ztbsv.f man page

ztbsv.f —

Synopsis

Functions/Subroutines

subroutine ztbsv (UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
ZTBSV

Function/Subroutine Documentation

subroutine ztbsv (characterUPLO, characterTRANS, characterDIAG, integerN, integerK, complex*16, dimension(lda,*)A, integerLDA, complex*16, dimension(*)X, integerINCX)

ZTBSV Purpose:

ZTBSV  solves one of the systems of equations

   A*x = b,   or   A**T*x = b,   or   A**H*x = b,

where b and x are n element vectors and A is an n by n unit, or
non-unit, upper or lower triangular band matrix, with ( k + 1 )
diagonals.

No test for singularity or near-singularity is included in this
routine. Such tests must be performed before calling this routine.

Parameters:

UPLO

UPLO is CHARACTER*1
 On entry, UPLO specifies whether the matrix is an upper or
 lower triangular matrix as follows:

    UPLO = 'U' or 'u'   A is an upper triangular matrix.

    UPLO = 'L' or 'l'   A is a lower triangular matrix.

TRANS

TRANS is CHARACTER*1
 On entry, TRANS specifies the equations to be solved as
 follows:

    TRANS = 'N' or 'n'   A*x = b.

    TRANS = 'T' or 't'   A**T*x = b.

    TRANS = 'C' or 'c'   A**H*x = b.

DIAG

DIAG is CHARACTER*1
 On entry, DIAG specifies whether or not A is unit
 triangular as follows:

    DIAG = 'U' or 'u'   A is assumed to be unit triangular.

    DIAG = 'N' or 'n'   A is not assumed to be unit
                        triangular.

N

N is INTEGER
 On entry, N specifies the order of the matrix A.
 N must be at least zero.

K

K is INTEGER
 On entry with UPLO = 'U' or 'u', K specifies the number of
 super-diagonals of the matrix A.
 On entry with UPLO = 'L' or 'l', K specifies the number of
 sub-diagonals of the matrix A.
 K must satisfy  0 .le. K.

A

A is COMPLEX*16 array of DIMENSION ( LDA, n ).
 Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
 by n part of the array A must contain the upper triangular
 band part of the matrix of coefficients, supplied column by
 column, with the leading diagonal of the matrix in row
 ( k + 1 ) of the array, the first super-diagonal starting at
 position 2 in row k, and so on. The top left k by k triangle
 of the array A is not referenced.
 The following program segment will transfer an upper
 triangular band matrix from conventional full matrix storage
 to band storage:

       DO 20, J = 1, N
          M = K + 1 - J
          DO 10, I = MAX( 1, J - K ), J
             A( M + I, J ) = matrix( I, J )
    10    CONTINUE
    20 CONTINUE

 Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
 by n part of the array A must contain the lower triangular
 band part of the matrix of coefficients, supplied column by
 column, with the leading diagonal of the matrix in row 1 of
 the array, the first sub-diagonal starting at position 1 in
 row 2, and so on. The bottom right k by k triangle of the
 array A is not referenced.
 The following program segment will transfer a lower
 triangular band matrix from conventional full matrix storage
 to band storage:

       DO 20, J = 1, N
          M = 1 - J
          DO 10, I = J, MIN( N, J + K )
             A( M + I, J ) = matrix( I, J )
    10    CONTINUE
    20 CONTINUE

 Note that when DIAG = 'U' or 'u' the elements of the array A
 corresponding to the diagonal elements of the matrix are not
 referenced, but are assumed to be unity.

LDA

LDA is INTEGER
 On entry, LDA specifies the first dimension of A as declared
 in the calling (sub) program. LDA must be at least
 ( k + 1 ).

X

X is COMPLEX*16 array of dimension at least
 ( 1 + ( n - 1 )*abs( INCX ) ).
 Before entry, the incremented array X must contain the n
 element right-hand side vector b. On exit, X is overwritten
 with the solution vector x.

INCX

INCX is INTEGER
 On entry, INCX specifies the increment for the elements of
 X. INCX must not be zero.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Further Details:

Level 2 Blas routine.

-- Written on 22-October-1986.
   Jack Dongarra, Argonne National Lab.
   Jeremy Du Croz, Nag Central Office.
   Sven Hammarling, Nag Central Office.
   Richard Hanson, Sandia National Labs.

Definition at line 190 of file ztbsv.f.

Author

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Referenced By

ztbsv(3) is an alias of ztbsv.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK