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authorSandeep Gupta2017-06-18 23:55:40 +0530
committerSandeep Gupta2017-06-18 23:55:40 +0530
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+ SUBROUTINE ZGEMM ( TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB,
+ $ BETA, C, LDC )
+* .. Scalar Arguments ..
+ CHARACTER*1 TRANSA, TRANSB
+ INTEGER M, N, K, LDA, LDB, LDC
+ COMPLEX*16 ALPHA, BETA
+* .. Array Arguments ..
+ COMPLEX*16 A( LDA, * ), B( LDB, * ), C( LDC, * )
+* ..
+*
+* Purpose
+* =======
+*
+* ZGEMM performs one of the matrix-matrix operations
+*
+* C := alpha*op( A )*op( B ) + beta*C,
+*
+* where op( X ) is one of
+*
+* op( X ) = X or op( X ) = X' or op( X ) = conjg( X' ),
+*
+* alpha and beta are scalars, and A, B and C are matrices, with op( A )
+* an m by k matrix, op( B ) a k by n matrix and C an m by n matrix.
+*
+* Parameters
+* ==========
+*
+* TRANSA - CHARACTER*1.
+* On entry, TRANSA specifies the form of op( A ) to be used in
+* the matrix multiplication as follows:
+*
+* TRANSA = 'N' or 'n', op( A ) = A.
+*
+* TRANSA = 'T' or 't', op( A ) = A'.
+*
+* TRANSA = 'C' or 'c', op( A ) = conjg( A' ).
+*
+* Unchanged on exit.
+*
+* TRANSB - CHARACTER*1.
+* On entry, TRANSB specifies the form of op( B ) to be used in
+* the matrix multiplication as follows:
+*
+* TRANSB = 'N' or 'n', op( B ) = B.
+*
+* TRANSB = 'T' or 't', op( B ) = B'.
+*
+* TRANSB = 'C' or 'c', op( B ) = conjg( B' ).
+*
+* Unchanged on exit.
+*
+* M - INTEGER.
+* On entry, M specifies the number of rows of the matrix
+* op( A ) and of the matrix C. M must be at least zero.
+* Unchanged on exit.
+*
+* N - INTEGER.
+* On entry, N specifies the number of columns of the matrix
+* op( B ) and the number of columns of the matrix C. N must be
+* at least zero.
+* Unchanged on exit.
+*
+* K - INTEGER.
+* On entry, K specifies the number of columns of the matrix
+* op( A ) and the number of rows of the matrix op( B ). K must
+* be at least zero.
+* Unchanged on exit.
+*
+* ALPHA - COMPLEX*16 .
+* On entry, ALPHA specifies the scalar alpha.
+* Unchanged on exit.
+*
+* A - COMPLEX*16 array of DIMENSION ( LDA, ka ), where ka is
+* k when TRANSA = 'N' or 'n', and is m otherwise.
+* Before entry with TRANSA = 'N' or 'n', the leading m by k
+* part of the array A must contain the matrix A, otherwise
+* the leading k by m part of the array A must contain the
+* matrix A.
+* Unchanged on exit.
+*
+* LDA - INTEGER.
+* On entry, LDA specifies the first dimension of A as declared
+* in the calling (sub) program. When TRANSA = 'N' or 'n' then
+* LDA must be at least max( 1, m ), otherwise LDA must be at
+* least max( 1, k ).
+* Unchanged on exit.
+*
+* B - COMPLEX*16 array of DIMENSION ( LDB, kb ), where kb is
+* n when TRANSB = 'N' or 'n', and is k otherwise.
+* Before entry with TRANSB = 'N' or 'n', the leading k by n
+* part of the array B must contain the matrix B, otherwise
+* the leading n by k part of the array B must contain the
+* matrix B.
+* Unchanged on exit.
+*
+* LDB - INTEGER.
+* On entry, LDB specifies the first dimension of B as declared
+* in the calling (sub) program. When TRANSB = 'N' or 'n' then
+* LDB must be at least max( 1, k ), otherwise LDB must be at
+* least max( 1, n ).
+* Unchanged on exit.
+*
+* BETA - COMPLEX*16 .
+* On entry, BETA specifies the scalar beta. When BETA is
+* supplied as zero then C need not be set on input.
+* Unchanged on exit.
+*
+* C - COMPLEX*16 array of DIMENSION ( LDC, n ).
+* Before entry, the leading m by n part of the array C must
+* contain the matrix C, except when beta is zero, in which
+* case C need not be set on entry.
+* On exit, the array C is overwritten by the m by n matrix
+* ( alpha*op( A )*op( B ) + beta*C ).
+*
+* LDC - INTEGER.
+* On entry, LDC specifies the first dimension of C as declared
+* in the calling (sub) program. LDC must be at least
+* max( 1, m ).
+* Unchanged on exit.
+*
+*
+* Level 3 Blas routine.
+*
+* -- Written on 8-February-1989.
+* Jack Dongarra, Argonne National Laboratory.
+* Iain Duff, AERE Harwell.
+* Jeremy Du Croz, Numerical Algorithms Group Ltd.
+* Sven Hammarling, Numerical Algorithms Group Ltd.
+*
+*
+* .. External Functions ..
+ LOGICAL LSAME
+ EXTERNAL LSAME
+* .. External Subroutines ..
+ EXTERNAL XERBLA
+* .. Intrinsic Functions ..
+ INTRINSIC DCONJG, MAX
+* .. Local Scalars ..
+ LOGICAL CONJA, CONJB, NOTA, NOTB
+ INTEGER I, INFO, J, L, NCOLA, NROWA, NROWB
+ COMPLEX*16 TEMP
+* .. Parameters ..
+ COMPLEX*16 ONE
+ PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
+ COMPLEX*16 ZERO
+ PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) )
+* ..
+* .. Executable Statements ..
+*
+* Set NOTA and NOTB as true if A and B respectively are not
+* conjugated or transposed, set CONJA and CONJB as true if A and
+* B respectively are to be transposed but not conjugated and set
+* NROWA, NCOLA and NROWB as the number of rows and columns of A
+* and the number of rows of B respectively.
+*
+ NOTA = LSAME( TRANSA, 'N' )
+ NOTB = LSAME( TRANSB, 'N' )
+ CONJA = LSAME( TRANSA, 'C' )
+ CONJB = LSAME( TRANSB, 'C' )
+ IF( NOTA )THEN
+ NROWA = M
+ NCOLA = K
+ ELSE
+ NROWA = K
+ NCOLA = M
+ END IF
+ IF( NOTB )THEN
+ NROWB = K
+ ELSE
+ NROWB = N
+ END IF
+*
+* Test the input parameters.
+*
+ INFO = 0
+ IF( ( .NOT.NOTA ).AND.
+ $ ( .NOT.CONJA ).AND.
+ $ ( .NOT.LSAME( TRANSA, 'T' ) ) )THEN
+ INFO = 1
+ ELSE IF( ( .NOT.NOTB ).AND.
+ $ ( .NOT.CONJB ).AND.
+ $ ( .NOT.LSAME( TRANSB, 'T' ) ) )THEN
+ INFO = 2
+ ELSE IF( M .LT.0 )THEN
+ INFO = 3
+ ELSE IF( N .LT.0 )THEN
+ INFO = 4
+ ELSE IF( K .LT.0 )THEN
+ INFO = 5
+ ELSE IF( LDA.LT.MAX( 1, NROWA ) )THEN
+ INFO = 8
+ ELSE IF( LDB.LT.MAX( 1, NROWB ) )THEN
+ INFO = 10
+ ELSE IF( LDC.LT.MAX( 1, M ) )THEN
+ INFO = 13
+ END IF
+ IF( INFO.NE.0 )THEN
+ CALL XERBLA( 'ZGEMM ', INFO )
+ RETURN
+ END IF
+*
+* Quick return if possible.
+*
+ IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR.
+ $ ( ( ( ALPHA.EQ.ZERO ).OR.( K.EQ.0 ) ).AND.( BETA.EQ.ONE ) ) )
+ $ RETURN
+*
+* And when alpha.eq.zero.
+*
+ IF( ALPHA.EQ.ZERO )THEN
+ IF( BETA.EQ.ZERO )THEN
+ DO 20, J = 1, N
+ DO 10, I = 1, M
+ C( I, J ) = ZERO
+ 10 CONTINUE
+ 20 CONTINUE
+ ELSE
+ DO 40, J = 1, N
+ DO 30, I = 1, M
+ C( I, J ) = BETA*C( I, J )
+ 30 CONTINUE
+ 40 CONTINUE
+ END IF
+ RETURN
+ END IF
+*
+* Start the operations.
+*
+ IF( NOTB )THEN
+ IF( NOTA )THEN
+*
+* Form C := alpha*A*B + beta*C.
+*
+ DO 90, J = 1, N
+ IF( BETA.EQ.ZERO )THEN
+ DO 50, I = 1, M
+ C( I, J ) = ZERO
+ 50 CONTINUE
+ ELSE IF( BETA.NE.ONE )THEN
+ DO 60, I = 1, M
+ C( I, J ) = BETA*C( I, J )
+ 60 CONTINUE
+ END IF
+ DO 80, L = 1, K
+ IF( B( L, J ).NE.ZERO )THEN
+ TEMP = ALPHA*B( L, J )
+ DO 70, I = 1, M
+ C( I, J ) = C( I, J ) + TEMP*A( I, L )
+ 70 CONTINUE
+ END IF
+ 80 CONTINUE
+ 90 CONTINUE
+ ELSE IF( CONJA )THEN
+*
+* Form C := alpha*conjg( A' )*B + beta*C.
+*
+ DO 120, J = 1, N
+ DO 110, I = 1, M
+ TEMP = ZERO
+ DO 100, L = 1, K
+ TEMP = TEMP + DCONJG( A( L, I ) )*B( L, J )
+ 100 CONTINUE
+ IF( BETA.EQ.ZERO )THEN
+ C( I, J ) = ALPHA*TEMP
+ ELSE
+ C( I, J ) = ALPHA*TEMP + BETA*C( I, J )
+ END IF
+ 110 CONTINUE
+ 120 CONTINUE
+ ELSE
+*
+* Form C := alpha*A'*B + beta*C
+*
+ DO 150, J = 1, N
+ DO 140, I = 1, M
+ TEMP = ZERO
+ DO 130, L = 1, K
+ TEMP = TEMP + A( L, I )*B( L, J )
+ 130 CONTINUE
+ IF( BETA.EQ.ZERO )THEN
+ C( I, J ) = ALPHA*TEMP
+ ELSE
+ C( I, J ) = ALPHA*TEMP + BETA*C( I, J )
+ END IF
+ 140 CONTINUE
+ 150 CONTINUE
+ END IF
+ ELSE IF( NOTA )THEN
+ IF( CONJB )THEN
+*
+* Form C := alpha*A*conjg( B' ) + beta*C.
+*
+ DO 200, J = 1, N
+ IF( BETA.EQ.ZERO )THEN
+ DO 160, I = 1, M
+ C( I, J ) = ZERO
+ 160 CONTINUE
+ ELSE IF( BETA.NE.ONE )THEN
+ DO 170, I = 1, M
+ C( I, J ) = BETA*C( I, J )
+ 170 CONTINUE
+ END IF
+ DO 190, L = 1, K
+ IF( B( J, L ).NE.ZERO )THEN
+ TEMP = ALPHA*DCONJG( B( J, L ) )
+ DO 180, I = 1, M
+ C( I, J ) = C( I, J ) + TEMP*A( I, L )
+ 180 CONTINUE
+ END IF
+ 190 CONTINUE
+ 200 CONTINUE
+ ELSE
+*
+* Form C := alpha*A*B' + beta*C
+*
+ DO 250, J = 1, N
+ IF( BETA.EQ.ZERO )THEN
+ DO 210, I = 1, M
+ C( I, J ) = ZERO
+ 210 CONTINUE
+ ELSE IF( BETA.NE.ONE )THEN
+ DO 220, I = 1, M
+ C( I, J ) = BETA*C( I, J )
+ 220 CONTINUE
+ END IF
+ DO 240, L = 1, K
+ IF( B( J, L ).NE.ZERO )THEN
+ TEMP = ALPHA*B( J, L )
+ DO 230, I = 1, M
+ C( I, J ) = C( I, J ) + TEMP*A( I, L )
+ 230 CONTINUE
+ END IF
+ 240 CONTINUE
+ 250 CONTINUE
+ END IF
+ ELSE IF( CONJA )THEN
+ IF( CONJB )THEN
+*
+* Form C := alpha*conjg( A' )*conjg( B' ) + beta*C.
+*
+ DO 280, J = 1, N
+ DO 270, I = 1, M
+ TEMP = ZERO
+ DO 260, L = 1, K
+ TEMP = TEMP +
+ $ DCONJG( A( L, I ) )*DCONJG( B( J, L ) )
+ 260 CONTINUE
+ IF( BETA.EQ.ZERO )THEN
+ C( I, J ) = ALPHA*TEMP
+ ELSE
+ C( I, J ) = ALPHA*TEMP + BETA*C( I, J )
+ END IF
+ 270 CONTINUE
+ 280 CONTINUE
+ ELSE
+*
+* Form C := alpha*conjg( A' )*B' + beta*C
+*
+ DO 310, J = 1, N
+ DO 300, I = 1, M
+ TEMP = ZERO
+ DO 290, L = 1, K
+ TEMP = TEMP + DCONJG( A( L, I ) )*B( J, L )
+ 290 CONTINUE
+ IF( BETA.EQ.ZERO )THEN
+ C( I, J ) = ALPHA*TEMP
+ ELSE
+ C( I, J ) = ALPHA*TEMP + BETA*C( I, J )
+ END IF
+ 300 CONTINUE
+ 310 CONTINUE
+ END IF
+ ELSE
+ IF( CONJB )THEN
+*
+* Form C := alpha*A'*conjg( B' ) + beta*C
+*
+ DO 340, J = 1, N
+ DO 330, I = 1, M
+ TEMP = ZERO
+ DO 320, L = 1, K
+ TEMP = TEMP + A( L, I )*DCONJG( B( J, L ) )
+ 320 CONTINUE
+ IF( BETA.EQ.ZERO )THEN
+ C( I, J ) = ALPHA*TEMP
+ ELSE
+ C( I, J ) = ALPHA*TEMP + BETA*C( I, J )
+ END IF
+ 330 CONTINUE
+ 340 CONTINUE
+ ELSE
+*
+* Form C := alpha*A'*B' + beta*C
+*
+ DO 370, J = 1, N
+ DO 360, I = 1, M
+ TEMP = ZERO
+ DO 350, L = 1, K
+ TEMP = TEMP + A( L, I )*B( J, L )
+ 350 CONTINUE
+ IF( BETA.EQ.ZERO )THEN
+ C( I, J ) = ALPHA*TEMP
+ ELSE
+ C( I, J ) = ALPHA*TEMP + BETA*C( I, J )
+ END IF
+ 360 CONTINUE
+ 370 CONTINUE
+ END IF
+ END IF
+*
+ RETURN
+*
+* End of ZGEMM .
+*
+ END