ctbsv - solve one of the systems of equations A*x = b, or A'*x = b, or conjg( A' )*x = b
SUBROUTINE CTBSV(UPLO, TRANSA, DIAG, N, K, A, LDA, Y, INCY) CHARACTER*1 UPLO, TRANSA, DIAG COMPLEX A(LDA,*), Y(*) INTEGER N, K, LDA, INCY SUBROUTINE CTBSV_64(UPLO, TRANSA, DIAG, N, K, A, LDA, Y, INCY) CHARACTER*1 UPLO, TRANSA, DIAG COMPLEX A(LDA,*), Y(*) INTEGER*8 N, K, LDA, INCY F95 INTERFACE SUBROUTINE TBSV(UPLO, TRANSA, DIAG, N, K, A, LDA, Y, INCY) CHARACTER(LEN=1) :: UPLO, TRANSA, DIAG COMPLEX, DIMENSION(:) :: Y COMPLEX, DIMENSION(:,:) :: A INTEGER :: N, K, LDA, INCY SUBROUTINE TBSV_64(UPLO, TRANSA, DIAG, N, K, A, LDA, Y, INCY) CHARACTER(LEN=1) :: UPLO, TRANSA, DIAG COMPLEX, DIMENSION(:) :: Y COMPLEX, DIMENSION(:,:) :: A INTEGER(8) :: N, K, LDA, INCY C INTERFACE #include <sunperf.h> void ctbsv(char uplo, char transa, char diag, int n, int k, complex *a, int lda, complex *y, int incy); void ctbsv_64(char uplo, char transa, char diag, long n, long k, com- plex *a, long lda, complex *y, long incy);
Oracle Solaris Studio Performance Library ctbsv(3P)
NAME
ctbsv - solve one of the systems of equations A*x = b, or A'*x = b,
or conjg( A' )*x = b
SYNOPSIS
SUBROUTINE CTBSV(UPLO, TRANSA, DIAG, N, K, A, LDA, Y, INCY)
CHARACTER*1 UPLO, TRANSA, DIAG
COMPLEX A(LDA,*), Y(*)
INTEGER N, K, LDA, INCY
SUBROUTINE CTBSV_64(UPLO, TRANSA, DIAG, N, K, A, LDA, Y, INCY)
CHARACTER*1 UPLO, TRANSA, DIAG
COMPLEX A(LDA,*), Y(*)
INTEGER*8 N, K, LDA, INCY
F95 INTERFACE
SUBROUTINE TBSV(UPLO, TRANSA, DIAG, N, K, A, LDA, Y, INCY)
CHARACTER(LEN=1) :: UPLO, TRANSA, DIAG
COMPLEX, DIMENSION(:) :: Y
COMPLEX, DIMENSION(:,:) :: A
INTEGER :: N, K, LDA, INCY
SUBROUTINE TBSV_64(UPLO, TRANSA, DIAG, N, K, A, LDA, Y,
INCY)
CHARACTER(LEN=1) :: UPLO, TRANSA, DIAG
COMPLEX, DIMENSION(:) :: Y
COMPLEX, DIMENSION(:,:) :: A
INTEGER(8) :: N, K, LDA, INCY
C INTERFACE
#include <sunperf.h>
void ctbsv(char uplo, char transa, char diag, int n, int k, complex *a,
int lda, complex *y, int incy);
void ctbsv_64(char uplo, char transa, char diag, long n, long k, com-
plex *a, long lda, complex *y, long incy);
PURPOSE
ctbsv solves one of the systems of equations A*x = b, or A'*x = b, or
conjg( A' )*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 rou-
tine. Such tests must be performed before calling this routine.
ARGUMENTS
UPLO (input)
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.
Unchanged on exit.
TRANSA (input)
On entry, TRANSA specifies the equations to be solved as fol-
lows:
TRANSA = 'N' or 'n' A*x = b.
TRANSA = 'T' or 't' A'*x = b.
TRANSA = 'C' or 'c' conjg( A' )*x = b.
Unchanged on exit.
DIAG (input)
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.
Unchanged on exit.
N (input)
On entry, N specifies the order of the matrix A. N >= 0.
Unchanged on exit.
K (input)
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 >= 0. Unchanged on exit.
A (input)
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 col-
umn, 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 conven-
tional 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 col-
umn, 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 trans-
fer 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. Unchanged on exit.
LDA (input)
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. LDA >= ( k + 1 ). Unchanged on
exit.
Y (input/output)
( 1 + ( n - 1 )*abs( INCY ) ). Before entry, the incremented
array Y must contain the n element right-hand side vector b.
On exit, Y is overwritten with the solution vector x.
INCY (input)
On entry, INCY specifies the increment for the elements of Y.
INCY <> 0. Unchanged on exit.
7 Nov 2015 ctbsv(3P)