.TH "laeda" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME laeda \- laeda: D&C step: z vector .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "subroutine \fBdlaeda\fP (n, tlvls, curlvl, curpbm, prmptr, perm, givptr, givcol, givnum, q, qptr, z, ztemp, info)" .br .RI "\fBDLAEDA\fP used by DSTEDC\&. Computes the Z vector determining the rank-one modification of the diagonal matrix\&. Used when the original matrix is dense\&. " .ti -1c .RI "subroutine \fBslaeda\fP (n, tlvls, curlvl, curpbm, prmptr, perm, givptr, givcol, givnum, q, qptr, z, ztemp, info)" .br .RI "\fBSLAEDA\fP used by SSTEDC\&. Computes the Z vector determining the rank-one modification of the diagonal matrix\&. Used when the original matrix is dense\&. " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "subroutine dlaeda (integer n, integer tlvls, integer curlvl, integer curpbm, integer, dimension( * ) prmptr, integer, dimension( * ) perm, integer, dimension( * ) givptr, integer, dimension( 2, * ) givcol, double precision, dimension( 2, * ) givnum, double precision, dimension( * ) q, integer, dimension( * ) qptr, double precision, dimension( * ) z, double precision, dimension( * ) ztemp, integer info)" .PP \fBDLAEDA\fP used by DSTEDC\&. Computes the Z vector determining the rank-one modification of the diagonal matrix\&. Used when the original matrix is dense\&. .PP \fBPurpose:\fP .RS 4 .PP .nf DLAEDA computes the Z vector corresponding to the merge step in the CURLVLth step of the merge process with TLVLS steps for the CURPBMth problem\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIN\fP .PP .nf N is INTEGER The dimension of the symmetric tridiagonal matrix\&. N >= 0\&. .fi .PP .br \fITLVLS\fP .PP .nf TLVLS is INTEGER The total number of merging levels in the overall divide and conquer tree\&. .fi .PP .br \fICURLVL\fP .PP .nf CURLVL is INTEGER The current level in the overall merge routine, 0 <= curlvl <= tlvls\&. .fi .PP .br \fICURPBM\fP .PP .nf CURPBM is INTEGER The current problem in the current level in the overall merge routine (counting from upper left to lower right)\&. .fi .PP .br \fIPRMPTR\fP .PP .nf PRMPTR is INTEGER array, dimension (N lg N) Contains a list of pointers which indicate where in PERM a level's permutation is stored\&. PRMPTR(i+1) - PRMPTR(i) indicates the size of the permutation and incidentally the size of the full, non-deflated problem\&. .fi .PP .br \fIPERM\fP .PP .nf PERM is INTEGER array, dimension (N lg N) Contains the permutations (from deflation and sorting) to be applied to each eigenblock\&. .fi .PP .br \fIGIVPTR\fP .PP .nf GIVPTR is INTEGER array, dimension (N lg N) Contains a list of pointers which indicate where in GIVCOL a level's Givens rotations are stored\&. GIVPTR(i+1) - GIVPTR(i) indicates the number of Givens rotations\&. .fi .PP .br \fIGIVCOL\fP .PP .nf GIVCOL is INTEGER array, dimension (2, N lg N) Each pair of numbers indicates a pair of columns to take place in a Givens rotation\&. .fi .PP .br \fIGIVNUM\fP .PP .nf GIVNUM is DOUBLE PRECISION array, dimension (2, N lg N) Each number indicates the S value to be used in the corresponding Givens rotation\&. .fi .PP .br \fIQ\fP .PP .nf Q is DOUBLE PRECISION array, dimension (N**2) Contains the square eigenblocks from previous levels, the starting positions for blocks are given by QPTR\&. .fi .PP .br \fIQPTR\fP .PP .nf QPTR is INTEGER array, dimension (N+2) Contains a list of pointers which indicate where in Q an eigenblock is stored\&. SQRT( QPTR(i+1) - QPTR(i) ) indicates the size of the block\&. .fi .PP .br \fIZ\fP .PP .nf Z is DOUBLE PRECISION array, dimension (N) On output this vector contains the updating vector (the last row of the first sub-eigenvector matrix and the first row of the second sub-eigenvector matrix)\&. .fi .PP .br \fIZTEMP\fP .PP .nf ZTEMP is DOUBLE PRECISION array, dimension (N) .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\&. .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 Jeff Rutter, Computer Science Division, University of California at Berkeley, USA .RE .PP .SS "subroutine slaeda (integer n, integer tlvls, integer curlvl, integer curpbm, integer, dimension( * ) prmptr, integer, dimension( * ) perm, integer, dimension( * ) givptr, integer, dimension( 2, * ) givcol, real, dimension( 2, * ) givnum, real, dimension( * ) q, integer, dimension( * ) qptr, real, dimension( * ) z, real, dimension( * ) ztemp, integer info)" .PP \fBSLAEDA\fP used by SSTEDC\&. Computes the Z vector determining the rank-one modification of the diagonal matrix\&. Used when the original matrix is dense\&. .PP \fBPurpose:\fP .RS 4 .PP .nf SLAEDA computes the Z vector corresponding to the merge step in the CURLVLth step of the merge process with TLVLS steps for the CURPBMth problem\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fIN\fP .PP .nf N is INTEGER The dimension of the symmetric tridiagonal matrix\&. N >= 0\&. .fi .PP .br \fITLVLS\fP .PP .nf TLVLS is INTEGER The total number of merging levels in the overall divide and conquer tree\&. .fi .PP .br \fICURLVL\fP .PP .nf CURLVL is INTEGER The current level in the overall merge routine, 0 <= curlvl <= tlvls\&. .fi .PP .br \fICURPBM\fP .PP .nf CURPBM is INTEGER The current problem in the current level in the overall merge routine (counting from upper left to lower right)\&. .fi .PP .br \fIPRMPTR\fP .PP .nf PRMPTR is INTEGER array, dimension (N lg N) Contains a list of pointers which indicate where in PERM a level's permutation is stored\&. PRMPTR(i+1) - PRMPTR(i) indicates the size of the permutation and incidentally the size of the full, non-deflated problem\&. .fi .PP .br \fIPERM\fP .PP .nf PERM is INTEGER array, dimension (N lg N) Contains the permutations (from deflation and sorting) to be applied to each eigenblock\&. .fi .PP .br \fIGIVPTR\fP .PP .nf GIVPTR is INTEGER array, dimension (N lg N) Contains a list of pointers which indicate where in GIVCOL a level's Givens rotations are stored\&. GIVPTR(i+1) - GIVPTR(i) indicates the number of Givens rotations\&. .fi .PP .br \fIGIVCOL\fP .PP .nf GIVCOL is INTEGER array, dimension (2, N lg N) Each pair of numbers indicates a pair of columns to take place in a Givens rotation\&. .fi .PP .br \fIGIVNUM\fP .PP .nf GIVNUM is REAL array, dimension (2, N lg N) Each number indicates the S value to be used in the corresponding Givens rotation\&. .fi .PP .br \fIQ\fP .PP .nf Q is REAL array, dimension (N**2) Contains the square eigenblocks from previous levels, the starting positions for blocks are given by QPTR\&. .fi .PP .br \fIQPTR\fP .PP .nf QPTR is INTEGER array, dimension (N+2) Contains a list of pointers which indicate where in Q an eigenblock is stored\&. SQRT( QPTR(i+1) - QPTR(i) ) indicates the size of the block\&. .fi .PP .br \fIZ\fP .PP .nf Z is REAL array, dimension (N) On output this vector contains the updating vector (the last row of the first sub-eigenvector matrix and the first row of the second sub-eigenvector matrix)\&. .fi .PP .br \fIZTEMP\fP .PP .nf ZTEMP is REAL array, dimension (N) .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\&. .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 Jeff Rutter, Computer Science Division, University of California at Berkeley, USA .RE .PP .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.