| SUBROUTINE CSPRF( UPLO, N, ALPHA, X, INCX, AP ) |
| * |
| * -- LAPACK auxiliary routine (version 3.1) -- |
| * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. |
| * November 2006 |
| * |
| * .. Scalar Arguments .. |
| CHARACTER UPLO |
| INTEGER INCX, N |
| COMPLEX ALPHA |
| * .. |
| * .. Array Arguments .. |
| COMPLEX AP( * ), X( * ) |
| * .. |
| * |
| * Purpose |
| * ======= |
| * |
| * CSPR performs the symmetric rank 1 operation |
| * |
| * A := alpha*x*conjg( x' ) + A, |
| * |
| * where alpha is a complex scalar, x is an n element vector and A is an |
| * n by n symmetric matrix, supplied in packed form. |
| * |
| * Arguments |
| * ========== |
| * |
| * UPLO (input) 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 (input) INTEGER |
| * On entry, N specifies the order of the matrix A. |
| * N must be at least zero. |
| * Unchanged on exit. |
| * |
| * ALPHA (input) COMPLEX |
| * On entry, ALPHA specifies the scalar alpha. |
| * Unchanged on exit. |
| * |
| * X (input) COMPLEX array, 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 (input) INTEGER |
| * On entry, INCX specifies the increment for the elements of |
| * X. INCX must not be zero. |
| * Unchanged on exit. |
| * |
| * AP (input/output) COMPLEX array, 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. On exit, the array |
| * AP is overwritten by the upper triangular part of the |
| * updated matrix. |
| * 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. On exit, the array |
| * AP is overwritten by the lower triangular part of the |
| * updated matrix. |
| * Note that the imaginary parts of the diagonal elements need |
| * not be set, they are assumed to be zero, and on exit they |
| * are set to zero. |
| * |
| * ===================================================================== |
| * |
| * .. Parameters .. |
| COMPLEX ZERO |
| PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) ) |
| * .. |
| * .. Local Scalars .. |
| INTEGER I, INFO, IX, J, JX, K, KK, KX |
| COMPLEX TEMP |
| * .. |
| * .. External Functions .. |
| LOGICAL LSAME |
| EXTERNAL LSAME |
| * .. |
| * .. External Subroutines .. |
| EXTERNAL XERBLA |
| * .. |
| * .. Executable Statements .. |
| * |
| * 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 = 5 |
| END IF |
| IF( INFO.NE.0 ) THEN |
| CALL XERBLA( 'CSPR ', INFO ) |
| RETURN |
| END IF |
| * |
| * Quick return if possible. |
| * |
| IF( ( N.EQ.0 ) .OR. ( ALPHA.EQ.ZERO ) ) |
| $ RETURN |
| * |
| * Set the start point in X if the increment is not unity. |
| * |
| 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 the array AP |
| * are accessed sequentially with one pass through AP. |
| * |
| KK = 1 |
| IF( LSAME( UPLO, 'U' ) ) THEN |
| * |
| * Form A when upper triangle is stored in AP. |
| * |
| IF( INCX.EQ.1 ) THEN |
| DO 20 J = 1, N |
| IF( X( J ).NE.ZERO ) THEN |
| TEMP = ALPHA*X( J ) |
| K = KK |
| DO 10 I = 1, J - 1 |
| AP( K ) = AP( K ) + X( I )*TEMP |
| K = K + 1 |
| 10 CONTINUE |
| AP( KK+J-1 ) = AP( KK+J-1 ) + X( J )*TEMP |
| ELSE |
| AP( KK+J-1 ) = AP( KK+J-1 ) |
| END IF |
| KK = KK + J |
| 20 CONTINUE |
| ELSE |
| JX = KX |
| DO 40 J = 1, N |
| IF( X( JX ).NE.ZERO ) THEN |
| TEMP = ALPHA*X( JX ) |
| IX = KX |
| DO 30 K = KK, KK + J - 2 |
| AP( K ) = AP( K ) + X( IX )*TEMP |
| IX = IX + INCX |
| 30 CONTINUE |
| AP( KK+J-1 ) = AP( KK+J-1 ) + X( JX )*TEMP |
| ELSE |
| AP( KK+J-1 ) = AP( KK+J-1 ) |
| END IF |
| JX = JX + INCX |
| KK = KK + J |
| 40 CONTINUE |
| END IF |
| ELSE |
| * |
| * Form A when lower triangle is stored in AP. |
| * |
| IF( INCX.EQ.1 ) THEN |
| DO 60 J = 1, N |
| IF( X( J ).NE.ZERO ) THEN |
| TEMP = ALPHA*X( J ) |
| AP( KK ) = AP( KK ) + TEMP*X( J ) |
| K = KK + 1 |
| DO 50 I = J + 1, N |
| AP( K ) = AP( K ) + X( I )*TEMP |
| K = K + 1 |
| 50 CONTINUE |
| ELSE |
| AP( KK ) = AP( KK ) |
| END IF |
| KK = KK + N - J + 1 |
| 60 CONTINUE |
| ELSE |
| JX = KX |
| DO 80 J = 1, N |
| IF( X( JX ).NE.ZERO ) THEN |
| TEMP = ALPHA*X( JX ) |
| AP( KK ) = AP( KK ) + TEMP*X( JX ) |
| IX = JX |
| DO 70 K = KK + 1, KK + N - J |
| IX = IX + INCX |
| AP( K ) = AP( K ) + X( IX )*TEMP |
| 70 CONTINUE |
| ELSE |
| AP( KK ) = AP( KK ) |
| END IF |
| JX = JX + INCX |
| KK = KK + N - J + 1 |
| 80 CONTINUE |
| END IF |
| END IF |
| * |
| RETURN |
| * |
| * End of CSPR |
| * |
| END |
