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SUBROUTINE CTBSV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX) |
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* .. Scalar Arguments .. |
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INTEGER INCX,K,LDA,N |
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CHARACTER DIAG,TRANS,UPLO |
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* .. |
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* .. Array Arguments .. |
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COMPLEX A(LDA,*),X(*) |
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* .. |
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* |
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* Purpose |
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* ======= |
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* |
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* CTBSV solves one of the systems of equations |
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* |
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* A*x = b, or A'*x = b, or conjg( A' )*x = b, |
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* |
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* where b and x are n element vectors and A is an n by n unit, or |
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* non-unit, upper or lower triangular band matrix, with ( k + 1 ) |
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* diagonals. |
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* |
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* No test for singularity or near-singularity is included in this |
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* routine. Such tests must be performed before calling this routine. |
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* |
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* Arguments |
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* ========== |
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* |
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* UPLO - CHARACTER*1. |
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* On entry, UPLO specifies whether the matrix is an upper or |
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* lower triangular matrix as follows: |
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* |
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* UPLO = 'U' or 'u' A is an upper triangular matrix. |
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* |
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* UPLO = 'L' or 'l' A is a lower triangular matrix. |
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* |
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* Unchanged on exit. |
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* |
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* TRANS - CHARACTER*1. |
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* On entry, TRANS specifies the equations to be solved as |
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* follows: |
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* |
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* TRANS = 'N' or 'n' A*x = b. |
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* |
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* TRANS = 'T' or 't' A'*x = b. |
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* |
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* TRANS = 'C' or 'c' conjg( A' )*x = b. |
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* |
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* Unchanged on exit. |
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* |
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* DIAG - CHARACTER*1. |
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* On entry, DIAG specifies whether or not A is unit |
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* triangular as follows: |
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* |
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* DIAG = 'U' or 'u' A is assumed to be unit triangular. |
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* |
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* DIAG = 'N' or 'n' A is not assumed to be unit |
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* triangular. |
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* |
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* Unchanged on exit. |
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* |
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* N - INTEGER. |
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* On entry, N specifies the order of the matrix A. |
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* N must be at least zero. |
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* Unchanged on exit. |
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* |
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* K - INTEGER. |
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* On entry with UPLO = 'U' or 'u', K specifies the number of |
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* super-diagonals of the matrix A. |
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* On entry with UPLO = 'L' or 'l', K specifies the number of |
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* sub-diagonals of the matrix A. |
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* K must satisfy 0 .le. K. |
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* Unchanged on exit. |
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* |
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* A - COMPLEX array of DIMENSION ( LDA, n ). |
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* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) |
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* by n part of the array A must contain the upper triangular |
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* band part of the matrix of coefficients, supplied column by |
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* column, with the leading diagonal of the matrix in row |
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* ( k + 1 ) of the array, the first super-diagonal starting at |
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* position 2 in row k, and so on. The top left k by k triangle |
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* of the array A is not referenced. |
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* The following program segment will transfer an upper |
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* triangular band matrix from conventional full matrix storage |
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* to band storage: |
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* |
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* DO 20, J = 1, N |
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* M = K + 1 - J |
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* DO 10, I = MAX( 1, J - K ), J |
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* A( M + I, J ) = matrix( I, J ) |
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* 10 CONTINUE |
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* 20 CONTINUE |
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* |
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* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) |
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* by n part of the array A must contain the lower triangular |
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* band part of the matrix of coefficients, supplied column by |
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* column, with the leading diagonal of the matrix in row 1 of |
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* the array, the first sub-diagonal starting at position 1 in |
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* row 2, and so on. The bottom right k by k triangle of the |
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* array A is not referenced. |
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* The following program segment will transfer a lower |
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* triangular band matrix from conventional full matrix storage |
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* to band storage: |
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* |
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* DO 20, J = 1, N |
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* M = 1 - J |
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* DO 10, I = J, MIN( N, J + K ) |
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* A( M + I, J ) = matrix( I, J ) |
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* 10 CONTINUE |
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* 20 CONTINUE |
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* |
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* Note that when DIAG = 'U' or 'u' the elements of the array A |
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* corresponding to the diagonal elements of the matrix are not |
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* referenced, but are assumed to be unity. |
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* Unchanged on exit. |
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* |
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* LDA - INTEGER. |
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* On entry, LDA specifies the first dimension of A as declared |
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* in the calling (sub) program. LDA must be at least |
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* ( k + 1 ). |
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* Unchanged on exit. |
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* |
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* X - COMPLEX array of dimension at least |
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* ( 1 + ( n - 1 )*abs( INCX ) ). |
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* Before entry, the incremented array X must contain the n |
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* element right-hand side vector b. On exit, X is overwritten |
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* with the solution vector x. |
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* |
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* INCX - INTEGER. |
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* On entry, INCX specifies the increment for the elements of |
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* X. INCX must not be zero. |
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* Unchanged on exit. |
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* |
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* |
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* Level 2 Blas routine. |
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* |
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* -- Written on 22-October-1986. |
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* Jack Dongarra, Argonne National Lab. |
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* Jeremy Du Croz, Nag Central Office. |
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* Sven Hammarling, Nag Central Office. |
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* Richard Hanson, Sandia National Labs. |
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* |
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* |
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* .. Parameters .. |
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COMPLEX ZERO |
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PARAMETER (ZERO= (0.0E+0,0.0E+0)) |
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* .. |
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* .. Local Scalars .. |
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COMPLEX TEMP |
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INTEGER I,INFO,IX,J,JX,KPLUS1,KX,L |
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LOGICAL NOCONJ,NOUNIT |
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* .. |
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* .. External Functions .. |
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LOGICAL LSAME |
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EXTERNAL LSAME |
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* .. |
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* .. External Subroutines .. |
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EXTERNAL XERBLA |
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* .. |
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* .. Intrinsic Functions .. |
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INTRINSIC CONJG,MAX,MIN |
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* .. |
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* |
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* Test the input parameters. |
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* |
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INFO = 0 |
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IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN |
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INFO = 1 |
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ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND. |
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+ .NOT.LSAME(TRANS,'C')) THEN |
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INFO = 2 |
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ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN |
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INFO = 3 |
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ELSE IF (N.LT.0) THEN |
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INFO = 4 |
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ELSE IF (K.LT.0) THEN |
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INFO = 5 |
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ELSE IF (LDA.LT. (K+1)) THEN |
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INFO = 7 |
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ELSE IF (INCX.EQ.0) THEN |
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INFO = 9 |
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END IF |
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IF (INFO.NE.0) THEN |
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CALL XERBLA('CTBSV ',INFO)
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RETURN |
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END IF |
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* |
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* Quick return if possible. |
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* |
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IF (N.EQ.0) RETURN |
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* |
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NOCONJ = LSAME(TRANS,'T') |
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NOUNIT = LSAME(DIAG,'N') |
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* |
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* Set up the start point in X if the increment is not unity. This |
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* will be ( N - 1 )*INCX too small for descending loops. |
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* |
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IF (INCX.LE.0) THEN |
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KX = 1 - (N-1)*INCX |
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ELSE IF (INCX.NE.1) THEN |
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KX = 1 |
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END IF |
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* |
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* Start the operations. In this version the elements of A are |
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* accessed by sequentially with one pass through A. |
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* |
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IF (LSAME(TRANS,'N')) THEN |
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* |
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* Form x := inv( A )*x. |
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* |
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IF (LSAME(UPLO,'U')) THEN |
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KPLUS1 = K + 1 |
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IF (INCX.EQ.1) THEN |
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DO 20 J = N,1,-1 |
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IF (X(J).NE.ZERO) THEN |
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L = KPLUS1 - J |
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IF (NOUNIT) X(J) = X(J)/A(KPLUS1,J) |
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TEMP = X(J) |
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DO 10 I = J - 1,MAX(1,J-K),-1 |
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X(I) = X(I) - TEMP*A(L+I,J) |
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10 CONTINUE |
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END IF |
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20 CONTINUE |
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ELSE |
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KX = KX + (N-1)*INCX |
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JX = KX |
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DO 40 J = N,1,-1 |
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KX = KX - INCX |
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IF (X(JX).NE.ZERO) THEN |
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IX = KX |
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L = KPLUS1 - J |
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IF (NOUNIT) X(JX) = X(JX)/A(KPLUS1,J) |
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TEMP = X(JX) |
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DO 30 I = J - 1,MAX(1,J-K),-1 |
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X(IX) = X(IX) - TEMP*A(L+I,J) |
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IX = IX - INCX |
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30 CONTINUE |
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END IF |
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JX = JX - INCX |
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40 CONTINUE |
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END IF |
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ELSE |
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IF (INCX.EQ.1) THEN |
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DO 60 J = 1,N |
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IF (X(J).NE.ZERO) THEN |
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L = 1 - J |
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IF (NOUNIT) X(J) = X(J)/A(1,J) |
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TEMP = X(J) |
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DO 50 I = J + 1,MIN(N,J+K) |
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X(I) = X(I) - TEMP*A(L+I,J) |
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50 CONTINUE |
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END IF |
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60 CONTINUE |
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ELSE |
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JX = KX |
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DO 80 J = 1,N |
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KX = KX + INCX |
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IF (X(JX).NE.ZERO) THEN |
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IX = KX |
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L = 1 - J |
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IF (NOUNIT) X(JX) = X(JX)/A(1,J) |
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TEMP = X(JX) |
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DO 70 I = J + 1,MIN(N,J+K) |
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X(IX) = X(IX) - TEMP*A(L+I,J) |
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IX = IX + INCX |
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70 CONTINUE |
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END IF |
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JX = JX + INCX |
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80 CONTINUE |
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END IF |
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END IF |
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ELSE |
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* |
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* Form x := inv( A' )*x or x := inv( conjg( A') )*x. |
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* |
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IF (LSAME(UPLO,'U')) THEN |
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KPLUS1 = K + 1 |
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IF (INCX.EQ.1) THEN |
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DO 110 J = 1,N |
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TEMP = X(J) |
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L = KPLUS1 - J |
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IF (NOCONJ) THEN |
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DO 90 I = MAX(1,J-K),J - 1 |
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TEMP = TEMP - A(L+I,J)*X(I) |
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90 CONTINUE |
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IF (NOUNIT) TEMP = TEMP/A(KPLUS1,J) |
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ELSE |
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DO 100 I = MAX(1,J-K),J - 1 |
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TEMP = TEMP - CONJG(A(L+I,J))*X(I) |
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100 CONTINUE |
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IF (NOUNIT) TEMP = TEMP/CONJG(A(KPLUS1,J)) |
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END IF |
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X(J) = TEMP |
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110 CONTINUE |
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ELSE |
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JX = KX |
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DO 140 J = 1,N |
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TEMP = X(JX) |
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IX = KX |
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L = KPLUS1 - J |
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IF (NOCONJ) THEN |
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DO 120 I = MAX(1,J-K),J - 1 |
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TEMP = TEMP - A(L+I,J)*X(IX) |
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IX = IX + INCX |
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120 CONTINUE |
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IF (NOUNIT) TEMP = TEMP/A(KPLUS1,J) |
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ELSE |
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DO 130 I = MAX(1,J-K),J - 1 |
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TEMP = TEMP - CONJG(A(L+I,J))*X(IX) |
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IX = IX + INCX |
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130 CONTINUE |
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IF (NOUNIT) TEMP = TEMP/CONJG(A(KPLUS1,J)) |
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END IF |
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X(JX) = TEMP |
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JX = JX + INCX |
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IF (J.GT.K) KX = KX + INCX |
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140 CONTINUE |
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END IF |
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ELSE |
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IF (INCX.EQ.1) THEN |
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DO 170 J = N,1,-1 |
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TEMP = X(J) |
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L = 1 - J |
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IF (NOCONJ) THEN |
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DO 150 I = MIN(N,J+K),J + 1,-1 |
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TEMP = TEMP - A(L+I,J)*X(I) |
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150 CONTINUE |
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IF (NOUNIT) TEMP = TEMP/A(1,J) |
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ELSE |
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DO 160 I = MIN(N,J+K),J + 1,-1 |
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TEMP = TEMP - CONJG(A(L+I,J))*X(I) |
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160 CONTINUE |
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IF (NOUNIT) TEMP = TEMP/CONJG(A(1,J)) |
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END IF |
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X(J) = TEMP |
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170 CONTINUE |
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ELSE |
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KX = KX + (N-1)*INCX |
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JX = KX |
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DO 200 J = N,1,-1 |
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TEMP = X(JX) |
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IX = KX |
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L = 1 - J |
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IF (NOCONJ) THEN |
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DO 180 I = MIN(N,J+K),J + 1,-1 |
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TEMP = TEMP - A(L+I,J)*X(IX) |
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IX = IX - INCX |
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180 CONTINUE |
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IF (NOUNIT) TEMP = TEMP/A(1,J) |
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ELSE |
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DO 190 I = MIN(N,J+K),J + 1,-1 |
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TEMP = TEMP - CONJG(A(L+I,J))*X(IX) |
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IX = IX - INCX |
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190 CONTINUE |
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IF (NOUNIT) TEMP = TEMP/CONJG(A(1,J)) |
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END IF |
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X(JX) = TEMP |
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JX = JX - INCX |
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IF ((N-J).GE.K) KX = KX - INCX |
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200 CONTINUE |
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END IF |
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END IF |
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END IF |
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* |
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RETURN |
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* |
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* End of CTBSV . |
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* |
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END |