LAPACK 3.3.1 Linear Algebra PACKage

# zspr.f

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```00001       SUBROUTINE ZSPR( UPLO, N, ALPHA, X, INCX, AP )
00002 *
00003 *  -- LAPACK auxiliary routine (version 3.2) --
00004 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
00005 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
00006 *     November 2006
00007 *
00008 *     .. Scalar Arguments ..
00009       CHARACTER          UPLO
00010       INTEGER            INCX, N
00011       COMPLEX*16         ALPHA
00012 *     ..
00013 *     .. Array Arguments ..
00014       COMPLEX*16         AP( * ), X( * )
00015 *     ..
00016 *
00017 *  Purpose
00018 *  =======
00019 *
00020 *  ZSPR    performs the symmetric rank 1 operation
00021 *
00022 *     A := alpha*x*x**H + A,
00023 *
00024 *  where alpha is a complex scalar, x is an n element vector and A is an
00025 *  n by n symmetric matrix, supplied in packed form.
00026 *
00027 *  Arguments
00028 *  ==========
00029 *
00030 *  UPLO     (input) CHARACTER*1
00031 *           On entry, UPLO specifies whether the upper or lower
00032 *           triangular part of the matrix A is supplied in the packed
00033 *           array AP as follows:
00034 *
00035 *              UPLO = 'U' or 'u'   The upper triangular part of A is
00036 *                                  supplied in AP.
00037 *
00038 *              UPLO = 'L' or 'l'   The lower triangular part of A is
00039 *                                  supplied in AP.
00040 *
00041 *           Unchanged on exit.
00042 *
00043 *  N        (input) INTEGER
00044 *           On entry, N specifies the order of the matrix A.
00045 *           N must be at least zero.
00046 *           Unchanged on exit.
00047 *
00048 *  ALPHA    (input) COMPLEX*16
00049 *           On entry, ALPHA specifies the scalar alpha.
00050 *           Unchanged on exit.
00051 *
00052 *  X        (input) COMPLEX*16 array, dimension at least
00053 *           ( 1 + ( N - 1 )*abs( INCX ) ).
00054 *           Before entry, the incremented array X must contain the N-
00055 *           element vector x.
00056 *           Unchanged on exit.
00057 *
00058 *  INCX     (input) INTEGER
00059 *           On entry, INCX specifies the increment for the elements of
00060 *           X. INCX must not be zero.
00061 *           Unchanged on exit.
00062 *
00063 *  AP       (input/output) COMPLEX*16 array, dimension at least
00064 *           ( ( N*( N + 1 ) )/2 ).
00065 *           Before entry, with  UPLO = 'U' or 'u', the array AP must
00066 *           contain the upper triangular part of the symmetric matrix
00067 *           packed sequentially, column by column, so that AP( 1 )
00068 *           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
00069 *           and a( 2, 2 ) respectively, and so on. On exit, the array
00070 *           AP is overwritten by the upper triangular part of the
00071 *           updated matrix.
00072 *           Before entry, with UPLO = 'L' or 'l', the array AP must
00073 *           contain the lower triangular part of the symmetric matrix
00074 *           packed sequentially, column by column, so that AP( 1 )
00075 *           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
00076 *           and a( 3, 1 ) respectively, and so on. On exit, the array
00077 *           AP is overwritten by the lower triangular part of the
00078 *           updated matrix.
00079 *           Note that the imaginary parts of the diagonal elements need
00080 *           not be set, they are assumed to be zero, and on exit they
00081 *           are set to zero.
00082 *
00083 * =====================================================================
00084 *
00085 *     .. Parameters ..
00086       COMPLEX*16         ZERO
00087       PARAMETER          ( ZERO = ( 0.0D+0, 0.0D+0 ) )
00088 *     ..
00089 *     .. Local Scalars ..
00090       INTEGER            I, INFO, IX, J, JX, K, KK, KX
00091       COMPLEX*16         TEMP
00092 *     ..
00093 *     .. External Functions ..
00094       LOGICAL            LSAME
00095       EXTERNAL           LSAME
00096 *     ..
00097 *     .. External Subroutines ..
00098       EXTERNAL           XERBLA
00099 *     ..
00100 *     .. Executable Statements ..
00101 *
00102 *     Test the input parameters.
00103 *
00104       INFO = 0
00105       IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
00106          INFO = 1
00107       ELSE IF( N.LT.0 ) THEN
00108          INFO = 2
00109       ELSE IF( INCX.EQ.0 ) THEN
00110          INFO = 5
00111       END IF
00112       IF( INFO.NE.0 ) THEN
00113          CALL XERBLA( 'ZSPR  ', INFO )
00114          RETURN
00115       END IF
00116 *
00117 *     Quick return if possible.
00118 *
00119       IF( ( N.EQ.0 ) .OR. ( ALPHA.EQ.ZERO ) )
00120      \$   RETURN
00121 *
00122 *     Set the start point in X if the increment is not unity.
00123 *
00124       IF( INCX.LE.0 ) THEN
00125          KX = 1 - ( N-1 )*INCX
00126       ELSE IF( INCX.NE.1 ) THEN
00127          KX = 1
00128       END IF
00129 *
00130 *     Start the operations. In this version the elements of the array AP
00131 *     are accessed sequentially with one pass through AP.
00132 *
00133       KK = 1
00134       IF( LSAME( UPLO, 'U' ) ) THEN
00135 *
00136 *        Form  A  when upper triangle is stored in AP.
00137 *
00138          IF( INCX.EQ.1 ) THEN
00139             DO 20 J = 1, N
00140                IF( X( J ).NE.ZERO ) THEN
00141                   TEMP = ALPHA*X( J )
00142                   K = KK
00143                   DO 10 I = 1, J - 1
00144                      AP( K ) = AP( K ) + X( I )*TEMP
00145                      K = K + 1
00146    10             CONTINUE
00147                   AP( KK+J-1 ) = AP( KK+J-1 ) + X( J )*TEMP
00148                ELSE
00149                   AP( KK+J-1 ) = AP( KK+J-1 )
00150                END IF
00151                KK = KK + J
00152    20       CONTINUE
00153          ELSE
00154             JX = KX
00155             DO 40 J = 1, N
00156                IF( X( JX ).NE.ZERO ) THEN
00157                   TEMP = ALPHA*X( JX )
00158                   IX = KX
00159                   DO 30 K = KK, KK + J - 2
00160                      AP( K ) = AP( K ) + X( IX )*TEMP
00161                      IX = IX + INCX
00162    30             CONTINUE
00163                   AP( KK+J-1 ) = AP( KK+J-1 ) + X( JX )*TEMP
00164                ELSE
00165                   AP( KK+J-1 ) = AP( KK+J-1 )
00166                END IF
00167                JX = JX + INCX
00168                KK = KK + J
00169    40       CONTINUE
00170          END IF
00171       ELSE
00172 *
00173 *        Form  A  when lower triangle is stored in AP.
00174 *
00175          IF( INCX.EQ.1 ) THEN
00176             DO 60 J = 1, N
00177                IF( X( J ).NE.ZERO ) THEN
00178                   TEMP = ALPHA*X( J )
00179                   AP( KK ) = AP( KK ) + TEMP*X( J )
00180                   K = KK + 1
00181                   DO 50 I = J + 1, N
00182                      AP( K ) = AP( K ) + X( I )*TEMP
00183                      K = K + 1
00184    50             CONTINUE
00185                ELSE
00186                   AP( KK ) = AP( KK )
00187                END IF
00188                KK = KK + N - J + 1
00189    60       CONTINUE
00190          ELSE
00191             JX = KX
00192             DO 80 J = 1, N
00193                IF( X( JX ).NE.ZERO ) THEN
00194                   TEMP = ALPHA*X( JX )
00195                   AP( KK ) = AP( KK ) + TEMP*X( JX )
00196                   IX = JX
00197                   DO 70 K = KK + 1, KK + N - J
00198                      IX = IX + INCX
00199                      AP( K ) = AP( K ) + X( IX )*TEMP
00200    70             CONTINUE
00201                ELSE
00202                   AP( KK ) = AP( KK )
00203                END IF
00204                JX = JX + INCX
00205                KK = KK + N - J + 1
00206    80       CONTINUE
00207          END IF
00208       END IF
00209 *
00210       RETURN
00211 *
00212 *     End of ZSPR
00213 *
00214       END
```