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SUBROUTINE ZHER2K(UPLO,TRANS,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) |
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* .. Scalar Arguments .. |
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DOUBLE COMPLEX ALPHA |
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DOUBLE PRECISION BETA |
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INTEGER K,LDA,LDB,LDC,N |
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CHARACTER TRANS,UPLO |
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* .. |
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* .. Array Arguments .. |
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DOUBLE COMPLEX A(LDA,*),B(LDB,*),C(LDC,*) |
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* .. |
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* |
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* Purpose |
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* ======= |
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* |
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* ZHER2K performs one of the hermitian rank 2k operations |
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* |
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* C := alpha*A*conjg( B' ) + conjg( alpha )*B*conjg( A' ) + beta*C, |
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* |
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* or |
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* |
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* C := alpha*conjg( A' )*B + conjg( alpha )*conjg( B' )*A + beta*C, |
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* |
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* where alpha and beta are scalars with beta real, C is an n by n |
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* hermitian matrix and A and B are n by k matrices in the first case |
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* and k by n matrices in the second case. |
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* |
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* Arguments |
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* ========== |
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* |
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* UPLO - CHARACTER*1. |
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* On entry, UPLO specifies whether the upper or lower |
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* triangular part of the array C is to be referenced as |
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* follows: |
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* |
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* UPLO = 'U' or 'u' Only the upper triangular part of C |
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* is to be referenced. |
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* |
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* UPLO = 'L' or 'l' Only the lower triangular part of C |
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* is to be referenced. |
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* |
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* Unchanged on exit. |
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* |
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* TRANS - CHARACTER*1. |
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* On entry, TRANS specifies the operation to be performed as |
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* follows: |
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* |
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* TRANS = 'N' or 'n' C := alpha*A*conjg( B' ) + |
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* conjg( alpha )*B*conjg( A' ) + |
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* beta*C. |
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* |
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* TRANS = 'C' or 'c' C := alpha*conjg( A' )*B + |
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* conjg( alpha )*conjg( B' )*A + |
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* beta*C. |
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* |
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* Unchanged on exit. |
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* |
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* N - INTEGER. |
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* On entry, N specifies the order of the matrix C. N must be |
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* at least zero. |
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* Unchanged on exit. |
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* |
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* K - INTEGER. |
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* On entry with TRANS = 'N' or 'n', K specifies the number |
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* of columns of the matrices A and B, and on entry with |
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* TRANS = 'C' or 'c', K specifies the number of rows of the |
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* matrices A and B. K must be at least zero. |
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* Unchanged on exit. |
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* |
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* ALPHA - COMPLEX*16 . |
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* On entry, ALPHA specifies the scalar alpha. |
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* Unchanged on exit. |
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* |
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* A - COMPLEX*16 array of DIMENSION ( LDA, ka ), where ka is |
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* k when TRANS = 'N' or 'n', and is n otherwise. |
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* Before entry with TRANS = 'N' or 'n', the leading n by k |
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* part of the array A must contain the matrix A, otherwise |
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* the leading k by n part of the array A must contain the |
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* matrix A. |
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* Unchanged on exit. |
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* |
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* LDA - INTEGER. |
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* On entry, LDA specifies the first dimension of A as declared |
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* in the calling (sub) program. When TRANS = 'N' or 'n' |
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* then LDA must be at least max( 1, n ), otherwise LDA must |
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* be at least max( 1, k ). |
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* Unchanged on exit. |
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* |
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* B - COMPLEX*16 array of DIMENSION ( LDB, kb ), where kb is |
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* k when TRANS = 'N' or 'n', and is n otherwise. |
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* Before entry with TRANS = 'N' or 'n', the leading n by k |
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* part of the array B must contain the matrix B, otherwise |
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* the leading k by n part of the array B must contain the |
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* matrix B. |
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* Unchanged on exit. |
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* |
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* LDB - INTEGER. |
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* On entry, LDB specifies the first dimension of B as declared |
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* in the calling (sub) program. When TRANS = 'N' or 'n' |
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* then LDB must be at least max( 1, n ), otherwise LDB must |
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* be at least max( 1, k ). |
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* Unchanged on exit. |
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* |
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* BETA - DOUBLE PRECISION . |
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* On entry, BETA specifies the scalar beta. |
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* Unchanged on exit. |
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* |
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* C - COMPLEX*16 array of DIMENSION ( LDC, n ). |
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* Before entry with UPLO = 'U' or 'u', the leading n by n |
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* upper triangular part of the array C must contain the upper |
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* triangular part of the hermitian matrix and the strictly |
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* lower triangular part of C is not referenced. On exit, the |
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* upper triangular part of the array C is overwritten by the |
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* upper triangular part of the updated matrix. |
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* Before entry with UPLO = 'L' or 'l', the leading n by n |
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* lower triangular part of the array C must contain the lower |
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* triangular part of the hermitian matrix and the strictly |
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* upper triangular part of C is not referenced. On exit, the |
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* lower triangular part of the array C is overwritten by the |
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* lower triangular part of the updated matrix. |
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* Note that the imaginary parts of the diagonal elements need |
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* not be set, they are assumed to be zero, and on exit they |
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* are set to zero. |
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* |
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* LDC - INTEGER. |
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* On entry, LDC specifies the first dimension of C as declared |
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* in the calling (sub) program. LDC must be at least |
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* max( 1, n ). |
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* Unchanged on exit. |
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* |
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* |
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* Level 3 Blas routine. |
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* |
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* -- Written on 8-February-1989. |
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* Jack Dongarra, Argonne National Laboratory. |
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* Iain Duff, AERE Harwell. |
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* Jeremy Du Croz, Numerical Algorithms Group Ltd. |
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* Sven Hammarling, Numerical Algorithms Group Ltd. |
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* |
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* -- Modified 8-Nov-93 to set C(J,J) to DBLE( C(J,J) ) when BETA = 1. |
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* Ed Anderson, Cray Research Inc. |
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* |
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* |
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* .. External Functions .. |
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LOGICAL LSAME |
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EXTERNAL LSAME |
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* .. |
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* .. External Subroutines .. |
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EXTERNAL XERBLA |
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* .. |
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* .. Intrinsic Functions .. |
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INTRINSIC DBLE,DCONJG,MAX |
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* .. |
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* .. Local Scalars .. |
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DOUBLE COMPLEX TEMP1,TEMP2 |
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INTEGER I,INFO,J,L,NROWA |
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LOGICAL UPPER |
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* .. |
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* .. Parameters .. |
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DOUBLE PRECISION ONE |
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PARAMETER (ONE=1.0D+0) |
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DOUBLE COMPLEX ZERO |
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PARAMETER (ZERO= (0.0D+0,0.0D+0)) |
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* .. |
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* |
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* Test the input parameters. |
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* |
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IF (LSAME(TRANS,'N')) THEN |
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NROWA = N |
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ELSE |
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NROWA = K |
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END IF |
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UPPER = LSAME(UPLO,'U') |
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* |
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INFO = 0 |
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IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN |
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INFO = 1 |
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ELSE IF ((.NOT.LSAME(TRANS,'N')) .AND. |
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+ (.NOT.LSAME(TRANS,'C'))) THEN |
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INFO = 2 |
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ELSE IF (N.LT.0) THEN |
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INFO = 3 |
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ELSE IF (K.LT.0) THEN |
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INFO = 4 |
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ELSE IF (LDA.LT.MAX(1,NROWA)) THEN |
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INFO = 7 |
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ELSE IF (LDB.LT.MAX(1,NROWA)) THEN |
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INFO = 9 |
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ELSE IF (LDC.LT.MAX(1,N)) THEN |
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INFO = 12 |
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END IF |
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IF (INFO.NE.0) THEN |
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CALL XERBLA('ZHER2K',INFO)
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RETURN |
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END IF |
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* |
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* Quick return if possible. |
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* |
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IF ((N.EQ.0) .OR. (((ALPHA.EQ.ZERO).OR. |
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+ (K.EQ.0)).AND. (BETA.EQ.ONE))) RETURN |
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* |
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* And when alpha.eq.zero. |
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* |
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IF (ALPHA.EQ.ZERO) THEN |
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IF (UPPER) THEN |
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IF (BETA.EQ.DBLE(ZERO)) THEN |
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DO 20 J = 1,N |
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DO 10 I = 1,J |
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C(I,J) = ZERO |
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10 CONTINUE |
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20 CONTINUE |
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ELSE |
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DO 40 J = 1,N |
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DO 30 I = 1,J - 1 |
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C(I,J) = BETA*C(I,J) |
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30 CONTINUE |
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C(J,J) = BETA*DBLE(C(J,J)) |
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40 CONTINUE |
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END IF |
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ELSE |
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IF (BETA.EQ.DBLE(ZERO)) THEN |
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DO 60 J = 1,N |
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DO 50 I = J,N |
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C(I,J) = ZERO |
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50 CONTINUE |
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60 CONTINUE |
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ELSE |
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DO 80 J = 1,N |
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C(J,J) = BETA*DBLE(C(J,J)) |
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DO 70 I = J + 1,N |
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C(I,J) = BETA*C(I,J) |
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70 CONTINUE |
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80 CONTINUE |
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END IF |
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END IF |
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RETURN |
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END IF |
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* |
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* Start the operations. |
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* |
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IF (LSAME(TRANS,'N')) THEN |
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* |
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* Form C := alpha*A*conjg( B' ) + conjg( alpha )*B*conjg( A' ) + |
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* C. |
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* |
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IF (UPPER) THEN |
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DO 130 J = 1,N |
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IF (BETA.EQ.DBLE(ZERO)) THEN |
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DO 90 I = 1,J |
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C(I,J) = ZERO |
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90 CONTINUE |
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ELSE IF (BETA.NE.ONE) THEN |
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DO 100 I = 1,J - 1 |
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C(I,J) = BETA*C(I,J) |
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100 CONTINUE |
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C(J,J) = BETA*DBLE(C(J,J)) |
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ELSE |
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C(J,J) = DBLE(C(J,J)) |
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END IF |
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DO 120 L = 1,K |
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IF ((A(J,L).NE.ZERO) .OR. (B(J,L).NE.ZERO)) THEN |
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TEMP1 = ALPHA*DCONJG(B(J,L)) |
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TEMP2 = DCONJG(ALPHA*A(J,L)) |
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DO 110 I = 1,J - 1 |
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C(I,J) = C(I,J) + A(I,L)*TEMP1 + |
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+ B(I,L)*TEMP2 |
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110 CONTINUE |
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C(J,J) = DBLE(C(J,J)) + |
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+ DBLE(A(J,L)*TEMP1+B(J,L)*TEMP2) |
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END IF |
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120 CONTINUE |
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130 CONTINUE |
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ELSE |
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DO 180 J = 1,N |
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IF (BETA.EQ.DBLE(ZERO)) THEN |
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DO 140 I = J,N |
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C(I,J) = ZERO |
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140 CONTINUE |
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ELSE IF (BETA.NE.ONE) THEN |
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DO 150 I = J + 1,N |
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C(I,J) = BETA*C(I,J) |
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150 CONTINUE |
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C(J,J) = BETA*DBLE(C(J,J)) |
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ELSE |
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C(J,J) = DBLE(C(J,J)) |
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END IF |
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DO 170 L = 1,K |
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IF ((A(J,L).NE.ZERO) .OR. (B(J,L).NE.ZERO)) THEN |
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TEMP1 = ALPHA*DCONJG(B(J,L)) |
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TEMP2 = DCONJG(ALPHA*A(J,L)) |
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DO 160 I = J + 1,N |
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C(I,J) = C(I,J) + A(I,L)*TEMP1 + |
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+ B(I,L)*TEMP2 |
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160 CONTINUE |
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C(J,J) = DBLE(C(J,J)) + |
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+ DBLE(A(J,L)*TEMP1+B(J,L)*TEMP2) |
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END IF |
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170 CONTINUE |
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180 CONTINUE |
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END IF |
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ELSE |
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* |
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* Form C := alpha*conjg( A' )*B + conjg( alpha )*conjg( B' )*A + |
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* C. |
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* |
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IF (UPPER) THEN |
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DO 210 J = 1,N |
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DO 200 I = 1,J |
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TEMP1 = ZERO |
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TEMP2 = ZERO |
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DO 190 L = 1,K |
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TEMP1 = TEMP1 + DCONJG(A(L,I))*B(L,J) |
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TEMP2 = TEMP2 + DCONJG(B(L,I))*A(L,J) |
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190 CONTINUE |
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IF (I.EQ.J) THEN |
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IF (BETA.EQ.DBLE(ZERO)) THEN |
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C(J,J) = DBLE(ALPHA*TEMP1+ |
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+ DCONJG(ALPHA)*TEMP2) |
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ELSE |
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C(J,J) = BETA*DBLE(C(J,J)) + |
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+ DBLE(ALPHA*TEMP1+ |
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+ DCONJG(ALPHA)*TEMP2) |
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END IF |
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ELSE |
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IF (BETA.EQ.DBLE(ZERO)) THEN |
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C(I,J) = ALPHA*TEMP1 + DCONJG(ALPHA)*TEMP2 |
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ELSE |
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C(I,J) = BETA*C(I,J) + ALPHA*TEMP1 + |
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+ DCONJG(ALPHA)*TEMP2 |
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END IF |
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END IF |
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200 CONTINUE |
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210 CONTINUE |
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ELSE |
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DO 240 J = 1,N |
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DO 230 I = J,N |
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TEMP1 = ZERO |
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TEMP2 = ZERO |
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DO 220 L = 1,K |
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TEMP1 = TEMP1 + DCONJG(A(L,I))*B(L,J) |
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TEMP2 = TEMP2 + DCONJG(B(L,I))*A(L,J) |
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220 CONTINUE |
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IF (I.EQ.J) THEN |
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IF (BETA.EQ.DBLE(ZERO)) THEN |
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C(J,J) = DBLE(ALPHA*TEMP1+ |
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+ DCONJG(ALPHA)*TEMP2) |
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ELSE |
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C(J,J) = BETA*DBLE(C(J,J)) + |
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+ DBLE(ALPHA*TEMP1+ |
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+ DCONJG(ALPHA)*TEMP2) |
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END IF |
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ELSE |
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IF (BETA.EQ.DBLE(ZERO)) THEN |
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C(I,J) = ALPHA*TEMP1 + DCONJG(ALPHA)*TEMP2 |
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ELSE |
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C(I,J) = BETA*C(I,J) + ALPHA*TEMP1 + |
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+ DCONJG(ALPHA)*TEMP2 |
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END IF |
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END IF |
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230 CONTINUE |
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240 CONTINUE |
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END IF |
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END IF |
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* |
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RETURN |
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* |
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* End of ZHER2K. |
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* |
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END |