dsbgst (3p)

Name

dsbgst - lem A*x = lambda*B*x to standard form C*y = lambda*y,

Synopsis

SUBROUTINE DSBGST(VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X, LDX,
WORK, INFO)

CHARACTER*1 VECT, UPLO
INTEGER N, KA, KB, LDAB, LDBB, LDX, INFO
DOUBLE PRECISION AB(LDAB,*), BB(LDBB,*), X(LDX,*), WORK(*)

SUBROUTINE DSBGST_64(VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X,
LDX, WORK, INFO)

CHARACTER*1 VECT, UPLO
INTEGER*8 N, KA, KB, LDAB, LDBB, LDX, INFO
DOUBLE PRECISION AB(LDAB,*), BB(LDBB,*), X(LDX,*), WORK(*)




F95 INTERFACE
SUBROUTINE SBGST(VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X,
LDX, WORK, INFO)

CHARACTER(LEN=1) :: VECT, UPLO
INTEGER :: N, KA, KB, LDAB, LDBB, LDX, INFO
REAL(8), DIMENSION(:) :: WORK
REAL(8), DIMENSION(:,:) :: AB, BB, X

SUBROUTINE SBGST_64(VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB,
X, LDX, WORK, INFO)

CHARACTER(LEN=1) :: VECT, UPLO
INTEGER(8) :: N, KA, KB, LDAB, LDBB, LDX, INFO
REAL(8), DIMENSION(:) :: WORK
REAL(8), DIMENSION(:,:) :: AB, BB, X




C INTERFACE
#include <sunperf.h>

void dsbgst(char vect, char uplo, int n, int ka, int  kb,  double  *ab,
int  ldab,  double  *bb,  int  ldbb,  double *x, int ldx, int
*info);

void dsbgst_64(char vect, char uplo, long n, long ka, long  kb,  double
*ab,  long  ldab, double *bb, long ldbb, double *x, long ldx,
long *info);

Description

Oracle Solaris Studio Performance Library                           dsbgst(3P)



NAME
       dsbgst - reduce a real symmetric-definite banded generalized eigenprob-
       lem A*x = lambda*B*x to standard form C*y = lambda*y,


SYNOPSIS
       SUBROUTINE DSBGST(VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X, LDX,
             WORK, INFO)

       CHARACTER*1 VECT, UPLO
       INTEGER N, KA, KB, LDAB, LDBB, LDX, INFO
       DOUBLE PRECISION AB(LDAB,*), BB(LDBB,*), X(LDX,*), WORK(*)

       SUBROUTINE DSBGST_64(VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X,
             LDX, WORK, INFO)

       CHARACTER*1 VECT, UPLO
       INTEGER*8 N, KA, KB, LDAB, LDBB, LDX, INFO
       DOUBLE PRECISION AB(LDAB,*), BB(LDBB,*), X(LDX,*), WORK(*)




   F95 INTERFACE
       SUBROUTINE SBGST(VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X,
              LDX, WORK, INFO)

       CHARACTER(LEN=1) :: VECT, UPLO
       INTEGER :: N, KA, KB, LDAB, LDBB, LDX, INFO
       REAL(8), DIMENSION(:) :: WORK
       REAL(8), DIMENSION(:,:) :: AB, BB, X

       SUBROUTINE SBGST_64(VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB,
              X, LDX, WORK, INFO)

       CHARACTER(LEN=1) :: VECT, UPLO
       INTEGER(8) :: N, KA, KB, LDAB, LDBB, LDX, INFO
       REAL(8), DIMENSION(:) :: WORK
       REAL(8), DIMENSION(:,:) :: AB, BB, X




   C INTERFACE
       #include <sunperf.h>

       void dsbgst(char vect, char uplo, int n, int ka, int  kb,  double  *ab,
                 int  ldab,  double  *bb,  int  ldbb,  double *x, int ldx, int
                 *info);

       void dsbgst_64(char vect, char uplo, long n, long ka, long  kb,  double
                 *ab,  long  ldab, double *bb, long ldbb, double *x, long ldx,
                 long *info);



PURPOSE
       dsbgst reduces a real symmetric-definite banded generalized  eigenprob-
       lem   A*x  =  lambda*B*x  to standard form  C*y = lambda*y, such that C
       has the same bandwidth as A.

       B must have been previously factorized as S**T*S  by  SPBSTF,  using  a
       split Cholesky factorization. A is overwritten by C = X**T*A*X, where X
       = S**(-1)*Q and Q is an orthogonal matrix chosen to preserve the  band-
       width of A.


ARGUMENTS
       VECT (input)
                 = 'N':  do not form the transformation matrix X;
                 = 'V':  form X.


       UPLO (input)
                 = 'U':  Upper triangle of A is stored;
                 = 'L':  Lower triangle of A is stored.


       N (input) The order of the matrices A and B.  N >= 0.


       KA (input)
                 The  number  of superdiagonals of the matrix A if UPLO = 'U',
                 or the number of subdiagonals if UPLO = 'L'.  KA >= 0.


       KB (input)
                 The number of superdiagonals of the matrix B if UPLO  =  'U',
                 or  the number of subdiagonals if UPLO = 'L'.  KA >= KB >= 0.


       AB (input/output)
                 On entry, the upper or lower triangle of the  symmetric  band
                 matrix A, stored in the first ka+1 rows of the array.  The j-
                 th column of A is stored in the j-th column of the  array  AB
                 as  follows:  if  UPLO  =  'U',  AB(ka+1+i-j,j)  = A(i,j) for
                 max(1,j-ka)<=i<=j; if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for
                 j<=i<=min(n,j+ka).

                 On  exit, the transformed matrix X**T*A*X, stored in the same
                 format as A.


       LDAB (input)
                 The leading dimension of the array AB.  LDAB >= KA+1.


       BB (input)
                 The banded factor S from the split Cholesky factorization  of
                 B,  as  returned  by SPBSTF, stored in the first KB+1 rows of
                 the array.


       LDBB (input)
                 The leading dimension of the array BB.  LDBB >= KB+1.


       X (output)
                 If VECT = 'V', the n-by-n matrix X.  If VECT = 'N', the array
                 X is not referenced.


       LDX (input)
                 The  leading  dimension  of  the array X.  LDX >= max(1,N) if
                 VECT = 'V'; LDX >= 1 otherwise.


       WORK (workspace)
                 dimension(2*N)

       INFO (output)
                 = 0:  successful exit
                 < 0:  if INFO = -i, the i-th argument had an illegal value.




                                  7 Nov 2015                        dsbgst(3P)