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Updated: June 2017
 
 

cgebd2 (3p)

Name

cgebd2 - reduce a general matrix to bidiagonal form using an unblocked algorithm

Synopsis

SUBROUTINE CGEBD2(M, N, A, LDA, D, E, TAUQ, TAUP, WORK, INFO)


INTEGER INFO, LDA, M, N

REAL D(*), E(*)

COMPLEX A(LDA,*), TAUP(*), TAUQ(*), WORK(*)


SUBROUTINE CGEBD2_64(M, N, A, LDA, D, E, TAUQ, TAUP, WORK, INFO)


INTEGER*8 INFO, LDA, M, N

REAL D(*), E(*)

COMPLEX A(LDA,*), TAUP(*), TAUQ(*), WORK(*)


F95 INTERFACE
SUBROUTINE GEBD2(M, N, A, LDA, D, E, TAUQ, TAUP, WORK, INFO)


INTEGER :: M, N, LDA, INFO

REAL, DIMENSION(:) :: D, E

COMPLEX, DIMENSION(:) :: TAUQ, TAUP, WORK

COMPLEX, DIMENSION(:,:) :: A


SUBROUTINE GEBD2_64(M, N, A, LDA, D, E, TAUQ, TAUP, WORK, INFO)


INTEGER(8) :: M, N, LDA, INFO

REAL, DIMENSION(:) :: D, E

COMPLEX, DIMENSION(:) :: TAUQ, TAUP, WORK

COMPLEX, DIMENSION(:,:) :: A


C INTERFACE
#include <sunperf.h>

void cgebd2 (int m, int n, floatcomplex *a, int lda,  float  *d,  float
*e, floatcomplex *tauq, floatcomplex *taup, int *info);


void  cgebd2_64  (long  m, long n, floatcomplex *a, long lda, float *d,
float  *e,  floatcomplex  *tauq,  floatcomplex  *taup,   long
*info);

Description

Oracle Solaris Studio Performance Library                           cgebd2(3P)



NAME
       cgebd2  - reduce a general matrix to bidiagonal form using an unblocked
       algorithm


SYNOPSIS
       SUBROUTINE CGEBD2(M, N, A, LDA, D, E, TAUQ, TAUP, WORK, INFO)


       INTEGER INFO, LDA, M, N

       REAL D(*), E(*)

       COMPLEX A(LDA,*), TAUP(*), TAUQ(*), WORK(*)


       SUBROUTINE CGEBD2_64(M, N, A, LDA, D, E, TAUQ, TAUP, WORK, INFO)


       INTEGER*8 INFO, LDA, M, N

       REAL D(*), E(*)

       COMPLEX A(LDA,*), TAUP(*), TAUQ(*), WORK(*)


   F95 INTERFACE
       SUBROUTINE GEBD2(M, N, A, LDA, D, E, TAUQ, TAUP, WORK, INFO)


       INTEGER :: M, N, LDA, INFO

       REAL, DIMENSION(:) :: D, E

       COMPLEX, DIMENSION(:) :: TAUQ, TAUP, WORK

       COMPLEX, DIMENSION(:,:) :: A


       SUBROUTINE GEBD2_64(M, N, A, LDA, D, E, TAUQ, TAUP, WORK, INFO)


       INTEGER(8) :: M, N, LDA, INFO

       REAL, DIMENSION(:) :: D, E

       COMPLEX, DIMENSION(:) :: TAUQ, TAUP, WORK

       COMPLEX, DIMENSION(:,:) :: A


   C INTERFACE
       #include <sunperf.h>

       void cgebd2 (int m, int n, floatcomplex *a, int lda,  float  *d,  float
                 *e, floatcomplex *tauq, floatcomplex *taup, int *info);


       void  cgebd2_64  (long  m, long n, floatcomplex *a, long lda, float *d,
                 float  *e,  floatcomplex  *tauq,  floatcomplex  *taup,   long
                 *info);


PURPOSE
       cgebd2 reduces a complex general m by n matrix A to upper or lower real
       bidiagonal form B by a unitary transformation: Q**H*A*P=B.

       If m >= n, B is upper bidiagonal; if m < n, B is lower bidiagonal.


ARGUMENTS
       M (input)
                 M is INTEGER
                 The number of rows in the matrix A.  M >= 0.


       N (input)
                 N is INTEGER
                 The number of columns in the matrix A.  N >= 0.


       A (input/output)
                 A is COMPLEX array, dimension (LDA,N)
                 On entry, the m by n general matrix to be reduced.
                 On exit,
                 if m >= n, the diagonal and the first superdiagonal are over-
                 written  with  the  upper  bidiagonal  matrix B; the elements
                 below the diagonal, with the array TAUQ, represent  the  uni-
                 tary  matrix Q as a product of elementary reflectors, and the
                 elements above the first superdiagonal, with the array  TAUP,
                 represent  the  unitary  matrix  P as a product of elementary
                 reflectors;
                 if m < n, the diagonal and the first  subdiagonal  are  over-
                 written  with  the  lower  bidiagonal  matrix B; the elements
                 below the first subdiagonal, with the array  TAUQ,  represent
                 the  unitary  matrix Q as a product of elementary reflectors,
                 and the elements above the diagonal,  with  the  array  TAUP,
                 represent  the  unitary  matrix  P as a product of elementary
                 reflectors.  See Further Details.


       LDA (input)
                 LDA is INTEGER
                 The leading dimension of the array A. LDA >= max(1,M).


       D (output)
                 D is REAL array, dimension (min(M,N))
                 The diagonal elements of the bidiagonal matrix B:
                 D(i) = A(i,i).


       E (output)
                 E is REAL array, dimension (min(M,N)-1)
                 The off-diagonal elements of the bidiagonal matrix B:
                 if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n-1;
                 if m < n, E(i) = A(i+1,i) for i = 1,2,...,m-1.


       TAUQ (output)
                 TAUQ is COMPLEX array dimension (min(M,N))
                 The scalar factors of the elementary reflectors which  repre-
                 sent the unitary matrix Q. See Further Details.


       TAUP (output)
                 TAUP is COMPLEX array, dimension (min(M,N))
                 The  scalar factors of the elementary reflectors which repre-
                 sent the unitary matrix P. See Further Details.


       WORK (output)
                 WORK is COMPLEX array, dimension (max(M,N))


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


FURTHER DETAILS
       The matrices Q and P are represented as products of elementary
       reflectors:

       If m >= n,

       Q = H(1) H(2) . . . H(n)  and  P = G(1) G(2) . . . G(n-1)

       Each H(i) and G(i) has the form:

       H(i) = I - tauq * v * v**H  and G(i) = I - taup * u * u**H

       where tauq and taup are complex scalars, and v and u are complex
       vectors; v(1:i-1) = 0, v(i) = 1, and v(i+1:m) is stored on exit in
       A(i+1:m,i); u(1:i) = 0, u(i+1) = 1, and u(i+2:n) is stored on exit in
       A(i,i+2:n); tauq is stored in TAUQ(i) and taup in TAUP(i).

       If m < n,

       Q = H(1) H(2) . . . H(m-1)  and  P = G(1) G(2) . . . G(m)

       Each H(i) and G(i) has the form:

       H(i) = I - tauq * v * v**H  and G(i) = I - taup * u * u**H

       where tauq and taup are complex scalars, v and u are complex vectors;
       v(1:i) = 0, v(i+1) = 1, and v(i+2:m) is stored on exit in A(i+2:m,i);
       u(1:i-1) = 0, u(i) = 1, and u(i+1:n) is stored on exit in A(i,i+1:n);
       tauq is stored in TAUQ(i) and taup in TAUP(i).
       The contents of A on exit are illustrated by the following examples:
       m = 6 and n = 5 (m > n):          m = 5 and n = 6 (m < n):
        (  d   e   u1  u1  u1 )           (  d   u1  u1  u1  u1  u1 )
        (  v1  d   e   u2  u2 )           (  e   d   u2  u2  u2  u2 )
        (  v1  v2  d   e   u3 )           (  v1  e   d   u3  u3  u3 )
        (  v1  v2  v3  d   e  )           (  v1  v2  e   d   u4  u4 )
        (  v1  v2  v3  v4  d  )           (  v1  v2  v3  e   d   u5 )
        (  v1  v2  v3  v4  v5 )

       where d and e denote diagonal and off-diagonal elements of B, vi
       denotes an element of the vector defining H(i), and ui an element of
       the vector defining G(i).



                                  7 Nov 2015                        cgebd2(3P)