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authorSiddhesh Wani2015-05-25 14:46:31 +0530
committerSiddhesh Wani2015-05-25 14:46:31 +0530
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+ SUBROUTINE DTBMV ( UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX )
+* .. Scalar Arguments ..
+ INTEGER INCX, K, LDA, N
+ CHARACTER*1 DIAG, TRANS, UPLO
+* .. Array Arguments ..
+ DOUBLE PRECISION A( LDA, * ), X( * )
+* ..
+*
+* Purpose
+* =======
+*
+* DTBMV performs one of the matrix-vector operations
+*
+* x := A*x, or x := A'*x,
+*
+* where x is an n element vector and A is an n by n unit, or non-unit,
+* upper or lower triangular band matrix, with ( k + 1 ) diagonals.
+*
+* Parameters
+* ==========
+*
+* UPLO - 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.
+*
+* Unchanged on exit.
+*
+* TRANS - CHARACTER*1.
+* On entry, TRANS specifies the operation to be performed as
+* follows:
+*
+* TRANS = 'N' or 'n' x := A*x.
+*
+* TRANS = 'T' or 't' x := A'*x.
+*
+* TRANS = 'C' or 'c' x := A'*x.
+*
+* Unchanged on exit.
+*
+* DIAG - 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.
+*
+* Unchanged on exit.
+*
+* N - INTEGER.
+* On entry, N specifies the order of the matrix A.
+* N must be at least zero.
+* Unchanged on exit.
+*
+* K - 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.
+* Unchanged on exit.
+*
+* A - DOUBLE PRECISION 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.
+* Unchanged on exit.
+*
+* LDA - INTEGER.
+* On entry, LDA specifies the first dimension of A as declared
+* in the calling (sub) program. LDA must be at least
+* ( k + 1 ).
+* Unchanged on exit.
+*
+* X - DOUBLE PRECISION array of dimension at least
+* ( 1 + ( n - 1 )*abs( INCX ) ).
+* Before entry, the incremented array X must contain the n
+* element vector x. On exit, X is overwritten with the
+* tranformed vector x.
+*
+* INCX - INTEGER.
+* On entry, INCX specifies the increment for the elements of
+* X. INCX must not be zero.
+* Unchanged on exit.
+*
+*
+* 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.
+*
+*
+* .. Parameters ..
+ DOUBLE PRECISION ZERO
+ PARAMETER ( ZERO = 0.0D+0 )
+* .. Local Scalars ..
+ DOUBLE PRECISION TEMP
+ INTEGER I, INFO, IX, J, JX, KPLUS1, KX, L
+ LOGICAL NOUNIT
+* .. External Functions ..
+ LOGICAL LSAME
+ EXTERNAL LSAME
+* .. External Subroutines ..
+ EXTERNAL XERBLA
+* .. Intrinsic Functions ..
+ INTRINSIC MAX, MIN
+* ..
+* .. Executable Statements ..
+*
+* Test the input parameters.
+*
+ INFO = 0
+ IF ( .NOT.LSAME( UPLO , 'U' ).AND.
+ $ .NOT.LSAME( UPLO , 'L' ) )THEN
+ INFO = 1
+ ELSE IF( .NOT.LSAME( TRANS, 'N' ).AND.
+ $ .NOT.LSAME( TRANS, 'T' ).AND.
+ $ .NOT.LSAME( TRANS, 'C' ) )THEN
+ INFO = 2
+ ELSE IF( .NOT.LSAME( DIAG , 'U' ).AND.
+ $ .NOT.LSAME( DIAG , 'N' ) )THEN
+ INFO = 3
+ ELSE IF( N.LT.0 )THEN
+ INFO = 4
+ ELSE IF( K.LT.0 )THEN
+ INFO = 5
+ ELSE IF( LDA.LT.( K + 1 ) )THEN
+ INFO = 7
+ ELSE IF( INCX.EQ.0 )THEN
+ INFO = 9
+ END IF
+ IF( INFO.NE.0 )THEN
+ CALL XERBLA( 'DTBMV ', INFO )
+ RETURN
+ END IF
+*
+* Quick return if possible.
+*
+ IF( N.EQ.0 )
+ $ RETURN
+*
+ NOUNIT = LSAME( DIAG, 'N' )
+*
+* Set up the start point in X if the increment is not unity. This
+* will be ( N - 1 )*INCX too small for descending loops.
+*
+ IF( INCX.LE.0 )THEN
+ KX = 1 - ( N - 1 )*INCX
+ ELSE IF( INCX.NE.1 )THEN
+ KX = 1
+ END IF
+*
+* Start the operations. In this version the elements of A are
+* accessed sequentially with one pass through A.
+*
+ IF( LSAME( TRANS, 'N' ) )THEN
+*
+* Form x := A*x.
+*
+ IF( LSAME( UPLO, 'U' ) )THEN
+ KPLUS1 = K + 1
+ IF( INCX.EQ.1 )THEN
+ DO 20, J = 1, N
+ IF( X( J ).NE.ZERO )THEN
+ TEMP = X( J )
+ L = KPLUS1 - J
+ DO 10, I = MAX( 1, J - K ), J - 1
+ X( I ) = X( I ) + TEMP*A( L + I, J )
+ 10 CONTINUE
+ IF( NOUNIT )
+ $ X( J ) = X( J )*A( KPLUS1, J )
+ END IF
+ 20 CONTINUE
+ ELSE
+ JX = KX
+ DO 40, J = 1, N
+ IF( X( JX ).NE.ZERO )THEN
+ TEMP = X( JX )
+ IX = KX
+ L = KPLUS1 - J
+ DO 30, I = MAX( 1, J - K ), J - 1
+ X( IX ) = X( IX ) + TEMP*A( L + I, J )
+ IX = IX + INCX
+ 30 CONTINUE
+ IF( NOUNIT )
+ $ X( JX ) = X( JX )*A( KPLUS1, J )
+ END IF
+ JX = JX + INCX
+ IF( J.GT.K )
+ $ KX = KX + INCX
+ 40 CONTINUE
+ END IF
+ ELSE
+ IF( INCX.EQ.1 )THEN
+ DO 60, J = N, 1, -1
+ IF( X( J ).NE.ZERO )THEN
+ TEMP = X( J )
+ L = 1 - J
+ DO 50, I = MIN( N, J + K ), J + 1, -1
+ X( I ) = X( I ) + TEMP*A( L + I, J )
+ 50 CONTINUE
+ IF( NOUNIT )
+ $ X( J ) = X( J )*A( 1, J )
+ END IF
+ 60 CONTINUE
+ ELSE
+ KX = KX + ( N - 1 )*INCX
+ JX = KX
+ DO 80, J = N, 1, -1
+ IF( X( JX ).NE.ZERO )THEN
+ TEMP = X( JX )
+ IX = KX
+ L = 1 - J
+ DO 70, I = MIN( N, J + K ), J + 1, -1
+ X( IX ) = X( IX ) + TEMP*A( L + I, J )
+ IX = IX - INCX
+ 70 CONTINUE
+ IF( NOUNIT )
+ $ X( JX ) = X( JX )*A( 1, J )
+ END IF
+ JX = JX - INCX
+ IF( ( N - J ).GE.K )
+ $ KX = KX - INCX
+ 80 CONTINUE
+ END IF
+ END IF
+ ELSE
+*
+* Form x := A'*x.
+*
+ IF( LSAME( UPLO, 'U' ) )THEN
+ KPLUS1 = K + 1
+ IF( INCX.EQ.1 )THEN
+ DO 100, J = N, 1, -1
+ TEMP = X( J )
+ L = KPLUS1 - J
+ IF( NOUNIT )
+ $ TEMP = TEMP*A( KPLUS1, J )
+ DO 90, I = J - 1, MAX( 1, J - K ), -1
+ TEMP = TEMP + A( L + I, J )*X( I )
+ 90 CONTINUE
+ X( J ) = TEMP
+ 100 CONTINUE
+ ELSE
+ KX = KX + ( N - 1 )*INCX
+ JX = KX
+ DO 120, J = N, 1, -1
+ TEMP = X( JX )
+ KX = KX - INCX
+ IX = KX
+ L = KPLUS1 - J
+ IF( NOUNIT )
+ $ TEMP = TEMP*A( KPLUS1, J )
+ DO 110, I = J - 1, MAX( 1, J - K ), -1
+ TEMP = TEMP + A( L + I, J )*X( IX )
+ IX = IX - INCX
+ 110 CONTINUE
+ X( JX ) = TEMP
+ JX = JX - INCX
+ 120 CONTINUE
+ END IF
+ ELSE
+ IF( INCX.EQ.1 )THEN
+ DO 140, J = 1, N
+ TEMP = X( J )
+ L = 1 - J
+ IF( NOUNIT )
+ $ TEMP = TEMP*A( 1, J )
+ DO 130, I = J + 1, MIN( N, J + K )
+ TEMP = TEMP + A( L + I, J )*X( I )
+ 130 CONTINUE
+ X( J ) = TEMP
+ 140 CONTINUE
+ ELSE
+ JX = KX
+ DO 160, J = 1, N
+ TEMP = X( JX )
+ KX = KX + INCX
+ IX = KX
+ L = 1 - J
+ IF( NOUNIT )
+ $ TEMP = TEMP*A( 1, J )
+ DO 150, I = J + 1, MIN( N, J + K )
+ TEMP = TEMP + A( L + I, J )*X( IX )
+ IX = IX + INCX
+ 150 CONTINUE
+ X( JX ) = TEMP
+ JX = JX + INCX
+ 160 CONTINUE
+ END IF
+ END IF
+ END IF
+*
+ RETURN
+*
+* End of DTBMV .
+*
+ END