| SUBROUTINE SSPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY) | |
| * .. Scalar Arguments .. | |
| REAL ALPHA,BETA | |
| INTEGER INCX,INCY,N | |
| CHARACTER UPLO | |
| * .. | |
| * .. Array Arguments .. | |
| REAL AP(*),X(*),Y(*) | |
| * .. | |
| * | |
| * Purpose | |
| * ======= | |
| * | |
| * SSPMV performs the matrix-vector operation | |
| * | |
| * y := alpha*A*x + beta*y, | |
| * | |
| * where alpha and beta are scalars, x and y are n element vectors and | |
| * A is an n by n symmetric matrix, supplied in packed form. | |
| * | |
| * Arguments | |
| * ========== | |
| * | |
| * UPLO - CHARACTER*1. | |
| * On entry, UPLO specifies whether the upper or lower | |
| * triangular part of the matrix A is supplied in the packed | |
| * array AP as follows: | |
| * | |
| * UPLO = 'U' or 'u' The upper triangular part of A is | |
| * supplied in AP. | |
| * | |
| * UPLO = 'L' or 'l' The lower triangular part of A is | |
| * supplied in AP. | |
| * | |
| * Unchanged on exit. | |
| * | |
| * N - INTEGER. | |
| * On entry, N specifies the order of the matrix A. | |
| * N must be at least zero. | |
| * Unchanged on exit. | |
| * | |
| * ALPHA - REAL . | |
| * On entry, ALPHA specifies the scalar alpha. | |
| * Unchanged on exit. | |
| * | |
| * AP - REAL array of DIMENSION at least | |
| * ( ( n*( n + 1 ) )/2 ). | |
| * Before entry with UPLO = 'U' or 'u', the array AP must | |
| * contain the upper triangular part of the symmetric matrix | |
| * packed sequentially, column by column, so that AP( 1 ) | |
| * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 ) | |
| * and a( 2, 2 ) respectively, and so on. | |
| * Before entry with UPLO = 'L' or 'l', the array AP must | |
| * contain the lower triangular part of the symmetric matrix | |
| * packed sequentially, column by column, so that AP( 1 ) | |
| * contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 ) | |
| * and a( 3, 1 ) respectively, and so on. | |
| * 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. | |
| * Unchanged on exit. | |
| * | |
| * INCX - INTEGER. | |
| * On entry, INCX specifies the increment for the elements of | |
| * X. INCX must not be zero. | |
| * Unchanged on exit. | |
| * | |
| * BETA - REAL . | |
| * On entry, BETA specifies the scalar beta. When BETA is | |
| * supplied as zero then Y need not be set on input. | |
| * Unchanged on exit. | |
| * | |
| * Y - REAL array of dimension at least | |
| * ( 1 + ( n - 1 )*abs( INCY ) ). | |
| * Before entry, the incremented array Y must contain the n | |
| * element vector y. On exit, Y is overwritten by the updated | |
| * vector y. | |
| * | |
| * INCY - INTEGER. | |
| * On entry, INCY specifies the increment for the elements of | |
| * Y. INCY 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 ONE,ZERO | |
| PARAMETER (ONE=1.0E+0,ZERO=0.0E+0) | |
| * .. | |
| * .. Local Scalars .. | |
| REAL TEMP1,TEMP2 | |
| INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY | |
| * .. | |
| * .. External Functions .. | |
| LOGICAL LSAME | |
| EXTERNAL LSAME | |
| * .. | |
| * .. External Subroutines .. | |
| EXTERNAL XERBLA | |
| * .. | |
| * | |
| * Test the input parameters. | |
| * | |
| INFO = 0 | |
| IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN | |
| INFO = 1 | |
| ELSE IF (N.LT.0) THEN | |
| INFO = 2 | |
| ELSE IF (INCX.EQ.0) THEN | |
| INFO = 6 | |
| ELSE IF (INCY.EQ.0) THEN | |
| INFO = 9 | |
| END IF | |
| IF (INFO.NE.0) THEN | |
| CALL XERBLA('SSPMV ',INFO) | |
| RETURN | |
| END IF | |
| * | |
| * Quick return if possible. | |
| * | |
| IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN | |
| * | |
| * Set up the start points in X and Y. | |
| * | |
| IF (INCX.GT.0) THEN | |
| KX = 1 | |
| ELSE | |
| KX = 1 - (N-1)*INCX | |
| END IF | |
| IF (INCY.GT.0) THEN | |
| KY = 1 | |
| ELSE | |
| KY = 1 - (N-1)*INCY | |
| END IF | |
| * | |
| * Start the operations. In this version the elements of the array AP | |
| * are accessed sequentially with one pass through AP. | |
| * | |
| * First form y := beta*y. | |
| * | |
| IF (BETA.NE.ONE) THEN | |
| IF (INCY.EQ.1) THEN | |
| IF (BETA.EQ.ZERO) THEN | |
| DO 10 I = 1,N | |
| Y(I) = ZERO | |
| 10 CONTINUE | |
| ELSE | |
| DO 20 I = 1,N | |
| Y(I) = BETA*Y(I) | |
| 20 CONTINUE | |
| END IF | |
| ELSE | |
| IY = KY | |
| IF (BETA.EQ.ZERO) THEN | |
| DO 30 I = 1,N | |
| Y(IY) = ZERO | |
| IY = IY + INCY | |
| 30 CONTINUE | |
| ELSE | |
| DO 40 I = 1,N | |
| Y(IY) = BETA*Y(IY) | |
| IY = IY + INCY | |
| 40 CONTINUE | |
| END IF | |
| END IF | |
| END IF | |
| IF (ALPHA.EQ.ZERO) RETURN | |
| KK = 1 | |
| IF (LSAME(UPLO,'U')) THEN | |
| * | |
| * Form y when AP contains the upper triangle. | |
| * | |
| IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN | |
| DO 60 J = 1,N | |
| TEMP1 = ALPHA*X(J) | |
| TEMP2 = ZERO | |
| K = KK | |
| DO 50 I = 1,J - 1 | |
| Y(I) = Y(I) + TEMP1*AP(K) | |
| TEMP2 = TEMP2 + AP(K)*X(I) | |
| K = K + 1 | |
| 50 CONTINUE | |
| Y(J) = Y(J) + TEMP1*AP(KK+J-1) + ALPHA*TEMP2 | |
| KK = KK + J | |
| 60 CONTINUE | |
| ELSE | |
| JX = KX | |
| JY = KY | |
| DO 80 J = 1,N | |
| TEMP1 = ALPHA*X(JX) | |
| TEMP2 = ZERO | |
| IX = KX | |
| IY = KY | |
| DO 70 K = KK,KK + J - 2 | |
| Y(IY) = Y(IY) + TEMP1*AP(K) | |
| TEMP2 = TEMP2 + AP(K)*X(IX) | |
| IX = IX + INCX | |
| IY = IY + INCY | |
| 70 CONTINUE | |
| Y(JY) = Y(JY) + TEMP1*AP(KK+J-1) + ALPHA*TEMP2 | |
| JX = JX + INCX | |
| JY = JY + INCY | |
| KK = KK + J | |
| 80 CONTINUE | |
| END IF | |
| ELSE | |
| * | |
| * Form y when AP contains the lower triangle. | |
| * | |
| IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN | |
| DO 100 J = 1,N | |
| TEMP1 = ALPHA*X(J) | |
| TEMP2 = ZERO | |
| Y(J) = Y(J) + TEMP1*AP(KK) | |
| K = KK + 1 | |
| DO 90 I = J + 1,N | |
| Y(I) = Y(I) + TEMP1*AP(K) | |
| TEMP2 = TEMP2 + AP(K)*X(I) | |
| K = K + 1 | |
| 90 CONTINUE | |
| Y(J) = Y(J) + ALPHA*TEMP2 | |
| KK = KK + (N-J+1) | |
| 100 CONTINUE | |
| ELSE | |
| JX = KX | |
| JY = KY | |
| DO 120 J = 1,N | |
| TEMP1 = ALPHA*X(JX) | |
| TEMP2 = ZERO | |
| Y(JY) = Y(JY) + TEMP1*AP(KK) | |
| IX = JX | |
| IY = JY | |
| DO 110 K = KK + 1,KK + N - J | |
| IX = IX + INCX | |
| IY = IY + INCY | |
| Y(IY) = Y(IY) + TEMP1*AP(K) | |
| TEMP2 = TEMP2 + AP(K)*X(IX) | |
| 110 CONTINUE | |
| Y(JY) = Y(JY) + ALPHA*TEMP2 | |
| JX = JX + INCX | |
| JY = JY + INCY | |
| KK = KK + (N-J+1) | |
| 120 CONTINUE | |
| END IF | |
| END IF | |
| * | |
| RETURN | |
| * | |
| * End of SSPMV . | |
| * | |
| END |