.TH "hb2st_kernels" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME hb2st_kernels \- {hb,sb}2st_kernels: band to tridiagonal (2nd stage) .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBchb2st_kernels\fP (uplo, wantz, ttype, st, ed, sweep, n, nb, ib, a, lda, v, tau, ldvt, work)" .br .RI "\fBCHB2ST_KERNELS\fP " .ti -1c .RI "subroutine \fBdsb2st_kernels\fP (uplo, wantz, ttype, st, ed, sweep, n, nb, ib, a, lda, v, tau, ldvt, work)" .br .RI "\fBDSB2ST_KERNELS\fP " .ti -1c .RI "subroutine \fBssb2st_kernels\fP (uplo, wantz, ttype, st, ed, sweep, n, nb, ib, a, lda, v, tau, ldvt, work)" .br .RI "\fBSSB2ST_KERNELS\fP " .ti -1c .RI "subroutine \fBzhb2st_kernels\fP (uplo, wantz, ttype, st, ed, sweep, n, nb, ib, a, lda, v, tau, ldvt, work)" .br .RI "\fBZHB2ST_KERNELS\fP " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine chb2st_kernels (character uplo, logical wantz, integer ttype, integer st, integer ed, integer sweep, integer n, integer nb, integer ib, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) v, complex, dimension( * ) tau, integer ldvt, complex, dimension( * ) work)" .PP \fBCHB2ST_KERNELS\fP .PP \fBPurpose:\fP .RS 4 .PP .nf CHB2ST_KERNELS is an internal routine used by the CHETRD_HB2ST subroutine\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf UPLO is CHARACTER*1 .fi .PP .br \fIWANTZ\fP .PP .nf WANTZ is LOGICAL which indicate if Eigenvalue are requested or both Eigenvalue/Eigenvectors\&. .fi .PP .br \fITTYPE\fP .PP .nf TTYPE is INTEGER .fi .PP .br \fIST\fP .PP .nf ST is INTEGER internal parameter for indices\&. .fi .PP .br \fIED\fP .PP .nf ED is INTEGER internal parameter for indices\&. .fi .PP .br \fISWEEP\fP .PP .nf SWEEP is INTEGER internal parameter for indices\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER\&. The order of the matrix A\&. .fi .PP .br \fINB\fP .PP .nf NB is INTEGER\&. The size of the band\&. .fi .PP .br \fIIB\fP .PP .nf IB is INTEGER\&. .fi .PP .br \fIA\fP .PP .nf A is COMPLEX array\&. A pointer to the matrix A\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER\&. The leading dimension of the matrix A\&. .fi .PP .br \fIV\fP .PP .nf V is COMPLEX array, dimension 2*n if eigenvalues only are requested or to be queried for vectors\&. .fi .PP .br \fITAU\fP .PP .nf TAU is COMPLEX array, dimension (2*n)\&. The scalar factors of the Householder reflectors are stored in this array\&. .fi .PP .br \fILDVT\fP .PP .nf LDVT is INTEGER\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is COMPLEX array\&. Workspace of size nb\&. .fi .PP .RE .PP \fBFurther Details:\fP .RS 4 .PP .nf Implemented by Azzam Haidar\&. All details are available on technical report, SC11, SC13 papers\&. Azzam Haidar, Hatem Ltaief, and Jack Dongarra\&. Parallel reduction to condensed forms for symmetric eigenvalue problems using aggregated fine-grained and memory-aware kernels\&. In Proceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis (SC '11), New York, NY, USA, Article 8 , 11 pages\&. http://doi\&.acm\&.org/10\&.1145/2063384\&.2063394 A\&. Haidar, J\&. Kurzak, P\&. Luszczek, 2013\&. An improved parallel singular value algorithm and its implementation for multicore hardware, In Proceedings of 2013 International Conference for High Performance Computing, Networking, Storage and Analysis (SC '13)\&. Denver, Colorado, USA, 2013\&. Article 90, 12 pages\&. http://doi\&.acm\&.org/10\&.1145/2503210\&.2503292 A\&. Haidar, R\&. Solca, S\&. Tomov, T\&. Schulthess and J\&. Dongarra\&. A novel hybrid CPU-GPU generalized eigensolver for electronic structure calculations based on fine-grained memory aware tasks\&. International Journal of High Performance Computing Applications\&. Volume 28 Issue 2, Pages 196-209, May 2014\&. http://hpc\&.sagepub\&.com/content/28/2/196 .fi .PP .RE .PP .SS "subroutine dsb2st_kernels (character uplo, logical wantz, integer ttype, integer st, integer ed, integer sweep, integer n, integer nb, integer ib, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) v, double precision, dimension( * ) tau, integer ldvt, double precision, dimension( * ) work)" .PP \fBDSB2ST_KERNELS\fP .PP \fBPurpose:\fP .RS 4 .PP .nf DSB2ST_KERNELS is an internal routine used by the DSYTRD_SB2ST subroutine\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf UPLO is CHARACTER*1 .fi .PP .br \fIWANTZ\fP .PP .nf WANTZ is LOGICAL which indicate if Eigenvalue are requested or both Eigenvalue/Eigenvectors\&. .fi .PP .br \fITTYPE\fP .PP .nf TTYPE is INTEGER .fi .PP .br \fIST\fP .PP .nf ST is INTEGER internal parameter for indices\&. .fi .PP .br \fIED\fP .PP .nf ED is INTEGER internal parameter for indices\&. .fi .PP .br \fISWEEP\fP .PP .nf SWEEP is INTEGER internal parameter for indices\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER\&. The order of the matrix A\&. .fi .PP .br \fINB\fP .PP .nf NB is INTEGER\&. The size of the band\&. .fi .PP .br \fIIB\fP .PP .nf IB is INTEGER\&. .fi .PP .br \fIA\fP .PP .nf A is DOUBLE PRECISION array\&. A pointer to the matrix A\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER\&. The leading dimension of the matrix A\&. .fi .PP .br \fIV\fP .PP .nf V is DOUBLE PRECISION array, dimension 2*n if eigenvalues only are requested or to be queried for vectors\&. .fi .PP .br \fITAU\fP .PP .nf TAU is DOUBLE PRECISION array, dimension (2*n)\&. The scalar factors of the Householder reflectors are stored in this array\&. .fi .PP .br \fILDVT\fP .PP .nf LDVT is INTEGER\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is DOUBLE PRECISION array\&. Workspace of size nb\&. .fi .PP .RE .PP \fBFurther Details:\fP .RS 4 .PP .nf Implemented by Azzam Haidar\&. All details are available on technical report, SC11, SC13 papers\&. Azzam Haidar, Hatem Ltaief, and Jack Dongarra\&. Parallel reduction to condensed forms for symmetric eigenvalue problems using aggregated fine-grained and memory-aware kernels\&. In Proceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis (SC '11), New York, NY, USA, Article 8 , 11 pages\&. http://doi\&.acm\&.org/10\&.1145/2063384\&.2063394 A\&. Haidar, J\&. Kurzak, P\&. Luszczek, 2013\&. An improved parallel singular value algorithm and its implementation for multicore hardware, In Proceedings of 2013 International Conference for High Performance Computing, Networking, Storage and Analysis (SC '13)\&. Denver, Colorado, USA, 2013\&. Article 90, 12 pages\&. http://doi\&.acm\&.org/10\&.1145/2503210\&.2503292 A\&. Haidar, R\&. Solca, S\&. Tomov, T\&. Schulthess and J\&. Dongarra\&. A novel hybrid CPU-GPU generalized eigensolver for electronic structure calculations based on fine-grained memory aware tasks\&. International Journal of High Performance Computing Applications\&. Volume 28 Issue 2, Pages 196-209, May 2014\&. http://hpc\&.sagepub\&.com/content/28/2/196 .fi .PP .RE .PP .SS "subroutine ssb2st_kernels (character uplo, logical wantz, integer ttype, integer st, integer ed, integer sweep, integer n, integer nb, integer ib, real, dimension( lda, * ) a, integer lda, real, dimension( * ) v, real, dimension( * ) tau, integer ldvt, real, dimension( * ) work)" .PP \fBSSB2ST_KERNELS\fP .PP \fBPurpose:\fP .RS 4 .PP .nf SSB2ST_KERNELS is an internal routine used by the SSYTRD_SB2ST subroutine\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf UPLO is CHARACTER*1 .fi .PP .br \fIWANTZ\fP .PP .nf WANTZ is LOGICAL which indicate if Eigenvalue are requested or both Eigenvalue/Eigenvectors\&. .fi .PP .br \fITTYPE\fP .PP .nf TTYPE is INTEGER .fi .PP .br \fIST\fP .PP .nf ST is INTEGER internal parameter for indices\&. .fi .PP .br \fIED\fP .PP .nf ED is INTEGER internal parameter for indices\&. .fi .PP .br \fISWEEP\fP .PP .nf SWEEP is INTEGER internal parameter for indices\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER\&. The order of the matrix A\&. .fi .PP .br \fINB\fP .PP .nf NB is INTEGER\&. The size of the band\&. .fi .PP .br \fIIB\fP .PP .nf IB is INTEGER\&. .fi .PP .br \fIA\fP .PP .nf A is REAL array\&. A pointer to the matrix A\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER\&. The leading dimension of the matrix A\&. .fi .PP .br \fIV\fP .PP .nf V is REAL array, dimension 2*n if eigenvalues only are requested or to be queried for vectors\&. .fi .PP .br \fITAU\fP .PP .nf TAU is REAL array, dimension (2*n)\&. The scalar factors of the Householder reflectors are stored in this array\&. .fi .PP .br \fILDVT\fP .PP .nf LDVT is INTEGER\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is REAL array\&. Workspace of size nb\&. .fi .PP .RE .PP \fBFurther Details:\fP .RS 4 .PP .nf Implemented by Azzam Haidar\&. All details are available on technical report, SC11, SC13 papers\&. Azzam Haidar, Hatem Ltaief, and Jack Dongarra\&. Parallel reduction to condensed forms for symmetric eigenvalue problems using aggregated fine-grained and memory-aware kernels\&. In Proceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis (SC '11), New York, NY, USA, Article 8 , 11 pages\&. http://doi\&.acm\&.org/10\&.1145/2063384\&.2063394 A\&. Haidar, J\&. Kurzak, P\&. Luszczek, 2013\&. An improved parallel singular value algorithm and its implementation for multicore hardware, In Proceedings of 2013 International Conference for High Performance Computing, Networking, Storage and Analysis (SC '13)\&. Denver, Colorado, USA, 2013\&. Article 90, 12 pages\&. http://doi\&.acm\&.org/10\&.1145/2503210\&.2503292 A\&. Haidar, R\&. Solca, S\&. Tomov, T\&. Schulthess and J\&. Dongarra\&. A novel hybrid CPU-GPU generalized eigensolver for electronic structure calculations based on fine-grained memory aware tasks\&. International Journal of High Performance Computing Applications\&. Volume 28 Issue 2, Pages 196-209, May 2014\&. http://hpc\&.sagepub\&.com/content/28/2/196 .fi .PP .RE .PP .SS "subroutine zhb2st_kernels (character uplo, logical wantz, integer ttype, integer st, integer ed, integer sweep, integer n, integer nb, integer ib, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) v, complex*16, dimension( * ) tau, integer ldvt, complex*16, dimension( * ) work)" .PP \fBZHB2ST_KERNELS\fP .PP \fBPurpose:\fP .RS 4 .PP .nf ZHB2ST_KERNELS is an internal routine used by the ZHETRD_HB2ST subroutine\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIUPLO\fP .PP .nf UPLO is CHARACTER*1 .fi .PP .br \fIWANTZ\fP .PP .nf WANTZ is LOGICAL which indicate if Eigenvalue are requested or both Eigenvalue/Eigenvectors\&. .fi .PP .br \fITTYPE\fP .PP .nf TTYPE is INTEGER .fi .PP .br \fIST\fP .PP .nf ST is INTEGER internal parameter for indices\&. .fi .PP .br \fIED\fP .PP .nf ED is INTEGER internal parameter for indices\&. .fi .PP .br \fISWEEP\fP .PP .nf SWEEP is INTEGER internal parameter for indices\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER\&. The order of the matrix A\&. .fi .PP .br \fINB\fP .PP .nf NB is INTEGER\&. The size of the band\&. .fi .PP .br \fIIB\fP .PP .nf IB is INTEGER\&. .fi .PP .br \fIA\fP .PP .nf A is COMPLEX*16 array\&. A pointer to the matrix A\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER\&. The leading dimension of the matrix A\&. .fi .PP .br \fIV\fP .PP .nf V is COMPLEX*16 array, dimension 2*n if eigenvalues only are requested or to be queried for vectors\&. .fi .PP .br \fITAU\fP .PP .nf TAU is COMPLEX*16 array, dimension (2*n)\&. The scalar factors of the Householder reflectors are stored in this array\&. .fi .PP .br \fILDVT\fP .PP .nf LDVT is INTEGER\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is COMPLEX*16 array\&. Workspace of size nb\&. .fi .PP .RE .PP \fBFurther Details:\fP .RS 4 .PP .nf Implemented by Azzam Haidar\&. All details are available on technical report, SC11, SC13 papers\&. Azzam Haidar, Hatem Ltaief, and Jack Dongarra\&. Parallel reduction to condensed forms for symmetric eigenvalue problems using aggregated fine-grained and memory-aware kernels\&. In Proceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis (SC '11), New York, NY, USA, Article 8 , 11 pages\&. http://doi\&.acm\&.org/10\&.1145/2063384\&.2063394 A\&. Haidar, J\&. Kurzak, P\&. Luszczek, 2013\&. An improved parallel singular value algorithm and its implementation for multicore hardware, In Proceedings of 2013 International Conference for High Performance Computing, Networking, Storage and Analysis (SC '13)\&. Denver, Colorado, USA, 2013\&. Article 90, 12 pages\&. http://doi\&.acm\&.org/10\&.1145/2503210\&.2503292 A\&. Haidar, R\&. Solca, S\&. Tomov, T\&. Schulthess and J\&. Dongarra\&. A novel hybrid CPU-GPU generalized eigensolver for electronic structure calculations based on fine-grained memory aware tasks\&. International Journal of High Performance Computing Applications\&. Volume 28 Issue 2, Pages 196-209, May 2014\&. http://hpc\&.sagepub\&.com/content/28/2/196 .fi .PP .RE .PP .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.