Man page - hbtrd(3)

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Manual

hbtrd(3) LAPACK hbtrd(3)

hbtrd - {hb,sb}trd: reduction to tridiagonal


subroutine chbtrd (vect, uplo, n, kd, ab, ldab, d, e, q, ldq, work, info)
CHBTRD subroutine dsbtrd (vect, uplo, n, kd, ab, ldab, d, e, q, ldq, work, info)
DSBTRD subroutine ssbtrd (vect, uplo, n, kd, ab, ldab, d, e, q, ldq, work, info)
SSBTRD subroutine zhbtrd (vect, uplo, n, kd, ab, ldab, d, e, q, ldq, work, info)
ZHBTRD

CHBTRD

Purpose:



 CHBTRD reduces a complex Hermitian band matrix A to real symmetric


 tridiagonal form T by a unitary similarity transformation:


 Q**H * A * Q = T.

Parameters

VECT 



          VECT is CHARACTER*1


          = 'N':  do not form Q;


          = 'V':  form Q;


          = 'U':  update a matrix X, by forming X*Q.

UPLO



          UPLO is CHARACTER*1


          = 'U':  Upper triangle of A is stored;


          = 'L':  Lower triangle of A is stored.

N



          N is INTEGER


          The order of the matrix A.  N >= 0.

KD



          KD is INTEGER


          The number of superdiagonals of the matrix A if UPLO = 'U',


          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.

AB



          AB is COMPLEX array, dimension (LDAB,N)


          On entry, the upper or lower triangle of the Hermitian band


          matrix A, stored in the first KD+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(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;


          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).


          On exit, the diagonal elements of AB are overwritten by the


          diagonal elements of the tridiagonal matrix T; if KD > 0, the


          elements on the first superdiagonal (if UPLO = 'U') or the


          first subdiagonal (if UPLO = 'L') are overwritten by the


          off-diagonal elements of T; the rest of AB is overwritten by


          values generated during the reduction.

LDAB



          LDAB is INTEGER


          The leading dimension of the array AB.  LDAB >= KD+1.

D



          D is REAL array, dimension (N)


          The diagonal elements of the tridiagonal matrix T.

E



          E is REAL array, dimension (N-1)


          The off-diagonal elements of the tridiagonal matrix T:


          E(i) = T(i,i+1) if UPLO = 'U'; E(i) = T(i+1,i) if UPLO = 'L'.

Q



          Q is COMPLEX array, dimension (LDQ,N)


          On entry, if VECT = 'U', then Q must contain an N-by-N


          matrix X; if VECT = 'N' or 'V', then Q need not be set.


          On exit:


          if VECT = 'V', Q contains the N-by-N unitary matrix Q;


          if VECT = 'U', Q contains the product X*Q;


          if VECT = 'N', the array Q is not referenced.

LDQ



          LDQ is INTEGER


          The leading dimension of the array Q.


          LDQ >= 1, and LDQ >= N if VECT = 'V' or 'U'.

WORK



          WORK is COMPLEX array, dimension (N)

INFO



          INFO is INTEGER


          = 0:  successful exit


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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:



  Modified by Linda Kaufman, Bell Labs.

DSBTRD

Purpose:



 DSBTRD reduces a real symmetric band matrix A to symmetric


 tridiagonal form T by an orthogonal similarity transformation:


 Q**T * A * Q = T.

Parameters

VECT 



          VECT is CHARACTER*1


          = 'N':  do not form Q;


          = 'V':  form Q;


          = 'U':  update a matrix X, by forming X*Q.

UPLO



          UPLO is CHARACTER*1


          = 'U':  Upper triangle of A is stored;


          = 'L':  Lower triangle of A is stored.

N



          N is INTEGER


          The order of the matrix A.  N >= 0.

KD



          KD is INTEGER


          The number of superdiagonals of the matrix A if UPLO = 'U',


          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.

AB



          AB is DOUBLE PRECISION array, dimension (LDAB,N)


          On entry, the upper or lower triangle of the symmetric band


          matrix A, stored in the first KD+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(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;


          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).


          On exit, the diagonal elements of AB are overwritten by the


          diagonal elements of the tridiagonal matrix T; if KD > 0, the


          elements on the first superdiagonal (if UPLO = 'U') or the


          first subdiagonal (if UPLO = 'L') are overwritten by the


          off-diagonal elements of T; the rest of AB is overwritten by


          values generated during the reduction.

LDAB



          LDAB is INTEGER


          The leading dimension of the array AB.  LDAB >= KD+1.

D



          D is DOUBLE PRECISION array, dimension (N)


          The diagonal elements of the tridiagonal matrix T.

E



          E is DOUBLE PRECISION array, dimension (N-1)


          The off-diagonal elements of the tridiagonal matrix T:


          E(i) = T(i,i+1) if UPLO = 'U'; E(i) = T(i+1,i) if UPLO = 'L'.

Q



          Q is DOUBLE PRECISION array, dimension (LDQ,N)


          On entry, if VECT = 'U', then Q must contain an N-by-N


          matrix X; if VECT = 'N' or 'V', then Q need not be set.


          On exit:


          if VECT = 'V', Q contains the N-by-N orthogonal matrix Q;


          if VECT = 'U', Q contains the product X*Q;


          if VECT = 'N', the array Q is not referenced.

LDQ



          LDQ is INTEGER


          The leading dimension of the array Q.


          LDQ >= 1, and LDQ >= N if VECT = 'V' or 'U'.

WORK



          WORK is DOUBLE PRECISION array, dimension (N)

INFO



          INFO is INTEGER


          = 0:  successful exit


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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:



  Modified by Linda Kaufman, Bell Labs.

SSBTRD

Purpose:



 SSBTRD reduces a real symmetric band matrix A to symmetric


 tridiagonal form T by an orthogonal similarity transformation:


 Q**T * A * Q = T.

Parameters

VECT 



          VECT is CHARACTER*1


          = 'N':  do not form Q;


          = 'V':  form Q;


          = 'U':  update a matrix X, by forming X*Q.

UPLO



          UPLO is CHARACTER*1


          = 'U':  Upper triangle of A is stored;


          = 'L':  Lower triangle of A is stored.

N



          N is INTEGER


          The order of the matrix A.  N >= 0.

KD



          KD is INTEGER


          The number of superdiagonals of the matrix A if UPLO = 'U',


          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.

AB



          AB is REAL array, dimension (LDAB,N)


          On entry, the upper or lower triangle of the symmetric band


          matrix A, stored in the first KD+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(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;


          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).


          On exit, the diagonal elements of AB are overwritten by the


          diagonal elements of the tridiagonal matrix T; if KD > 0, the


          elements on the first superdiagonal (if UPLO = 'U') or the


          first subdiagonal (if UPLO = 'L') are overwritten by the


          off-diagonal elements of T; the rest of AB is overwritten by


          values generated during the reduction.

LDAB



          LDAB is INTEGER


          The leading dimension of the array AB.  LDAB >= KD+1.

D



          D is REAL array, dimension (N)


          The diagonal elements of the tridiagonal matrix T.

E



          E is REAL array, dimension (N-1)


          The off-diagonal elements of the tridiagonal matrix T:


          E(i) = T(i,i+1) if UPLO = 'U'; E(i) = T(i+1,i) if UPLO = 'L'.

Q



          Q is REAL array, dimension (LDQ,N)


          On entry, if VECT = 'U', then Q must contain an N-by-N


          matrix X; if VECT = 'N' or 'V', then Q need not be set.


          On exit:


          if VECT = 'V', Q contains the N-by-N orthogonal matrix Q;


          if VECT = 'U', Q contains the product X*Q;


          if VECT = 'N', the array Q is not referenced.

LDQ



          LDQ is INTEGER


          The leading dimension of the array Q.


          LDQ >= 1, and LDQ >= N if VECT = 'V' or 'U'.

WORK



          WORK is REAL array, dimension (N)

INFO



          INFO is INTEGER


          = 0:  successful exit


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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:



  Modified by Linda Kaufman, Bell Labs.

ZHBTRD

Purpose:



 ZHBTRD reduces a complex Hermitian band matrix A to real symmetric


 tridiagonal form T by a unitary similarity transformation:


 Q**H * A * Q = T.

Parameters

VECT 



          VECT is CHARACTER*1


          = 'N':  do not form Q;


          = 'V':  form Q;


          = 'U':  update a matrix X, by forming X*Q.

UPLO



          UPLO is CHARACTER*1


          = 'U':  Upper triangle of A is stored;


          = 'L':  Lower triangle of A is stored.

N



          N is INTEGER


          The order of the matrix A.  N >= 0.

KD



          KD is INTEGER


          The number of superdiagonals of the matrix A if UPLO = 'U',


          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.

AB



          AB is COMPLEX*16 array, dimension (LDAB,N)


          On entry, the upper or lower triangle of the Hermitian band


          matrix A, stored in the first KD+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(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;


          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).


          On exit, the diagonal elements of AB are overwritten by the


          diagonal elements of the tridiagonal matrix T; if KD > 0, the


          elements on the first superdiagonal (if UPLO = 'U') or the


          first subdiagonal (if UPLO = 'L') are overwritten by the


          off-diagonal elements of T; the rest of AB is overwritten by


          values generated during the reduction.

LDAB



          LDAB is INTEGER


          The leading dimension of the array AB.  LDAB >= KD+1.

D



          D is DOUBLE PRECISION array, dimension (N)


          The diagonal elements of the tridiagonal matrix T.

E



          E is DOUBLE PRECISION array, dimension (N-1)


          The off-diagonal elements of the tridiagonal matrix T:


          E(i) = T(i,i+1) if UPLO = 'U'; E(i) = T(i+1,i) if UPLO = 'L'.

Q



          Q is COMPLEX*16 array, dimension (LDQ,N)


          On entry, if VECT = 'U', then Q must contain an N-by-N


          matrix X; if VECT = 'N' or 'V', then Q need not be set.


          On exit:


          if VECT = 'V', Q contains the N-by-N unitary matrix Q;


          if VECT = 'U', Q contains the product X*Q;


          if VECT = 'N', the array Q is not referenced.

LDQ



          LDQ is INTEGER


          The leading dimension of the array Q.


          LDQ >= 1, and LDQ >= N if VECT = 'V' or 'U'.

WORK



          WORK is COMPLEX*16 array, dimension (N)

INFO



          INFO is INTEGER


          = 0:  successful exit


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

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:



  Modified by Linda Kaufman, Bell Labs.

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