases from 1 to !> n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 !> and 2-by-2 diagonal blocks D(k)\&. P(k) is a permutation matrix as !> defined by IPIV(k), and L(k) is a unit lower triangular matrix, such !> that if the diagonal block D(k) is of order s (s = 1 or 2), then !> !> ( I 0 0 ) k-1 !> L(k) = ( 0 I 0 ) s !> ( 0 v I ) n-k-s+1 !> k-1 s n-k-s+1 !> !> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k)\&. !> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k), !> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1)\&. !> .fi .PP .RE .PP \fBContributors:\fP .RS 4 .PP .nf !> !> June 2016, 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 .PP Definition at line \fB211\fP of file \fBchetrf_rook\&.f\fP\&. .SS "subroutine csytrf_rook (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( * ) work, integer lwork, integer info)" .PP \fBCSYTRF_ROOK\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> CSYTRF_ROOK computes the factorization of a complex symmetric matrix A !> using the bounded Bunch-Kaufman () diagonal pivoting method\&. !> The form of the factorization is !> !> A = U*D*U**T or A = L*D*L**T !> !> where U (or L) is a product of permutation and unit upper (lower) !> triangular matrices, and D is symmetric and block diagonal with !> 1-by-1 and 2-by-2 diagonal blocks\&. !> !> This is the blocked version of the algorithm, calling Level 3 BLAS\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrix A\&. N >= 0\&. !> .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, the block diagonal matrix D and the multipliers used !> to obtain the factor U or L (see below for further details)\&. !> .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': !> 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': !> 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 \fIWORK\fP .PP .nf !> WORK is COMPLEX array, dimension (MAX(1,LWORK))\&. !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&. !> .fi .PP .br \fILWORK\fP .PP .nf !> LWORK is INTEGER !> The length of WORK\&. LWORK >=1\&. For best performance !> LWORK >= N*NB, where NB is the block size returned by ILAENV\&. !> !> If LWORK = -1, then a workspace query is assumed; the routine !> only calculates the optimal size of the WORK array, returns !> this value as the first entry of the WORK array, and no error !> message related to LWORK is issued by XERBLA\&. !> .fi .PP .br \fIINFO\fP .PP .nf !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> > 0: if INFO = i, D(i,i) is exactly zero\&. The factorization !> has been completed, but the block diagonal matrix D is !> exactly singular, and division by zero will occur if it !> is used to solve a system of equations\&. !> .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 \fBFurther Details:\fP .RS 4 .PP .nf !> !> If UPLO = 'U', then A = U*D*U**T, where !> U = P(n)*U(n)* \&.\&.\&. *P(k)U(k)* \&.\&.\&., !> i\&.e\&., U is a product of terms P(k)*U(k), where k decreases from n to !> 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 !> and 2-by-2 diagonal blocks D(k)\&. P(k) is a permutation matrix as !> defined by IPIV(k), and U(k) is a unit upper triangular matrix, such !> that if the diagonal block D(k) is of order s (s = 1 or 2), then !> !> ( I v 0 ) k-s !> U(k) = ( 0 I 0 ) s !> ( 0 0 I ) n-k !> k-s s n-k !> !> If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k)\&. !> If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), !> and A(k,k), and v overwrites A(1:k-2,k-1:k)\&. !> !> If UPLO = 'L', then A = L*D*L**T, where !> L = P(1)*L(1)* \&.\&.\&. *P(k)*L(k)* \&.\&.\&., !> i\&.e\&., L is a product of terms P(k)*L(k), where k increases from 1 to !> n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 !> and 2-by-2 diagonal blocks D(k)\&. P(k) is a permutation matrix as !> defined by IPIV(k), and L(k) is a unit lower triangular matrix, such !> that if the diagonal block D(k) is of order s (s = 1 or 2), then !> !> ( I 0 0 ) k-1 !> L(k) = ( 0 I 0 ) s !> ( 0 v I ) n-k-s+1 !> k-1 s n-k-s+1 !> !> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k)\&. !> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k), !> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1)\&. !> .fi .PP .RE .PP \fBContributors:\fP .RS 4 .PP .nf !> !> June 2016, 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 .PP Definition at line \fB207\fP of file \fBcsytrf_rook\&.f\fP\&. .SS "subroutine dsytrf_rook (character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precision, dimension( * ) work, integer lwork, integer info)" .PP \fBDSYTRF_ROOK\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> DSYTRF_ROOK computes the factorization of a real symmetric matrix A !> using the bounded Bunch-Kaufman () diagonal pivoting method\&. !> The form of the factorization is !> !> A = U*D*U**T or A = L*D*L**T !> !> where U (or L) is a product of permutation and unit upper (lower) !> triangular matrices, and D is symmetric and block diagonal with !> 1-by-1 and 2-by-2 diagonal blocks\&. !> !> This is the blocked version of the algorithm, calling Level 3 BLAS\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrix A\&. N >= 0\&. !> .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, the block diagonal matrix D and the multipliers used !> to obtain the factor U or L (see below for further details)\&. !> .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': !> 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': !> 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 \fIWORK\fP .PP .nf !> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))\&. !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&. !> .fi .PP .br \fILWORK\fP .PP .nf !> LWORK is INTEGER !> The length of WORK\&. LWORK >= 1\&. For best performance !> LWORK >= N*NB, where NB is the block size returned by ILAENV\&. !> !> If LWORK = -1, then a workspace query is assumed; the routine !> only calculates the optimal size of the WORK array, returns !> this value as the first entry of the WORK array, and no error !> message related to LWORK is issued by XERBLA\&. !> .fi .PP .br \fIINFO\fP .PP .nf !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> > 0: if INFO = i, D(i,i) is exactly zero\&. The factorization !> has been completed, but the block diagonal matrix D is !> exactly singular, and division by zero will occur if it !> is used to solve a system of equations\&. !> .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 \fBFurther Details:\fP .RS 4 .PP .nf !> !> If UPLO = 'U', then A = U*D*U**T, where !> U = P(n)*U(n)* \&.\&.\&. *P(k)U(k)* \&.\&.\&., !> i\&.e\&., U is a product of terms P(k)*U(k), where k decreases from n to !> 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 !> and 2-by-2 diagonal blocks D(k)\&. P(k) is a permutation matrix as !> defined by IPIV(k), and U(k) is a unit upper triangular matrix, such !> that if the diagonal block D(k) is of order s (s = 1 or 2), then !> !> ( I v 0 ) k-s !> U(k) = ( 0 I 0 ) s !> ( 0 0 I ) n-k !> k-s s n-k !> !> If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k)\&. !> If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), !> and A(k,k), and v overwrites A(1:k-2,k-1:k)\&. !> !> If UPLO = 'L', then A = L*D*L**T, where !> L = P(1)*L(1)* \&.\&.\&. *P(k)*L(k)* \&.\&.\&., !> i\&.e\&., L is a product of terms P(k)*L(k), where k increases from 1 to !> n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 !> and 2-by-2 diagonal blocks D(k)\&. P(k) is a permutation matrix as !> defined by IPIV(k), and L(k) is a unit lower triangular matrix, such !> that if the diagonal block D(k) is of order s (s = 1 or 2), then !> !> ( I 0 0 ) k-1 !> L(k) = ( 0 I 0 ) s !> ( 0 v I ) n-k-s+1 !> k-1 s n-k-s+1 !> !> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k)\&. !> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k), !> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1)\&. !> .fi .PP .RE .PP \fBContributors:\fP .RS 4 .PP .nf !> !> April 2012, 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 .PP Definition at line \fB207\fP of file \fBdsytrf_rook\&.f\fP\&. .SS "subroutine ssytrf_rook (character uplo, integer n, real, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, real, dimension( * ) work, integer lwork, integer info)" .PP \fBSSYTRF_ROOK\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> SSYTRF_ROOK computes the factorization of a real symmetric matrix A !> using the bounded Bunch-Kaufman () diagonal pivoting method\&. !> The form of the factorization is !> !> A = U*D*U**T or A = L*D*L**T !> !> where U (or L) is a product of permutation and unit upper (lower) !> triangular matrices, and D is symmetric and block diagonal with !> 1-by-1 and 2-by-2 diagonal blocks\&. !> !> This is the blocked version of the algorithm, calling Level 3 BLAS\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrix A\&. N >= 0\&. !> .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, the block diagonal matrix D and the multipliers used !> to obtain the factor U or L (see below for further details)\&. !> .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': !> 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': !> 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 \fIWORK\fP .PP .nf !> WORK is REAL array, dimension (MAX(1,LWORK))\&. !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&. !> .fi .PP .br \fILWORK\fP .PP .nf !> LWORK is INTEGER !> The length of WORK\&. LWORK >= 1\&. For best performance !> LWORK >= N*NB, where NB is the block size returned by ILAENV\&. !> !> If LWORK = -1, then a workspace query is assumed; the routine !> only calculates the optimal size of the WORK array, returns !> this value as the first entry of the WORK array, and no error !> message related to LWORK is issued by XERBLA\&. !> .fi .PP .br \fIINFO\fP .PP .nf !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> > 0: if INFO = i, D(i,i) is exactly zero\&. The factorization !> has been completed, but the block diagonal matrix D is !> exactly singular, and division by zero will occur if it !> is used to solve a system of equations\&. !> .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 \fBFurther Details:\fP .RS 4 .PP .nf !> !> If UPLO = 'U', then A = U*D*U**T, where !> U = P(n)*U(n)* \&.\&.\&. *P(k)U(k)* \&.\&.\&., !> i\&.e\&., U is a product of terms P(k)*U(k), where k decreases from n to !> 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 !> and 2-by-2 diagonal blocks D(k)\&. P(k) is a permutation matrix as !> defined by IPIV(k), and U(k) is a unit upper triangular matrix, such !> that if the diagonal block D(k) is of order s (s = 1 or 2), then !> !> ( I v 0 ) k-s !> U(k) = ( 0 I 0 ) s !> ( 0 0 I ) n-k !> k-s s n-k !> !> If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k)\&. !> If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), !> and A(k,k), and v overwrites A(1:k-2,k-1:k)\&. !> !> If UPLO = 'L', then A = L*D*L**T, where !> L = P(1)*L(1)* \&.\&.\&. *P(k)*L(k)* \&.\&.\&., !> i\&.e\&., L is a product of terms P(k)*L(k), where k increases from 1 to !> n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 !> and 2-by-2 diagonal blocks D(k)\&. P(k) is a permutation matrix as !> defined by IPIV(k), and L(k) is a unit lower triangular matrix, such !> that if the diagonal block D(k) is of order s (s = 1 or 2), then !> !> ( I 0 0 ) k-1 !> L(k) = ( 0 I 0 ) s !> ( 0 v I ) n-k-s+1 !> k-1 s n-k-s+1 !> !> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k)\&. !> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k), !> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1)\&. !> .fi .PP .RE .PP \fBContributors:\fP .RS 4 .PP .nf !> !> June 2016, 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 .PP Definition at line \fB207\fP of file \fBssytrf_rook\&.f\fP\&. .SS "subroutine zhetrf_rook (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( * ) work, integer lwork, integer info)" .PP \fBZHETRF_ROOK\fP computes the factorization of a complex Hermitian indefinite matrix using the bounded Bunch-Kaufman ("rook") diagonal pivoting method (blocked algorithm, calling Level 3 BLAS)\&. .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> ZHETRF_ROOK computes the factorization of a complex Hermitian matrix A !> using the bounded Bunch-Kaufman () diagonal pivoting method\&. !> The form of the factorization is !> !> A = U*D*U**T or A = L*D*L**T !> !> where U (or L) is a product of permutation and unit upper (lower) !> triangular matrices, and D is Hermitian and block diagonal with !> 1-by-1 and 2-by-2 diagonal blocks\&. !> !> This is the blocked version of the algorithm, calling Level 3 BLAS\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrix A\&. N >= 0\&. !> .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, the block diagonal matrix D and the multipliers used !> to obtain the factor U or L (see below for further details)\&. !> .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 \fIWORK\fP .PP .nf !> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))\&. !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&. !> .fi .PP .br \fILWORK\fP .PP .nf !> LWORK is INTEGER !> The length of WORK\&. LWORK >= 1\&. For best performance !> LWORK >= N*NB, where NB is the block size returned by ILAENV\&. !> !> If LWORK = -1, then a workspace query is assumed; the routine !> only calculates the optimal size of the WORK array, returns !> this value as the first entry of the WORK array, and no error !> message related to LWORK is issued by XERBLA\&. !> .fi .PP .br \fIINFO\fP .PP .nf !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> > 0: if INFO = i, D(i,i) is exactly zero\&. The factorization !> has been completed, but the block diagonal matrix D is !> exactly singular, and division by zero will occur if it !> is used to solve a system of equations\&. !> .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 \fBFurther Details:\fP .RS 4 .PP .nf !> !> If UPLO = 'U', then A = U*D*U**T, where !> U = P(n)*U(n)* \&.\&.\&. *P(k)U(k)* \&.\&.\&., !> i\&.e\&., U is a product of terms P(k)*U(k), where k decreases from n to !> 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 !> and 2-by-2 diagonal blocks D(k)\&. P(k) is a permutation matrix as !> defined by IPIV(k), and U(k) is a unit upper triangular matrix, such !> that if the diagonal block D(k) is of order s (s = 1 or 2), then !> !> ( I v 0 ) k-s !> U(k) = ( 0 I 0 ) s !> ( 0 0 I ) n-k !> k-s s n-k !> !> If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k)\&. !> If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), !> and A(k,k), and v overwrites A(1:k-2,k-1:k)\&. !> !> If UPLO = 'L', then A = L*D*L**T, where !> L = P(1)*L(1)* \&.\&.\&. *P(k)*L(k)* \&.\&.\&., !> i\&.e\&., L is a product of terms P(k)*L(k), where k increases from 1 to !> n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 !> and 2-by-2 diagonal blocks D(k)\&. P(k) is a permutation matrix as !> defined by IPIV(k), and L(k) is a unit lower triangular matrix, such !> that if the diagonal block D(k) is of order s (s = 1 or 2), then !> !> ( I 0 0 ) k-1 !> L(k) = ( 0 I 0 ) s !> ( 0 v I ) n-k-s+1 !> k-1 s n-k-s+1 !> !> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k)\&. !> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k), !> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1)\&. !> .fi .PP .RE .PP \fBContributors:\fP .RS 4 .PP .nf !> !> June 2016, 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 .PP Definition at line \fB211\fP of file \fBzhetrf_rook\&.f\fP\&. .SS "subroutine zsytrf_rook (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( * ) work, integer lwork, integer info)" .PP \fBZSYTRF_ROOK\fP .PP \fBPurpose:\fP .RS 4 .PP .nf !> !> ZSYTRF_ROOK computes the factorization of a complex symmetric matrix A !> using the bounded Bunch-Kaufman () diagonal pivoting method\&. !> The form of the factorization is !> !> A = U*D*U**T or A = L*D*L**T !> !> where U (or L) is a product of permutation and unit upper (lower) !> triangular matrices, and D is symmetric and block diagonal with !> 1-by-1 and 2-by-2 diagonal blocks\&. !> !> This is the blocked version of the algorithm, calling Level 3 BLAS\&. !> .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf !> UPLO is CHARACTER*1 !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored\&. !> .fi .PP .br \fIN\fP .PP .nf !> N is INTEGER !> The order of the matrix A\&. N >= 0\&. !> .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, the block diagonal matrix D and the multipliers used !> to obtain the factor U or L (see below for further details)\&. !> .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': !> 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': !> 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 \fIWORK\fP .PP .nf !> WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))\&. !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&. !> .fi .PP .br \fILWORK\fP .PP .nf !> LWORK is INTEGER !> The length of WORK\&. LWORK >=1\&. For best performance !> LWORK >= N*NB, where NB is the block size returned by ILAENV\&. !> !> If LWORK = -1, then a workspace query is assumed; the routine !> only calculates the optimal size of the WORK array, returns !> this value as the first entry of the WORK array, and no error !> message related to LWORK is issued by XERBLA\&. !> .fi .PP .br \fIINFO\fP .PP .nf !> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !> > 0: if INFO = i, D(i,i) is exactly zero\&. The factorization !> has been completed, but the block diagonal matrix D is !> exactly singular, and division by zero will occur if it !> is used to solve a system of equations\&. !> .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 \fBFurther Details:\fP .RS 4 .PP .nf !> !> If UPLO = 'U', then A = U*D*U**T, where !> U = P(n)*U(n)* \&.\&.\&. *P(k)U(k)* \&.\&.\&., !> i\&.e\&., U is a product of terms P(k)*U(k), where k decreases from n to !> 1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 !> and 2-by-2 diagonal blocks D(k)\&. P(k) is a permutation matrix as !> defined by IPIV(k), and U(k) is a unit upper triangular matrix, such !> that if the diagonal block D(k) is of order s (s = 1 or 2), then !> !> ( I v 0 ) k-s !> U(k) = ( 0 I 0 ) s !> ( 0 0 I ) n-k !> k-s s n-k !> !> If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k)\&. !> If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), !> and A(k,k), and v overwrites A(1:k-2,k-1:k)\&. !> !> If UPLO = 'L', then A = L*D*L**T, where !> L = P(1)*L(1)* \&.\&.\&. *P(k)*L(k)* \&.\&.\&., !> i\&.e\&., L is a product of terms P(k)*L(k), where k increases from 1 to !> n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 !> and 2-by-2 diagonal blocks D(k)\&. P(k) is a permutation matrix as !> defined by IPIV(k), and L(k) is a unit lower triangular matrix, such !> that if the diagonal block D(k) is of order s (s = 1 or 2), then !> !> ( I 0 0 ) k-1 !> L(k) = ( 0 I 0 ) s !> ( 0 v I ) n-k-s+1 !> k-1 s n-k-s+1 !> !> If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k)\&. !> If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k), !> and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1)\&. !> .fi .PP .RE .PP \fBContributors:\fP .RS 4 .PP .nf !> !> June 2016, 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 .PP Definition at line \fB207\fP of file \fBzsytrf_rook\&.f\fP\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.