• NAME
• SYNOPSIS
• F95 INTERFACE
• C INTERFACE
• PURPOSE
• ARGUMENTS

NAME

sgbbrd - reduce a real general m-by-n band matrix A to upper bidiagonal form B by an orthogonal transformation

SYNOPSIS

  SUBROUTINE SGBBRD( VECT, M, N, NCC, KL, KU, AB, LDAB, D, E, Q, LDQ, 
 *      PT, LDPT, C, LDC, WORK, INFO)
  CHARACTER * 1 VECT
  INTEGER M, N, NCC, KL, KU, LDAB, LDQ, LDPT, LDC, INFO
  REAL AB(LDAB,*), D(*), E(*), Q(LDQ,*), PT(LDPT,*), C(LDC,*), WORK(*)

  SUBROUTINE SGBBRD_64( VECT, M, N, NCC, KL, KU, AB, LDAB, D, E, Q, 
 *      LDQ, PT, LDPT, C, LDC, WORK, INFO)
  CHARACTER * 1 VECT
  INTEGER*8 M, N, NCC, KL, KU, LDAB, LDQ, LDPT, LDC, INFO
  REAL AB(LDAB,*), D(*), E(*), Q(LDQ,*), PT(LDPT,*), C(LDC,*), WORK(*)

F95 INTERFACE

  SUBROUTINE GBBRD( VECT, [M], [N], [NCC], KL, KU, AB, [LDAB], D, E, 
 *       Q, [LDQ], PT, [LDPT], C, [LDC], [WORK], [INFO])
  CHARACTER(LEN=1) :: VECT
  INTEGER :: M, N, NCC, KL, KU, LDAB, LDQ, LDPT, LDC, INFO
  REAL, DIMENSION(:) :: D, E, WORK
  REAL, DIMENSION(:,:) :: AB, Q, PT, C

  SUBROUTINE GBBRD_64( VECT, [M], [N], [NCC], KL, KU, AB, [LDAB], D, 
 *       E, Q, [LDQ], PT, [LDPT], C, [LDC], [WORK], [INFO])
  CHARACTER(LEN=1) :: VECT
  INTEGER(8) :: M, N, NCC, KL, KU, LDAB, LDQ, LDPT, LDC, INFO
  REAL, DIMENSION(:) :: D, E, WORK
  REAL, DIMENSION(:,:) :: AB, Q, PT, C

C INTERFACE

#include <sunperf.h>

void sgbbrd(char vect, int m, int n, int ncc, int kl, int ku, float *ab, int ldab, float *d, float *e, float *q, int ldq, float *pt, int ldpt, float *c, int ldc, int *info);

void sgbbrd_64(char vect, long m, long n, long ncc, long kl, long ku, float *ab, long ldab, float *d, float *e, float *q, long ldq, float *pt, long ldpt, float *c, long ldc, long *info);

PURPOSE

sgbbrd reduces a real general m-by-n band matrix A to upper bidiagonal form B by an orthogonal transformation: Q' * A * P = B.

The routine computes B, and optionally forms Q or P', or computes Q'*C for a given matrix C.

ARGUMENTS

• VECT (input)
  Specifies whether or not the matrices Q and P' are to be formed. = 'N': do not form Q or P';

   = 'Q': form Q only;

   = 'P': form P' only;

   = 'B': form both.

• M (input)
  The number of rows of the matrix A. M > = 0.

• N (input)
  The number of columns of the matrix A. N > = 0.

• NCC (input)
  The number of columns of the matrix C. NCC > = 0.

• KL (input)
  The number of subdiagonals of the matrix A. KL > = 0.

• KU (input)
  The number of superdiagonals of the matrix A. KU > = 0.

• AB (input/output)
  On entry, the m-by-n band matrix A, stored in rows 1 to KL+KU+1. The j-th column of A is stored in the j-th column of the array AB as follows: AB(ku+1+i-j,j) = A(i,j) for max(1,j-ku) < =i < =min(m,j+kl). On exit, A is overwritten by values generated during the reduction.

• LDAB (input)
  The leading dimension of the array A. LDAB > = KL+KU+1.

• D (output)
  The diagonal elements of the bidiagonal matrix B.

• E (output)
  The superdiagonal elements of the bidiagonal matrix B.

• Q (output)
  If VECT = 'Q' or 'B', the m-by-m orthogonal matrix Q. If VECT = 'N' or 'P', the array Q is not referenced.

• LDQ (input)
  The leading dimension of the array Q. LDQ > = max(1,M) if VECT = 'Q' or 'B'; LDQ > = 1 otherwise.

• PT (output)
  If VECT = 'P' or 'B', the n-by-n orthogonal matrix P'. If VECT = 'N' or 'Q', the array PT is not referenced.

• LDPT (input)
  The leading dimension of the array PT. LDPT > = max(1,N) if VECT = 'P' or 'B'; LDPT > = 1 otherwise.

• C (input/output)
  On entry, an m-by-ncc matrix C. On exit, C is overwritten by Q'*C. C is not referenced if NCC = 0.

• LDC (input)
  The leading dimension of the array C. LDC > = max(1,M) if NCC > 0; LDC > = 1 if NCC = 0.

• WORK (workspace)
  dimension(MAX(M,N))

• INFO (output)
  

   = 0:  successful exit.

   < 0:  if INFO  = -i, the i-th argument had an illegal value.