| SUBROUTINE STBMV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX) | |
| * .. Scalar Arguments .. | |
| INTEGER INCX,K,LDA,N | |
| CHARACTER DIAG,TRANS,UPLO | |
| * .. | |
| * .. Array Arguments .. | |
| REAL A(LDA,*),X(*) | |
| * .. | |
| * | |
| * Purpose | |
| * ======= | |
| * | |
| * STBMV 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. | |
| * | |
| * Arguments | |
| * ========== | |
| * | |
| * 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 - REAL 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 - REAL 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. | |
| * | |
| * 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. | |
| * | |
| * ===================================================================== | |
| * | |
| * .. Parameters .. | |
| REAL ZERO | |
| PARAMETER (ZERO=0.0E+0) | |
| * .. | |
| * .. Local Scalars .. | |
| REAL 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 | |
| * .. | |
| * | |
| * 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('STBMV ',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 STBMV . | |
| * | |
| END |