.TH "lahef_aa" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME lahef_aa \- la{he,sy}f_aa: triangular factor partial factor .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBclahef_aa\fP (uplo, j1, m, nb, a, lda, ipiv, h, ldh, work)" .br .RI "\fBCLAHEF_AA\fP " .ti -1c .RI "subroutine \fBclasyf_aa\fP (uplo, j1, m, nb, a, lda, ipiv, h, ldh, work)" .br .RI "\fBCLASYF_AA\fP " .ti -1c .RI "subroutine \fBdlasyf_aa\fP (uplo, j1, m, nb, a, lda, ipiv, h, ldh, work)" .br .RI "\fBDLASYF_AA\fP " .ti -1c .RI "subroutine \fBslasyf_aa\fP (uplo, j1, m, nb, a, lda, ipiv, h, ldh, work)" .br .RI "\fBSLASYF_AA\fP " .ti -1c .RI "subroutine \fBzlahef_aa\fP (uplo, j1, m, nb, a, lda, ipiv, h, ldh, work)" .br .RI "\fBZLAHEF_AA\fP " .ti -1c .RI "subroutine \fBzlasyf_aa\fP (uplo, j1, m, nb, a, lda, ipiv, h, ldh, work)" .br .RI "\fBZLASYF_AA\fP " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine clahef_aa (character uplo, integer j1, integer m, integer nb, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( ldh, * ) h, integer ldh, complex, dimension( * ) work)" .PP \fBCLAHEF_AA\fP .PP \fBPurpose:\fP .RS 4 .PP .nf CLAHEF_AA factorizes a panel of a complex hermitian matrix A using the Aasen's algorithm\&. The panel consists of a set of NB rows of A when UPLO is U, or a set of NB columns when UPLO is L\&. In order to factorize the panel, the Aasen's algorithm requires the last row, or column, of the previous panel\&. The first row, or column, of A is set to be the first row, or column, of an identity matrix, which is used to factorize the first panel\&. The resulting J-th row of U, or J-th column of L, is stored in the (J-1)-th row, or column, of A (without the unit diagonals), while the diagonal and subdiagonal of A are overwritten by those of T\&. .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 \fIJ1\fP .PP .nf J1 is INTEGER The location of the first row, or column, of the panel within the submatrix of A, passed to this routine, e\&.g\&., when called by CHETRF_AA, for the first panel, J1 is 1, while for the remaining panels, J1 is 2\&. .fi .PP .br \fIM\fP .PP .nf M is INTEGER The dimension of the submatrix\&. M >= 0\&. .fi .PP .br \fINB\fP .PP .nf NB is INTEGER The dimension of the panel to be facotorized\&. .fi .PP .br \fIA\fP .PP .nf A is COMPLEX array, dimension (LDA,M) for the first panel, while dimension (LDA,M+1) for the remaining panels\&. On entry, A contains the last row, or column, of the previous panel, and the trailing submatrix of A to be factorized, except for the first panel, only the panel is passed\&. On exit, the leading panel is factorized\&. .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 row and column interchanges, the row and column k were interchanged with the row and column IPIV(k)\&. .fi .PP .br \fIH\fP .PP .nf H is COMPLEX workspace, dimension (LDH,NB)\&. .fi .PP .br \fILDH\fP .PP .nf LDH is INTEGER The leading dimension of the workspace H\&. LDH >= max(1,M)\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is COMPLEX workspace, dimension (M)\&. .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 .SS "subroutine clasyf_aa (character uplo, integer j1, integer m, integer nb, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( ldh, * ) h, integer ldh, complex, dimension( * ) work)" .PP \fBCLASYF_AA\fP .PP \fBPurpose:\fP .RS 4 .PP .nf DLATRF_AA factorizes a panel of a complex symmetric matrix A using the Aasen's algorithm\&. The panel consists of a set of NB rows of A when UPLO is U, or a set of NB columns when UPLO is L\&. In order to factorize the panel, the Aasen's algorithm requires the last row, or column, of the previous panel\&. The first row, or column, of A is set to be the first row, or column, of an identity matrix, which is used to factorize the first panel\&. The resulting J-th row of U, or J-th column of L, is stored in the (J-1)-th row, or column, of A (without the unit diagonals), while the diagonal and subdiagonal of A are overwritten by those of T\&. .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 \fIJ1\fP .PP .nf J1 is INTEGER The location of the first row, or column, of the panel within the submatrix of A, passed to this routine, e\&.g\&., when called by CSYTRF_AA, for the first panel, J1 is 1, while for the remaining panels, J1 is 2\&. .fi .PP .br \fIM\fP .PP .nf M is INTEGER The dimension of the submatrix\&. M >= 0\&. .fi .PP .br \fINB\fP .PP .nf NB is INTEGER The dimension of the panel to be facotorized\&. .fi .PP .br \fIA\fP .PP .nf A is COMPLEX array, dimension (LDA,M) for the first panel, while dimension (LDA,M+1) for the remaining panels\&. On entry, A contains the last row, or column, of the previous panel, and the trailing submatrix of A to be factorized, except for the first panel, only the panel is passed\&. On exit, the leading panel is factorized\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A\&. LDA >= max(1,M)\&. .fi .PP .br \fIIPIV\fP .PP .nf IPIV is INTEGER array, dimension (M) Details of the row and column interchanges, the row and column k were interchanged with the row and column IPIV(k)\&. .fi .PP .br \fIH\fP .PP .nf H is COMPLEX workspace, dimension (LDH,NB)\&. .fi .PP .br \fILDH\fP .PP .nf LDH is INTEGER The leading dimension of the workspace H\&. LDH >= max(1,M)\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is COMPLEX workspace, dimension (M)\&. .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 .SS "subroutine dlasyf_aa (character uplo, integer j1, integer m, integer nb, double precision, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precision, dimension( ldh, * ) h, integer ldh, double precision, dimension( * ) work)" .PP \fBDLASYF_AA\fP .PP \fBPurpose:\fP .RS 4 .PP .nf DLATRF_AA factorizes a panel of a real symmetric matrix A using the Aasen's algorithm\&. The panel consists of a set of NB rows of A when UPLO is U, or a set of NB columns when UPLO is L\&. In order to factorize the panel, the Aasen's algorithm requires the last row, or column, of the previous panel\&. The first row, or column, of A is set to be the first row, or column, of an identity matrix, which is used to factorize the first panel\&. The resulting J-th row of U, or J-th column of L, is stored in the (J-1)-th row, or column, of A (without the unit diagonals), while the diagonal and subdiagonal of A are overwritten by those of T\&. .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 \fIJ1\fP .PP .nf J1 is INTEGER The location of the first row, or column, of the panel within the submatrix of A, passed to this routine, e\&.g\&., when called by DSYTRF_AA, for the first panel, J1 is 1, while for the remaining panels, J1 is 2\&. .fi .PP .br \fIM\fP .PP .nf M is INTEGER The dimension of the submatrix\&. M >= 0\&. .fi .PP .br \fINB\fP .PP .nf NB is INTEGER The dimension of the panel to be facotorized\&. .fi .PP .br \fIA\fP .PP .nf A is DOUBLE PRECISION array, dimension (LDA,M) for the first panel, while dimension (LDA,M+1) for the remaining panels\&. On entry, A contains the last row, or column, of the previous panel, and the trailing submatrix of A to be factorized, except for the first panel, only the panel is passed\&. On exit, the leading panel is factorized\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A\&. LDA >= max(1,M)\&. .fi .PP .br \fIIPIV\fP .PP .nf IPIV is INTEGER array, dimension (M) Details of the row and column interchanges, the row and column k were interchanged with the row and column IPIV(k)\&. .fi .PP .br \fIH\fP .PP .nf H is DOUBLE PRECISION workspace, dimension (LDH,NB)\&. .fi .PP .br \fILDH\fP .PP .nf LDH is INTEGER The leading dimension of the workspace H\&. LDH >= max(1,M)\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is DOUBLE PRECISION workspace, dimension (M)\&. .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 .SS "subroutine slasyf_aa (character uplo, integer j1, integer m, integer nb, real, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, real, dimension( ldh, * ) h, integer ldh, real, dimension( * ) work)" .PP \fBSLASYF_AA\fP .PP \fBPurpose:\fP .RS 4 .PP .nf DLATRF_AA factorizes a panel of a real symmetric matrix A using the Aasen's algorithm\&. The panel consists of a set of NB rows of A when UPLO is U, or a set of NB columns when UPLO is L\&. In order to factorize the panel, the Aasen's algorithm requires the last row, or column, of the previous panel\&. The first row, or column, of A is set to be the first row, or column, of an identity matrix, which is used to factorize the first panel\&. The resulting J-th row of U, or J-th column of L, is stored in the (J-1)-th row, or column, of A (without the unit diagonals), while the diagonal and subdiagonal of A are overwritten by those of T\&. .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 \fIJ1\fP .PP .nf J1 is INTEGER The location of the first row, or column, of the panel within the submatrix of A, passed to this routine, e\&.g\&., when called by SSYTRF_AA, for the first panel, J1 is 1, while for the remaining panels, J1 is 2\&. .fi .PP .br \fIM\fP .PP .nf M is INTEGER The dimension of the submatrix\&. M >= 0\&. .fi .PP .br \fINB\fP .PP .nf NB is INTEGER The dimension of the panel to be facotorized\&. .fi .PP .br \fIA\fP .PP .nf A is REAL array, dimension (LDA,M) for the first panel, while dimension (LDA,M+1) for the remaining panels\&. On entry, A contains the last row, or column, of the previous panel, and the trailing submatrix of A to be factorized, except for the first panel, only the panel is passed\&. On exit, the leading panel is factorized\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A\&. LDA >= max(1,M)\&. .fi .PP .br \fIIPIV\fP .PP .nf IPIV is INTEGER array, dimension (M) Details of the row and column interchanges, the row and column k were interchanged with the row and column IPIV(k)\&. .fi .PP .br \fIH\fP .PP .nf H is REAL workspace, dimension (LDH,NB)\&. .fi .PP .br \fILDH\fP .PP .nf LDH is INTEGER The leading dimension of the workspace H\&. LDH >= max(1,M)\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is REAL workspace, dimension (M)\&. .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 .SS "subroutine zlahef_aa (character uplo, integer j1, integer m, integer nb, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( ldh, * ) h, integer ldh, complex*16, dimension( * ) work)" .PP \fBZLAHEF_AA\fP .PP \fBPurpose:\fP .RS 4 .PP .nf DLAHEF_AA factorizes a panel of a complex hermitian matrix A using the Aasen's algorithm\&. The panel consists of a set of NB rows of A when UPLO is U, or a set of NB columns when UPLO is L\&. In order to factorize the panel, the Aasen's algorithm requires the last row, or column, of the previous panel\&. The first row, or column, of A is set to be the first row, or column, of an identity matrix, which is used to factorize the first panel\&. The resulting J-th row of U, or J-th column of L, is stored in the (J-1)-th row, or column, of A (without the unit diagonals), while the diagonal and subdiagonal of A are overwritten by those of T\&. .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 \fIJ1\fP .PP .nf J1 is INTEGER The location of the first row, or column, of the panel within the submatrix of A, passed to this routine, e\&.g\&., when called by ZHETRF_AA, for the first panel, J1 is 1, while for the remaining panels, J1 is 2\&. .fi .PP .br \fIM\fP .PP .nf M is INTEGER The dimension of the submatrix\&. M >= 0\&. .fi .PP .br \fINB\fP .PP .nf NB is INTEGER The dimension of the panel to be facotorized\&. .fi .PP .br \fIA\fP .PP .nf A is COMPLEX*16 array, dimension (LDA,M) for the first panel, while dimension (LDA,M+1) for the remaining panels\&. On entry, A contains the last row, or column, of the previous panel, and the trailing submatrix of A to be factorized, except for the first panel, only the panel is passed\&. On exit, the leading panel is factorized\&. .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 row and column interchanges, the row and column k were interchanged with the row and column IPIV(k)\&. .fi .PP .br \fIH\fP .PP .nf H is COMPLEX*16 workspace, dimension (LDH,NB)\&. .fi .PP .br \fILDH\fP .PP .nf LDH is INTEGER The leading dimension of the workspace H\&. LDH >= max(1,M)\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is COMPLEX*16 workspace, dimension (M)\&. .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 .SS "subroutine zlasyf_aa (character uplo, integer j1, integer m, integer nb, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( ldh, * ) h, integer ldh, complex*16, dimension( * ) work)" .PP \fBZLASYF_AA\fP .PP \fBPurpose:\fP .RS 4 .PP .nf DLATRF_AA factorizes a panel of a complex symmetric matrix A using the Aasen's algorithm\&. The panel consists of a set of NB rows of A when UPLO is U, or a set of NB columns when UPLO is L\&. In order to factorize the panel, the Aasen's algorithm requires the last row, or column, of the previous panel\&. The first row, or column, of A is set to be the first row, or column, of an identity matrix, which is used to factorize the first panel\&. The resulting J-th row of U, or J-th column of L, is stored in the (J-1)-th row, or column, of A (without the unit diagonals), while the diagonal and subdiagonal of A are overwritten by those of T\&. .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 \fIJ1\fP .PP .nf J1 is INTEGER The location of the first row, or column, of the panel within the submatrix of A, passed to this routine, e\&.g\&., when called by ZSYTRF_AA, for the first panel, J1 is 1, while for the remaining panels, J1 is 2\&. .fi .PP .br \fIM\fP .PP .nf M is INTEGER The dimension of the submatrix\&. M >= 0\&. .fi .PP .br \fINB\fP .PP .nf NB is INTEGER The dimension of the panel to be facotorized\&. .fi .PP .br \fIA\fP .PP .nf A is COMPLEX*16 array, dimension (LDA,M) for the first panel, while dimension (LDA,M+1) for the remaining panels\&. On entry, A contains the last row, or column, of the previous panel, and the trailing submatrix of A to be factorized, except for the first panel, only the panel is passed\&. On exit, the leading panel is factorized\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A\&. LDA >= max(1,M)\&. .fi .PP .br \fIIPIV\fP .PP .nf IPIV is INTEGER array, dimension (M) Details of the row and column interchanges, the row and column k were interchanged with the row and column IPIV(k)\&. .fi .PP .br \fIH\fP .PP .nf H is COMPLEX*16 workspace, dimension (LDH,NB)\&. .fi .PP .br \fILDH\fP .PP .nf LDH is INTEGER The leading dimension of the workspace H\&. LDH >= max(1,M)\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is COMPLEX*16 workspace, dimension (M)\&. .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 .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.