SUBROUTINE DAXPY(N,DA,DX,INCX,DY,INCY) C C CONSTANT TIMES A VECTOR PLUS A VECTOR. C USES UNROLLED LOOPS FOR INCREMENTS EQUAL TO ONE. C JACK DONGARRA, LINPACK, 3/11/78. C DOUBLE PRECISION DX(1),DY(1),DA INTEGER I,INCX,INCY,IX,IY,M,MP1,N C IF(N.LE.0)RETURN IF (DA .EQ. 0.0D0) RETURN IF(INCX.EQ.1.AND.INCY.EQ.1)GO TO 20 C C CODE FOR UNEQUAL INCREMENTS OR EQUAL INCREMENTS C NOT EQUAL TO 1 C IX = 1 IY = 1 IF(INCX.LT.0)IX = (-N+1)*INCX + 1 IF(INCY.LT.0)IY = (-N+1)*INCY + 1 DO 10 I = 1,N DY(IY) = DY(IY) + DA*DX(IX) IX = IX + INCX IY = IY + INCY 10 CONTINUE RETURN C C CODE FOR BOTH INCREMENTS EQUAL TO 1 C C C CLEAN-UP LOOP C 20 M = MOD(N,4) IF( M .EQ. 0 ) GO TO 40 DO 30 I = 1,M DY(I) = DY(I) + DA*DX(I) 30 CONTINUE IF( N .LT. 4 ) RETURN 40 MP1 = M + 1 DO 50 I = MP1,N,4 DY(I) = DY(I) + DA*DX(I) DY(I + 1) = DY(I + 1) + DA*DX(I + 1) DY(I + 2) = DY(I + 2) + DA*DX(I + 2) DY(I + 3) = DY(I + 3) + DA*DX(I + 3) 50 CONTINUE RETURN END DOUBLE PRECISION FUNCTION DDOT(N,DX,INCX,DY,INCY) C C FORMS THE DOT PRODUCT OF TWO VECTORS. C USES UNROLLED LOOPS FOR INCREMENTS EQUAL TO ONE. C JACK DONGARRA, LINPACK, 3/11/78. C DOUBLE PRECISION DX(1),DY(1),DTEMP INTEGER I,INCX,INCY,IX,IY,M,MP1,N C DDOT = 0.0D0 DTEMP = 0.0D0 IF(N.LE.0)RETURN IF(INCX.EQ.1.AND.INCY.EQ.1)GO TO 20 C C CODE FOR UNEQUAL INCREMENTS OR EQUAL INCREMENTS C NOT EQUAL TO 1 C IX = 1 IY = 1 IF(INCX.LT.0)IX = (-N+1)*INCX + 1 IF(INCY.LT.0)IY = (-N+1)*INCY + 1 DO 10 I = 1,N DTEMP = DTEMP + DX(IX)*DY(IY) IX = IX + INCX IY = IY + INCY 10 CONTINUE DDOT = DTEMP RETURN C C CODE FOR BOTH INCREMENTS EQUAL TO 1 C C C CLEAN-UP LOOP C 20 M = MOD(N,5) IF( M .EQ. 0 ) GO TO 40 DO 30 I = 1,M DTEMP = DTEMP + DX(I)*DY(I) 30 CONTINUE IF( N .LT. 5 ) GO TO 60 40 MP1 = M + 1 DO 50 I = MP1,N,5 DTEMP = DTEMP + DX(I)*DY(I) + DX(I + 1)*DY(I + 1) + * DX(I + 2)*DY(I + 2) + DX(I + 3)*DY(I + 3) + DX(I + 4)*DY(I + 4) 50 CONTINUE 60 DDOT = DTEMP RETURN END SUBROUTINE DGEMM ( 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 DOUBLE PRECISION ALPHA, BETA * .. ARRAY ARGUMENTS .. DOUBLE PRECISION A( LDA, * ), B( LDB, * ), C( LDC, * ) * .. * * PURPOSE * ======= * * DGEMM 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', * * 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 ) = 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 ) = 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 - DOUBLE PRECISION. * ON ENTRY, ALPHA SPECIFIES THE SCALAR ALPHA. * UNCHANGED ON EXIT. * * A - DOUBLE PRECISION 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 - DOUBLE PRECISION 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 - DOUBLE PRECISION. * 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 - DOUBLE PRECISION 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 MAX * .. LOCAL SCALARS .. LOGICAL NOTA, NOTB INTEGER I, INFO, J, L, NCOLA, NROWA, NROWB DOUBLE PRECISION TEMP * .. PARAMETERS .. DOUBLE PRECISION ONE , ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. EXECUTABLE STATEMENTS .. * * SET NOTA AND NOTB AS TRUE IF A AND B RESPECTIVELY ARE NOT * TRANSPOSED 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' ) 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.LSAME( TRANSA, 'C' ) ).AND. $ ( .NOT.LSAME( TRANSA, 'T' ) ) )THEN INFO = 1 ELSE IF( ( .NOT.NOTB ).AND. $ ( .NOT.LSAME( TRANSB, 'C' ) ).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( 'DGEMM ', 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 IF 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 * * FORM C := ALPHA*A'*B + BETA*C * DO 120, J = 1, N DO 110, I = 1, M TEMP = ZERO DO 100, L = 1, K TEMP = TEMP + 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 END IF ELSE IF( NOTA )THEN * * FORM C := ALPHA*A*B' + BETA*C * DO 170, J = 1, N IF( BETA.EQ.ZERO )THEN DO 130, I = 1, M C( I, J ) = ZERO 130 CONTINUE ELSE IF( BETA.NE.ONE )THEN DO 140, I = 1, M C( I, J ) = BETA*C( I, J ) 140 CONTINUE END IF DO 160, L = 1, K IF( B( J, L ).NE.ZERO )THEN TEMP = ALPHA*B( J, L ) DO 150, I = 1, M C( I, J ) = C( I, J ) + TEMP*A( I, L ) 150 CONTINUE END IF 160 CONTINUE 170 CONTINUE ELSE * * FORM C := ALPHA*A'*B' + BETA*C * DO 200, J = 1, N DO 190, I = 1, M TEMP = ZERO DO 180, L = 1, K TEMP = TEMP + A( L, I )*B( J, L ) 180 CONTINUE IF( BETA.EQ.ZERO )THEN C( I, J ) = ALPHA*TEMP ELSE C( I, J ) = ALPHA*TEMP + BETA*C( I, J ) END IF 190 CONTINUE 200 CONTINUE END IF END IF * RETURN * * END OF DGEMM . * END SUBROUTINE DGEMV ( TRANS, M, N, ALPHA, A, LDA, X, INCX, $ BETA, Y, INCY ) * .. SCALAR ARGUMENTS .. DOUBLE PRECISION ALPHA, BETA INTEGER INCX, INCY, LDA, M, N CHARACTER*1 TRANS * .. ARRAY ARGUMENTS .. DOUBLE PRECISION A( LDA, * ), X( * ), Y( * ) * .. * * PURPOSE * ======= * * DGEMV PERFORMS ONE OF THE MATRIX-VECTOR OPERATIONS * * Y := ALPHA*A*X + BETA*Y, OR Y := ALPHA*A'*X + BETA*Y, * * WHERE ALPHA AND BETA ARE SCALARS, X AND Y ARE VECTORS AND A IS AN * M BY N MATRIX. * * PARAMETERS * ========== * * TRANS - CHARACTER*1. * ON ENTRY, TRANS SPECIFIES THE OPERATION TO BE PERFORMED AS * FOLLOWS: * * TRANS = 'N' OR 'N' Y := ALPHA*A*X + BETA*Y. * * TRANS = 'T' OR 'T' Y := ALPHA*A'*X + BETA*Y. * * TRANS = 'C' OR 'C' Y := ALPHA*A'*X + BETA*Y. * * UNCHANGED ON EXIT. * * M - INTEGER. * ON ENTRY, M SPECIFIES THE NUMBER OF ROWS OF THE MATRIX A. * M MUST BE AT LEAST ZERO. * UNCHANGED ON EXIT. * * N - INTEGER. * ON ENTRY, N SPECIFIES THE NUMBER OF COLUMNS OF THE MATRIX A. * N MUST BE AT LEAST ZERO. * UNCHANGED ON EXIT. * * ALPHA - DOUBLE PRECISION. * ON ENTRY, ALPHA SPECIFIES THE SCALAR ALPHA. * UNCHANGED ON EXIT. * * A - DOUBLE PRECISION ARRAY OF DIMENSION ( LDA, N ). * BEFORE ENTRY, THE LEADING M BY N PART OF THE ARRAY A MUST * CONTAIN THE MATRIX OF COEFFICIENTS. * UNCHANGED ON EXIT. * * LDA - INTEGER. * ON ENTRY, LDA SPECIFIES THE FIRST DIMENSION OF A AS DECLARED * IN THE CALLING (SUB) PROGRAM. LDA MUST BE AT LEAST * MAX( 1, M ). * UNCHANGED ON EXIT. * * X - DOUBLE PRECISION ARRAY OF DIMENSION AT LEAST * ( 1 + ( N - 1 )*ABS( INCX ) ) WHEN TRANS = 'N' OR 'N' * AND AT LEAST * ( 1 + ( M - 1 )*ABS( INCX ) ) OTHERWISE. * BEFORE ENTRY, THE INCREMENTED ARRAY X MUST CONTAIN THE * 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 - DOUBLE PRECISION. * 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 - DOUBLE PRECISION ARRAY OF DIMENSION AT LEAST * ( 1 + ( M - 1 )*ABS( INCY ) ) WHEN TRANS = 'N' OR 'N' * AND AT LEAST * ( 1 + ( N - 1 )*ABS( INCY ) ) OTHERWISE. * BEFORE ENTRY WITH BETA NON-ZERO, THE INCREMENTED ARRAY Y * MUST CONTAIN THE 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. * * * 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 .. DOUBLE PRECISION ONE , ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. LOCAL SCALARS .. DOUBLE PRECISION TEMP INTEGER I, INFO, IX, IY, J, JX, JY, KX, KY, LENX, LENY * .. EXTERNAL FUNCTIONS .. LOGICAL LSAME EXTERNAL LSAME * .. EXTERNAL SUBROUTINES .. EXTERNAL XERBLA * .. INTRINSIC FUNCTIONS .. INTRINSIC MAX * .. * .. EXECUTABLE STATEMENTS .. * * TEST THE INPUT PARAMETERS. * INFO = 0 IF ( .NOT.LSAME( TRANS, 'N' ).AND. $ .NOT.LSAME( TRANS, 'T' ).AND. $ .NOT.LSAME( TRANS, 'C' ) )THEN INFO = 1 ELSE IF( M.LT.0 )THEN INFO = 2 ELSE IF( N.LT.0 )THEN INFO = 3 ELSE IF( LDA.LT.MAX( 1, M ) )THEN INFO = 6 ELSE IF( INCX.EQ.0 )THEN INFO = 8 ELSE IF( INCY.EQ.0 )THEN INFO = 11 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'DGEMV ', INFO ) RETURN END IF * * QUICK RETURN IF POSSIBLE. * IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR. $ ( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) ) $ RETURN * * SET LENX AND LENY, THE LENGTHS OF THE VECTORS X AND Y, AND SET * UP THE START POINTS IN X AND Y. * IF( LSAME( TRANS, 'N' ) )THEN LENX = N LENY = M ELSE LENX = M LENY = N END IF IF( INCX.GT.0 )THEN KX = 1 ELSE KX = 1 - ( LENX - 1 )*INCX END IF IF( INCY.GT.0 )THEN KY = 1 ELSE KY = 1 - ( LENY - 1 )*INCY END IF * * START THE OPERATIONS. IN THIS VERSION THE ELEMENTS OF A ARE * ACCESSED SEQUENTIALLY WITH ONE PASS THROUGH A. * * FIRST FORM Y := BETA*Y. * IF( BETA.NE.ONE )THEN IF( INCY.EQ.1 )THEN IF( BETA.EQ.ZERO )THEN DO 10, I = 1, LENY Y( I ) = ZERO 10 CONTINUE ELSE DO 20, I = 1, LENY Y( I ) = BETA*Y( I ) 20 CONTINUE END IF ELSE IY = KY IF( BETA.EQ.ZERO )THEN DO 30, I = 1, LENY Y( IY ) = ZERO IY = IY + INCY 30 CONTINUE ELSE DO 40, I = 1, LENY Y( IY ) = BETA*Y( IY ) IY = IY + INCY 40 CONTINUE END IF END IF END IF IF( ALPHA.EQ.ZERO ) $ RETURN IF( LSAME( TRANS, 'N' ) )THEN * * FORM Y := ALPHA*A*X + Y. * JX = KX IF( INCY.EQ.1 )THEN DO 60, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = ALPHA*X( JX ) DO 50, I = 1, M Y( I ) = Y( I ) + TEMP*A( I, J ) 50 CONTINUE END IF JX = JX + INCX 60 CONTINUE ELSE DO 80, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = ALPHA*X( JX ) IY = KY DO 70, I = 1, M Y( IY ) = Y( IY ) + TEMP*A( I, J ) IY = IY + INCY 70 CONTINUE END IF JX = JX + INCX 80 CONTINUE END IF ELSE * * FORM Y := ALPHA*A'*X + Y. * JY = KY IF( INCX.EQ.1 )THEN DO 100, J = 1, N TEMP = ZERO DO 90, I = 1, M TEMP = TEMP + A( I, J )*X( I ) 90 CONTINUE Y( JY ) = Y( JY ) + ALPHA*TEMP JY = JY + INCY 100 CONTINUE ELSE DO 120, J = 1, N TEMP = ZERO IX = KX DO 110, I = 1, M TEMP = TEMP + A( I, J )*X( IX ) IX = IX + INCX 110 CONTINUE Y( JY ) = Y( JY ) + ALPHA*TEMP JY = JY + INCY 120 CONTINUE END IF END IF * RETURN * * END OF DGEMV . * END SUBROUTINE DGER ( M, N, ALPHA, X, INCX, Y, INCY, A, LDA ) * .. SCALAR ARGUMENTS .. DOUBLE PRECISION ALPHA INTEGER INCX, INCY, LDA, M, N * .. ARRAY ARGUMENTS .. DOUBLE PRECISION A( LDA, * ), X( * ), Y( * ) * .. * * PURPOSE * ======= * * DGER PERFORMS THE RANK 1 OPERATION * * A := ALPHA*X*Y' + A, * * WHERE ALPHA IS A SCALAR, X IS AN M ELEMENT VECTOR, Y IS AN N ELEMENT * VECTOR AND A IS AN M BY N MATRIX. * * PARAMETERS * ========== * * M - INTEGER. * ON ENTRY, M SPECIFIES THE NUMBER OF ROWS OF THE MATRIX A. * M MUST BE AT LEAST ZERO. * UNCHANGED ON EXIT. * * N - INTEGER. * ON ENTRY, N SPECIFIES THE NUMBER OF COLUMNS OF THE MATRIX A. * N MUST BE AT LEAST ZERO. * UNCHANGED ON EXIT. * * ALPHA - DOUBLE PRECISION. * ON ENTRY, ALPHA SPECIFIES THE SCALAR ALPHA. * UNCHANGED ON EXIT. * * X - DOUBLE PRECISION ARRAY OF DIMENSION AT LEAST * ( 1 + ( M - 1 )*ABS( INCX ) ). * BEFORE ENTRY, THE INCREMENTED ARRAY X MUST CONTAIN THE M * 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. * * Y - DOUBLE PRECISION ARRAY OF DIMENSION AT LEAST * ( 1 + ( N - 1 )*ABS( INCY ) ). * BEFORE ENTRY, THE INCREMENTED ARRAY Y MUST CONTAIN THE N * ELEMENT VECTOR Y. * UNCHANGED ON EXIT. * * INCY - INTEGER. * ON ENTRY, INCY SPECIFIES THE INCREMENT FOR THE ELEMENTS OF * Y. INCY MUST NOT BE ZERO. * UNCHANGED ON EXIT. * * A - DOUBLE PRECISION ARRAY OF DIMENSION ( LDA, N ). * BEFORE ENTRY, THE LEADING M BY N PART OF THE ARRAY A MUST * CONTAIN THE MATRIX OF COEFFICIENTS. ON EXIT, A IS * OVERWRITTEN BY THE UPDATED MATRIX. * * LDA - INTEGER. * ON ENTRY, LDA SPECIFIES THE FIRST DIMENSION OF A AS DECLARED * IN THE CALLING (SUB) PROGRAM. LDA MUST BE AT LEAST * MAX( 1, M ). * UNCHANGED ON EXIT. * * * 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 .. DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D+0 ) * .. LOCAL SCALARS .. DOUBLE PRECISION TEMP INTEGER I, INFO, IX, J, JY, KX * .. EXTERNAL SUBROUTINES .. EXTERNAL XERBLA * .. INTRINSIC FUNCTIONS .. INTRINSIC MAX * .. * .. EXECUTABLE STATEMENTS .. * * TEST THE INPUT PARAMETERS. * INFO = 0 IF ( M.LT.0 )THEN INFO = 1 ELSE IF( N.LT.0 )THEN INFO = 2 ELSE IF( INCX.EQ.0 )THEN INFO = 5 ELSE IF( INCY.EQ.0 )THEN INFO = 7 ELSE IF( LDA.LT.MAX( 1, M ) )THEN INFO = 9 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'DGER ', INFO ) RETURN END IF * * QUICK RETURN IF POSSIBLE. * IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR.( ALPHA.EQ.ZERO ) ) $ RETURN * * START THE OPERATIONS. IN THIS VERSION THE ELEMENTS OF A ARE * ACCESSED SEQUENTIALLY WITH ONE PASS THROUGH A. * IF( INCY.GT.0 )THEN JY = 1 ELSE JY = 1 - ( N - 1 )*INCY END IF IF( INCX.EQ.1 )THEN DO 20, J = 1, N IF( Y( JY ).NE.ZERO )THEN TEMP = ALPHA*Y( JY ) DO 10, I = 1, M A( I, J ) = A( I, J ) + X( I )*TEMP 10 CONTINUE END IF JY = JY + INCY 20 CONTINUE ELSE IF( INCX.GT.0 )THEN KX = 1 ELSE KX = 1 - ( M - 1 )*INCX END IF DO 40, J = 1, N IF( Y( JY ).NE.ZERO )THEN TEMP = ALPHA*Y( JY ) IX = KX DO 30, I = 1, M A( I, J ) = A( I, J ) + X( IX )*TEMP IX = IX + INCX 30 CONTINUE END IF JY = JY + INCY 40 CONTINUE END IF * RETURN * * END OF DGER . * END subroutine dscal(n,da,dx,incx) c c scales a vector by a constant. c uses unrolled loops for increment equal to one. c jack dongarra, linpack, 3/11/78. c modified 3/93 to return if incx .le. 0. c modified 12/3/93, array(1) declarations changed to array(*) c double precision da,dx(*) integer i,incx,m,mp1,n,nincx c if( n.le.0 .or. incx.le.0 )return if(incx.eq.1)go to 20 c c code for increment not equal to 1 c nincx = n*incx do 10 i = 1,nincx,incx dx(i) = da*dx(i) 10 continue return c c code for increment equal to 1 c c c clean-up loop c 20 m = mod(n,5) if( m .eq. 0 ) go to 40 do 30 i = 1,m dx(i) = da*dx(i) 30 continue if( n .lt. 5 ) return 40 mp1 = m + 1 do 50 i = mp1,n,5 dx(i) = da*dx(i) dx(i + 1) = da*dx(i + 1) dx(i + 2) = da*dx(i + 2) dx(i + 3) = da*dx(i + 3) dx(i + 4) = da*dx(i + 4) 50 continue return end SUBROUTINE DSPMV ( UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY ) * .. Scalar Arguments .. DOUBLE PRECISION ALPHA, BETA INTEGER INCX, INCY, N CHARACTER*1 UPLO * .. Array Arguments .. DOUBLE PRECISION AP( * ), X( * ), Y( * ) * .. * * Purpose * ======= * * DSPMV 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. * * Parameters * ========== * * 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 - DOUBLE PRECISION. * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * AP - DOUBLE PRECISION 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 - DOUBLE PRECISION 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 - DOUBLE PRECISION. * 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 - DOUBLE PRECISION 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. * * * 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 .. DOUBLE PRECISION ONE , ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. Local Scalars .. DOUBLE PRECISION TEMP1, TEMP2 INTEGER I, INFO, IX, IY, J, JX, JY, K, KK, KX, KY * .. 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 = 6 ELSE IF( INCY.EQ.0 )THEN INFO = 9 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'DSPMV ', 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 DSPMV . * END SUBROUTINE DSPR2 ( UPLO, N, ALPHA, X, INCX, Y, INCY, AP ) * .. Scalar Arguments .. DOUBLE PRECISION ALPHA INTEGER INCX, INCY, N CHARACTER*1 UPLO * .. Array Arguments .. DOUBLE PRECISION AP( * ), X( * ), Y( * ) * .. * * Purpose * ======= * * DSPR2 performs the symmetric rank 2 operation * * A := alpha*x*y' + alpha*y*x' + A, * * where alpha is a scalar, x and y are n element vectors and A is an * n by n symmetric matrix, supplied in packed form. * * Parameters * ========== * * 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 - DOUBLE PRECISION. * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * X - DOUBLE PRECISION 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. * * Y - DOUBLE PRECISION array of dimension at least * ( 1 + ( n - 1 )*abs( INCY ) ). * Before entry, the incremented array Y must contain the n * element vector y. * Unchanged on exit. * * INCY - INTEGER. * On entry, INCY specifies the increment for the elements of * Y. INCY must not be zero. * Unchanged on exit. * * AP - DOUBLE PRECISION 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. 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. * * * 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 .. DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D+0 ) * .. Local Scalars .. DOUBLE PRECISION TEMP1, TEMP2 INTEGER I, INFO, IX, IY, J, JX, JY, K, KK, KX, KY * .. 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 ELSE IF( INCY.EQ.0 )THEN INFO = 7 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'DSPR2 ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( N.EQ.0 ).OR.( ALPHA.EQ.ZERO ) ) $ RETURN * * Set up the start points in X and Y if the increments are not both * unity. * IF( ( INCX.NE.1 ).OR.( INCY.NE.1 ) )THEN 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 JX = KX JY = KY 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 ).AND.( INCY.EQ.1 ) )THEN DO 20, J = 1, N IF( ( X( J ).NE.ZERO ).OR.( Y( J ).NE.ZERO ) )THEN TEMP1 = ALPHA*Y( J ) TEMP2 = ALPHA*X( J ) K = KK DO 10, I = 1, J AP( K ) = AP( K ) + X( I )*TEMP1 + Y( I )*TEMP2 K = K + 1 10 CONTINUE END IF KK = KK + J 20 CONTINUE ELSE DO 40, J = 1, N IF( ( X( JX ).NE.ZERO ).OR.( Y( JY ).NE.ZERO ) )THEN TEMP1 = ALPHA*Y( JY ) TEMP2 = ALPHA*X( JX ) IX = KX IY = KY DO 30, K = KK, KK + J - 1 AP( K ) = AP( K ) + X( IX )*TEMP1 + Y( IY )*TEMP2 IX = IX + INCX IY = IY + INCY 30 CONTINUE END IF JX = JX + INCX JY = JY + INCY KK = KK + J 40 CONTINUE END IF ELSE * * Form A when lower triangle is stored in AP. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 60, J = 1, N IF( ( X( J ).NE.ZERO ).OR.( Y( J ).NE.ZERO ) )THEN TEMP1 = ALPHA*Y( J ) TEMP2 = ALPHA*X( J ) K = KK DO 50, I = J, N AP( K ) = AP( K ) + X( I )*TEMP1 + Y( I )*TEMP2 K = K + 1 50 CONTINUE END IF KK = KK + N - J + 1 60 CONTINUE ELSE DO 80, J = 1, N IF( ( X( JX ).NE.ZERO ).OR.( Y( JY ).NE.ZERO ) )THEN TEMP1 = ALPHA*Y( JY ) TEMP2 = ALPHA*X( JX ) IX = JX IY = JY DO 70, K = KK, KK + N - J AP( K ) = AP( K ) + X( IX )*TEMP1 + Y( IY )*TEMP2 IX = IX + INCX IY = IY + INCY 70 CONTINUE END IF JX = JX + INCX JY = JY + INCY KK = KK + N - J + 1 80 CONTINUE END IF END IF * RETURN * * End of DSPR2 . * END subroutine dswap (n,dx,incx,dy,incy) c c interchanges two vectors. c uses unrolled loops for increments equal one. c jack dongarra, linpack, 3/11/78. c modified 12/3/93, array(1) declarations changed to array(*) c double precision dx(*),dy(*),dtemp integer i,incx,incy,ix,iy,m,mp1,n c if(n.le.0)return if(incx.eq.1.and.incy.eq.1)go to 20 c c code for unequal increments or equal increments not equal c to 1 c ix = 1 iy = 1 if(incx.lt.0)ix = (-n+1)*incx + 1 if(incy.lt.0)iy = (-n+1)*incy + 1 do 10 i = 1,n dtemp = dx(ix) dx(ix) = dy(iy) dy(iy) = dtemp ix = ix + incx iy = iy + incy 10 continue return c c code for both increments equal to 1 c c c clean-up loop c 20 m = mod(n,3) if( m .eq. 0 ) go to 40 do 30 i = 1,m dtemp = dx(i) dx(i) = dy(i) dy(i) = dtemp 30 continue if( n .lt. 3 ) return 40 mp1 = m + 1 do 50 i = mp1,n,3 dtemp = dx(i) dx(i) = dy(i) dy(i) = dtemp dtemp = dx(i + 1) dx(i + 1) = dy(i + 1) dy(i + 1) = dtemp dtemp = dx(i + 2) dx(i + 2) = dy(i + 2) dy(i + 2) = dtemp 50 continue return end subroutine zscal(n,za,zx,incx) c c scales a vector by a constant. c jack dongarra, 3/11/78. c modified 3/93 to return if incx .le. 0. c modified 12/3/93, array(1) declarations changed to array(*) c double complex za,zx(*) integer i,incx,ix,n c if( n.le.0 .or. incx.le.0 )return if(incx.eq.1)go to 20 c c code for increment not equal to 1 c ix = 1 do 10 i = 1,n zx(ix) = za*zx(ix) ix = ix + incx 10 continue return c c code for increment equal to 1 c 20 do 30 i = 1,n zx(i) = za*zx(i) 30 continue return end integer function idamax(n,dx,incx) c c finds the index of element having max. absolute value. c jack dongarra, linpack, 3/11/78. c modified 3/93 to return if incx .le. 0. c modified 12/3/93, array(1) declarations changed to array(*) c double precision dx(*),dmax integer i,incx,ix,n c idamax = 0 if( n.lt.1 .or. incx.le.0 ) return idamax = 1 if(n.eq.1)return if(incx.eq.1)go to 20 c c code for increment not equal to 1 c ix = 1 dmax = dabs(dx(1)) ix = ix + incx do 10 i = 2,n if(dabs(dx(ix)).le.dmax) go to 5 idamax = i dmax = dabs(dx(ix)) 5 ix = ix + incx 10 continue return c c code for increment equal to 1 c 20 dmax = dabs(dx(1)) do 30 i = 2,n if(dabs(dx(i)).le.dmax) go to 30 idamax = i dmax = dabs(dx(i)) 30 continue return end 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 subroutine zswap (n,zx,incx,zy,incy) c c interchanges two vectors. c jack dongarra, 3/11/78. c modified 12/3/93, array(1) declarations changed to array(*) c double complex zx(*),zy(*),ztemp integer i,incx,incy,ix,iy,n c if(n.le.0)return if(incx.eq.1.and.incy.eq.1)go to 20 c c code for unequal increments or equal increments not equal c to 1 c ix = 1 iy = 1 if(incx.lt.0)ix = (-n+1)*incx + 1 if(incy.lt.0)iy = (-n+1)*incy + 1 do 10 i = 1,n ztemp = zx(ix) zx(ix) = zy(iy) zy(iy) = ztemp ix = ix + incx iy = iy + incy 10 continue return c c code for both increments equal to 1 20 do 30 i = 1,n ztemp = zx(i) zx(i) = zy(i) zy(i) = ztemp 30 continue return end subroutine zaxpy(n,za,zx,incx,zy,incy) c c constant times a vector plus a vector. c jack dongarra, 3/11/78. c modified 12/3/93, array(1) declarations changed to array(*) c double complex zx(*),zy(*),za integer i,incx,incy,ix,iy,n double precision dcabs1 if(n.le.0)return if (dcabs1(za) .eq. 0.0d0) return if (incx.eq.1.and.incy.eq.1)go to 20 c c code for unequal increments or equal increments c not equal to 1 c ix = 1 iy = 1 if(incx.lt.0)ix = (-n+1)*incx + 1 if(incy.lt.0)iy = (-n+1)*incy + 1 do 10 i = 1,n zy(iy) = zy(iy) + za*zx(ix) ix = ix + incx iy = iy + incy 10 continue return c c code for both increments equal to 1 c 20 do 30 i = 1,n zy(i) = zy(i) + za*zx(i) 30 continue return end subroutine zdscal(n,da,zx,incx) c c scales a vector by a constant. c jack dongarra, 3/11/78. c modified 3/93 to return if incx .le. 0. c modified 12/3/93, array(1) declarations changed to array(*) c double complex zx(*) double precision da integer i,incx,ix,n c if( n.le.0 .or. incx.le.0 )return if(incx.eq.1)go to 20 c c code for increment not equal to 1 c ix = 1 do 10 i = 1,n zx(ix) = dcmplx(da,0.0d0)*zx(ix) ix = ix + incx 10 continue return c c code for increment equal to 1 c 20 do 30 i = 1,n zx(i) = dcmplx(da,0.0d0)*zx(i) 30 continue return end DOUBLE PRECISION FUNCTION DZNRM2( N, X, INCX ) * .. Scalar Arguments .. INTEGER INCX, N * .. Array Arguments .. COMPLEX*16 X( * ) * .. * * DZNRM2 returns the euclidean norm of a vector via the function * name, so that * * DZNRM2 := sqrt( conjg( x' )*x ) * * * * -- This version written on 25-October-1982. * Modified on 14-October-1993 to inline the call to ZLASSQ. * Sven Hammarling, Nag Ltd. * * * .. Parameters .. DOUBLE PRECISION ONE , ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. Local Scalars .. INTEGER IX DOUBLE PRECISION NORM, SCALE, SSQ, TEMP * .. Intrinsic Functions .. INTRINSIC ABS, DIMAG, DBLE, SQRT * .. * .. Executable Statements .. IF( N.LT.1 .OR. INCX.LT.1 )THEN NORM = ZERO ELSE SCALE = ZERO SSQ = ONE * The following loop is equivalent to this call to the LAPACK * auxiliary routine: * CALL ZLASSQ( N, X, INCX, SCALE, SSQ ) * DO 10, IX = 1, 1 + ( N - 1 )*INCX, INCX IF( DBLE( X( IX ) ).NE.ZERO )THEN TEMP = ABS( DBLE( X( IX ) ) ) IF( SCALE.LT.TEMP )THEN SSQ = ONE + SSQ*( SCALE/TEMP )**2 SCALE = TEMP ELSE SSQ = SSQ + ( TEMP/SCALE )**2 END IF END IF IF( DIMAG( X( IX ) ).NE.ZERO )THEN TEMP = ABS( DIMAG( X( IX ) ) ) IF( SCALE.LT.TEMP )THEN SSQ = ONE + SSQ*( SCALE/TEMP )**2 SCALE = TEMP ELSE SSQ = SSQ + ( TEMP/SCALE )**2 END IF END IF 10 CONTINUE NORM = SCALE * SQRT( SSQ ) END IF * DZNRM2 = NORM RETURN * * End of DZNRM2. * END SUBROUTINE ZGEMV ( TRANS, M, N, ALPHA, A, LDA, X, INCX, $ BETA, Y, INCY ) * .. Scalar Arguments .. COMPLEX*16 ALPHA, BETA INTEGER INCX, INCY, LDA, M, N CHARACTER*1 TRANS * .. Array Arguments .. COMPLEX*16 A( LDA, * ), X( * ), Y( * ) * .. * * Purpose * ======= * * ZGEMV performs one of the matrix-vector operations * * y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, or * * y := alpha*conjg( A' )*x + beta*y, * * where alpha and beta are scalars, x and y are vectors and A is an * m by n matrix. * * Parameters * ========== * * TRANS - CHARACTER*1. * On entry, TRANS specifies the operation to be performed as * follows: * * TRANS = 'N' or 'n' y := alpha*A*x + beta*y. * * TRANS = 'T' or 't' y := alpha*A'*x + beta*y. * * TRANS = 'C' or 'c' y := alpha*conjg( A' )*x + beta*y. * * Unchanged on exit. * * M - INTEGER. * On entry, M specifies the number of rows of the matrix A. * M must be at least zero. * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the number of columns of the matrix A. * N 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, n ). * Before entry, the leading m by n part of the array A must * contain the matrix of coefficients. * Unchanged on exit. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * max( 1, m ). * Unchanged on exit. * * X - COMPLEX*16 array of DIMENSION at least * ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' * and at least * ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. * Before entry, the incremented array X must contain the * 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 - COMPLEX*16 . * 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 - COMPLEX*16 array of DIMENSION at least * ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' * and at least * ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. * Before entry with BETA non-zero, the incremented array Y * must contain the 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. * * * 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 .. COMPLEX*16 ONE PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) COMPLEX*16 ZERO PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) ) * .. Local Scalars .. COMPLEX*16 TEMP INTEGER I, INFO, IX, IY, J, JX, JY, KX, KY, LENX, LENY LOGICAL NOCONJ * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC DCONJG, MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( TRANS, 'N' ).AND. $ .NOT.LSAME( TRANS, 'T' ).AND. $ .NOT.LSAME( TRANS, 'C' ) )THEN INFO = 1 ELSE IF( M.LT.0 )THEN INFO = 2 ELSE IF( N.LT.0 )THEN INFO = 3 ELSE IF( LDA.LT.MAX( 1, M ) )THEN INFO = 6 ELSE IF( INCX.EQ.0 )THEN INFO = 8 ELSE IF( INCY.EQ.0 )THEN INFO = 11 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'ZGEMV ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR. $ ( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) ) $ RETURN * NOCONJ = LSAME( TRANS, 'T' ) * * Set LENX and LENY, the lengths of the vectors x and y, and set * up the start points in X and Y. * IF( LSAME( TRANS, 'N' ) )THEN LENX = N LENY = M ELSE LENX = M LENY = N END IF IF( INCX.GT.0 )THEN KX = 1 ELSE KX = 1 - ( LENX - 1 )*INCX END IF IF( INCY.GT.0 )THEN KY = 1 ELSE KY = 1 - ( LENY - 1 )*INCY END IF * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through A. * * First form y := beta*y. * IF( BETA.NE.ONE )THEN IF( INCY.EQ.1 )THEN IF( BETA.EQ.ZERO )THEN DO 10, I = 1, LENY Y( I ) = ZERO 10 CONTINUE ELSE DO 20, I = 1, LENY Y( I ) = BETA*Y( I ) 20 CONTINUE END IF ELSE IY = KY IF( BETA.EQ.ZERO )THEN DO 30, I = 1, LENY Y( IY ) = ZERO IY = IY + INCY 30 CONTINUE ELSE DO 40, I = 1, LENY Y( IY ) = BETA*Y( IY ) IY = IY + INCY 40 CONTINUE END IF END IF END IF IF( ALPHA.EQ.ZERO ) $ RETURN IF( LSAME( TRANS, 'N' ) )THEN * * Form y := alpha*A*x + y. * JX = KX IF( INCY.EQ.1 )THEN DO 60, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = ALPHA*X( JX ) DO 50, I = 1, M Y( I ) = Y( I ) + TEMP*A( I, J ) 50 CONTINUE END IF JX = JX + INCX 60 CONTINUE ELSE DO 80, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = ALPHA*X( JX ) IY = KY DO 70, I = 1, M Y( IY ) = Y( IY ) + TEMP*A( I, J ) IY = IY + INCY 70 CONTINUE END IF JX = JX + INCX 80 CONTINUE END IF ELSE * * Form y := alpha*A'*x + y or y := alpha*conjg( A' )*x + y. * JY = KY IF( INCX.EQ.1 )THEN DO 110, J = 1, N TEMP = ZERO IF( NOCONJ )THEN DO 90, I = 1, M TEMP = TEMP + A( I, J )*X( I ) 90 CONTINUE ELSE DO 100, I = 1, M TEMP = TEMP + DCONJG( A( I, J ) )*X( I ) 100 CONTINUE END IF Y( JY ) = Y( JY ) + ALPHA*TEMP JY = JY + INCY 110 CONTINUE ELSE DO 140, J = 1, N TEMP = ZERO IX = KX IF( NOCONJ )THEN DO 120, I = 1, M TEMP = TEMP + A( I, J )*X( IX ) IX = IX + INCX 120 CONTINUE ELSE DO 130, I = 1, M TEMP = TEMP + DCONJG( A( I, J ) )*X( IX ) IX = IX + INCX 130 CONTINUE END IF Y( JY ) = Y( JY ) + ALPHA*TEMP JY = JY + INCY 140 CONTINUE END IF END IF * RETURN * * End of ZGEMV . * END subroutine zcopy(n,zx,incx,zy,incy) c c copies a vector, x, to a vector, y. c jack dongarra, linpack, 4/11/78. c modified 12/3/93, array(1) declarations changed to array(*) c double complex zx(*),zy(*) integer i,incx,incy,ix,iy,n c if(n.le.0)return if(incx.eq.1.and.incy.eq.1)go to 20 c c code for unequal increments or equal increments c not equal to 1 c ix = 1 iy = 1 if(incx.lt.0)ix = (-n+1)*incx + 1 if(incy.lt.0)iy = (-n+1)*incy + 1 do 10 i = 1,n zy(iy) = zx(ix) ix = ix + incx iy = iy + incy 10 continue return c c code for both increments equal to 1 c 20 do 30 i = 1,n zy(i) = zx(i) 30 continue return end subroutine dcopy(n,dx,incx,dy,incy) c c copies a vector, x, to a vector, y. c uses unrolled loops for increments equal to one. c jack dongarra, linpack, 3/11/78. c modified 12/3/93, array(1) declarations changed to array(*) c double precision dx(*),dy(*) integer i,incx,incy,ix,iy,m,mp1,n c if(n.le.0)return if(incx.eq.1.and.incy.eq.1)go to 20 c c code for unequal increments or equal increments c not equal to 1 c ix = 1 iy = 1 if(incx.lt.0)ix = (-n+1)*incx + 1 if(incy.lt.0)iy = (-n+1)*incy + 1 do 10 i = 1,n dy(iy) = dx(ix) ix = ix + incx iy = iy + incy 10 continue return c c code for both increments equal to 1 c c c clean-up loop c 20 m = mod(n,7) if( m .eq. 0 ) go to 40 do 30 i = 1,m dy(i) = dx(i) 30 continue if( n .lt. 7 ) return 40 mp1 = m + 1 do 50 i = mp1,n,7 dy(i) = dx(i) dy(i + 1) = dx(i + 1) dy(i + 2) = dx(i + 2) dy(i + 3) = dx(i + 3) dy(i + 4) = dx(i + 4) dy(i + 5) = dx(i + 5) dy(i + 6) = dx(i + 6) 50 continue return end double complex function zdotu(n,zx,incx,zy,incy) c c forms the dot product of two vectors. c jack dongarra, 3/11/78. c modified 12/3/93, array(1) declarations changed to array(*) c double complex zx(*),zy(*),ztemp integer i,incx,incy,ix,iy,n ztemp = (0.0d0,0.0d0) zdotu = (0.0d0,0.0d0) if(n.le.0)return if(incx.eq.1.and.incy.eq.1)go to 20 c c code for unequal increments or equal increments c not equal to 1 c ix = 1 iy = 1 if(incx.lt.0)ix = (-n+1)*incx + 1 if(incy.lt.0)iy = (-n+1)*incy + 1 do 10 i = 1,n ztemp = ztemp + zx(ix)*zy(iy) ix = ix + incx iy = iy + incy 10 continue zdotu = ztemp return c c code for both increments equal to 1 c 20 do 30 i = 1,n ztemp = ztemp + zx(i)*zy(i) 30 continue zdotu = ztemp return end double precision function dcabs1(z) double complex z,zz double precision t(2) equivalence (zz,t(1)) zz = z dcabs1 = dabs(t(1)) + dabs(t(2)) return end integer function izamax(n,zx,incx) c c finds the index of element having max. absolute value. c jack dongarra, 1/15/85. c modified 3/93 to return if incx .le. 0. c modified 12/3/93, array(1) declarations changed to array(*) c double complex zx(*) double precision smax integer i,incx,ix,n double precision dcabs1 c izamax = 0 if( n.lt.1 .or. incx.le.0 )return izamax = 1 if(n.eq.1)return if(incx.eq.1)go to 20 c c code for increment not equal to 1 c ix = 1 smax = dcabs1(zx(1)) ix = ix + incx do 10 i = 2,n if(dcabs1(zx(ix)).le.smax) go to 5 izamax = i smax = dcabs1(zx(ix)) 5 ix = ix + incx 10 continue return c c code for increment equal to 1 c 20 smax = dcabs1(zx(1)) do 30 i = 2,n if(dcabs1(zx(i)).le.smax) go to 30 izamax = i smax = dcabs1(zx(i)) 30 continue return end SUBROUTINE ZGERU ( M, N, ALPHA, X, INCX, Y, INCY, A, LDA ) * .. Scalar Arguments .. COMPLEX*16 ALPHA INTEGER INCX, INCY, LDA, M, N * .. Array Arguments .. COMPLEX*16 A( LDA, * ), X( * ), Y( * ) * .. * * Purpose * ======= * * ZGERU performs the rank 1 operation * * A := alpha*x*y' + A, * * where alpha is a scalar, x is an m element vector, y is an n element * vector and A is an m by n matrix. * * Parameters * ========== * * M - INTEGER. * On entry, M specifies the number of rows of the matrix A. * M must be at least zero. * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the number of columns of the matrix A. * N must be at least zero. * Unchanged on exit. * * ALPHA - COMPLEX*16 . * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * X - COMPLEX*16 array of dimension at least * ( 1 + ( m - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the m * 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. * * Y - COMPLEX*16 array of dimension at least * ( 1 + ( n - 1 )*abs( INCY ) ). * Before entry, the incremented array Y must contain the n * element vector y. * Unchanged on exit. * * INCY - INTEGER. * On entry, INCY specifies the increment for the elements of * Y. INCY must not be zero. * Unchanged on exit. * * A - COMPLEX*16 array of DIMENSION ( LDA, n ). * Before entry, the leading m by n part of the array A must * contain the matrix of coefficients. On exit, A is * overwritten by the updated matrix. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * max( 1, m ). * Unchanged on exit. * * * 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 .. COMPLEX*16 ZERO PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) ) * .. Local Scalars .. COMPLEX*16 TEMP INTEGER I, INFO, IX, J, JY, KX * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( M.LT.0 )THEN INFO = 1 ELSE IF( N.LT.0 )THEN INFO = 2 ELSE IF( INCX.EQ.0 )THEN INFO = 5 ELSE IF( INCY.EQ.0 )THEN INFO = 7 ELSE IF( LDA.LT.MAX( 1, M ) )THEN INFO = 9 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'ZGERU ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR.( ALPHA.EQ.ZERO ) ) $ RETURN * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through A. * IF( INCY.GT.0 )THEN JY = 1 ELSE JY = 1 - ( N - 1 )*INCY END IF IF( INCX.EQ.1 )THEN DO 20, J = 1, N IF( Y( JY ).NE.ZERO )THEN TEMP = ALPHA*Y( JY ) DO 10, I = 1, M A( I, J ) = A( I, J ) + X( I )*TEMP 10 CONTINUE END IF JY = JY + INCY 20 CONTINUE ELSE IF( INCX.GT.0 )THEN KX = 1 ELSE KX = 1 - ( M - 1 )*INCX END IF DO 40, J = 1, N IF( Y( JY ).NE.ZERO )THEN TEMP = ALPHA*Y( JY ) IX = KX DO 30, I = 1, M A( I, J ) = A( I, J ) + X( IX )*TEMP IX = IX + INCX 30 CONTINUE END IF JY = JY + INCY 40 CONTINUE END IF * RETURN * * End of ZGERU . * END SUBROUTINE DSPR ( UPLO, N, ALPHA, X, INCX, AP ) * .. Scalar Arguments .. DOUBLE PRECISION ALPHA INTEGER INCX, N CHARACTER*1 UPLO * .. Array Arguments .. DOUBLE PRECISION AP( * ), X( * ) * .. * * Purpose * ======= * * DSPR performs the symmetric rank 1 operation * * A := alpha*x*x' + A, * * where alpha is a real scalar, x is an n element vector and A is an * n by n symmetric matrix, supplied in packed form. * * Parameters * ========== * * 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 - DOUBLE PRECISION. * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * X - DOUBLE PRECISION 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. * * AP - DOUBLE PRECISION 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. 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. * * * 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 .. DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D+0 ) * .. Local Scalars .. DOUBLE PRECISION TEMP INTEGER I, INFO, IX, J, JX, K, KK, KX * .. 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( 'DSPR ', 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 AP( K ) = AP( K ) + X( I )*TEMP K = K + 1 10 CONTINUE 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 - 1 AP( K ) = AP( K ) + X( IX )*TEMP IX = IX + INCX 30 CONTINUE 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 ) K = KK DO 50, I = J, N AP( K ) = AP( K ) + X( I )*TEMP K = K + 1 50 CONTINUE 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 ) IX = JX DO 70, K = KK, KK + N - J AP( K ) = AP( K ) + X( IX )*TEMP IX = IX + INCX 70 CONTINUE END IF JX = JX + INCX KK = KK + N - J + 1 80 CONTINUE END IF END IF * RETURN * * End of DSPR . * END SUBROUTINE ZHPR ( UPLO, N, ALPHA, X, INCX, AP ) * .. Scalar Arguments .. DOUBLE PRECISION ALPHA INTEGER INCX, N CHARACTER*1 UPLO * .. Array Arguments .. COMPLEX*16 AP( * ), X( * ) * .. * * Purpose * ======= * * ZHPR performs the hermitian rank 1 operation * * A := alpha*x*conjg( x' ) + A, * * where alpha is a real scalar, x is an n element vector and A is an * n by n hermitian matrix, supplied in packed form. * * Parameters * ========== * * 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 - DOUBLE PRECISION. * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * X - COMPLEX*16 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. * * AP - COMPLEX*16 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 hermitian 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 hermitian 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. * * * 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 .. COMPLEX*16 ZERO PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) ) * .. Local Scalars .. COMPLEX*16 TEMP INTEGER I, INFO, IX, J, JX, K, KK, KX * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC DCONJG, DBLE * .. * .. 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( 'ZHPR ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( N.EQ.0 ).OR.( ALPHA.EQ.DBLE( 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*DCONJG( 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 ) = DBLE( AP( KK + J - 1 ) ) $ + DBLE( X( J )*TEMP ) ELSE AP( KK + J - 1 ) = DBLE( 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*DCONJG( 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 ) = DBLE( AP( KK + J - 1 ) ) $ + DBLE( X( JX )*TEMP ) ELSE AP( KK + J - 1 ) = DBLE( 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*DCONJG( X( J ) ) AP( KK ) = DBLE( AP( KK ) ) + DBLE( 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 ) = DBLE( 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*DCONJG( X( JX ) ) AP( KK ) = DBLE( AP( KK ) ) + DBLE( 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 ) = DBLE( AP( KK ) ) END IF JX = JX + INCX KK = KK + N - J + 1 80 CONTINUE END IF END IF * RETURN * * End of ZHPR . * END SUBROUTINE ZHPR2 ( UPLO, N, ALPHA, X, INCX, Y, INCY, AP ) * .. Scalar Arguments .. COMPLEX*16 ALPHA INTEGER INCX, INCY, N CHARACTER*1 UPLO * .. Array Arguments .. COMPLEX*16 AP( * ), X( * ), Y( * ) * .. * * Purpose * ======= * * ZHPR2 performs the hermitian rank 2 operation * * A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A, * * where alpha is a scalar, x and y are n element vectors and A is an * n by n hermitian matrix, supplied in packed form. * * Parameters * ========== * * 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 - COMPLEX*16 . * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * X - COMPLEX*16 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. * * Y - COMPLEX*16 array of dimension at least * ( 1 + ( n - 1 )*abs( INCY ) ). * Before entry, the incremented array Y must contain the n * element vector y. * Unchanged on exit. * * INCY - INTEGER. * On entry, INCY specifies the increment for the elements of * Y. INCY must not be zero. * Unchanged on exit. * * AP - COMPLEX*16 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 hermitian 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 hermitian 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. * * * 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 .. COMPLEX*16 ZERO PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) ) * .. Local Scalars .. COMPLEX*16 TEMP1, TEMP2 INTEGER I, INFO, IX, IY, J, JX, JY, K, KK, KX, KY * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC DCONJG, DBLE * .. * .. 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 ELSE IF( INCY.EQ.0 )THEN INFO = 7 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'ZHPR2 ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( N.EQ.0 ).OR.( ALPHA.EQ.ZERO ) ) $ RETURN * * Set up the start points in X and Y if the increments are not both * unity. * IF( ( INCX.NE.1 ).OR.( INCY.NE.1 ) )THEN 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 JX = KX JY = KY 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 ).AND.( INCY.EQ.1 ) )THEN DO 20, J = 1, N IF( ( X( J ).NE.ZERO ).OR.( Y( J ).NE.ZERO ) )THEN TEMP1 = ALPHA*DCONJG( Y( J ) ) TEMP2 = DCONJG( ALPHA*X( J ) ) K = KK DO 10, I = 1, J - 1 AP( K ) = AP( K ) + X( I )*TEMP1 + Y( I )*TEMP2 K = K + 1 10 CONTINUE AP( KK + J - 1 ) = DBLE( AP( KK + J - 1 ) ) + $ DBLE( X( J )*TEMP1 + Y( J )*TEMP2 ) ELSE AP( KK + J - 1 ) = DBLE( AP( KK + J - 1 ) ) END IF KK = KK + J 20 CONTINUE ELSE DO 40, J = 1, N IF( ( X( JX ).NE.ZERO ).OR.( Y( JY ).NE.ZERO ) )THEN TEMP1 = ALPHA*DCONJG( Y( JY ) ) TEMP2 = DCONJG( ALPHA*X( JX ) ) IX = KX IY = KY DO 30, K = KK, KK + J - 2 AP( K ) = AP( K ) + X( IX )*TEMP1 + Y( IY )*TEMP2 IX = IX + INCX IY = IY + INCY 30 CONTINUE AP( KK + J - 1 ) = DBLE( AP( KK + J - 1 ) ) + $ DBLE( X( JX )*TEMP1 + $ Y( JY )*TEMP2 ) ELSE AP( KK + J - 1 ) = DBLE( AP( KK + J - 1 ) ) END IF JX = JX + INCX JY = JY + INCY KK = KK + J 40 CONTINUE END IF ELSE * * Form A when lower triangle is stored in AP. * IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN DO 60, J = 1, N IF( ( X( J ).NE.ZERO ).OR.( Y( J ).NE.ZERO ) )THEN TEMP1 = ALPHA*DCONJG( Y( J ) ) TEMP2 = DCONJG( ALPHA*X( J ) ) AP( KK ) = DBLE( AP( KK ) ) + $ DBLE( X( J )*TEMP1 + Y( J )*TEMP2 ) K = KK + 1 DO 50, I = J + 1, N AP( K ) = AP( K ) + X( I )*TEMP1 + Y( I )*TEMP2 K = K + 1 50 CONTINUE ELSE AP( KK ) = DBLE( AP( KK ) ) END IF KK = KK + N - J + 1 60 CONTINUE ELSE DO 80, J = 1, N IF( ( X( JX ).NE.ZERO ).OR.( Y( JY ).NE.ZERO ) )THEN TEMP1 = ALPHA*DCONJG( Y( JY ) ) TEMP2 = DCONJG( ALPHA*X( JX ) ) AP( KK ) = DBLE( AP( KK ) ) + $ DBLE( X( JX )*TEMP1 + Y( JY )*TEMP2 ) IX = JX IY = JY DO 70, K = KK + 1, KK + N - J IX = IX + INCX IY = IY + INCY AP( K ) = AP( K ) + X( IX )*TEMP1 + Y( IY )*TEMP2 70 CONTINUE ELSE AP( KK ) = DBLE( AP( KK ) ) END IF JX = JX + INCX JY = JY + INCY KK = KK + N - J + 1 80 CONTINUE END IF END IF * RETURN * * End of ZHPR2 . * END SUBROUTINE ZHPMV ( UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY ) * .. Scalar Arguments .. COMPLEX*16 ALPHA, BETA INTEGER INCX, INCY, N CHARACTER*1 UPLO * .. Array Arguments .. COMPLEX*16 AP( * ), X( * ), Y( * ) * .. * * Purpose * ======= * * ZHPMV 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 hermitian matrix, supplied in packed form. * * Parameters * ========== * * 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 - COMPLEX*16 . * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * AP - COMPLEX*16 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 hermitian 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 hermitian 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. * Note that the imaginary parts of the diagonal elements need * not be set and are assumed to be zero. * Unchanged on exit. * * X - COMPLEX*16 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 - COMPLEX*16 . * 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 - COMPLEX*16 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. * * * 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 .. COMPLEX*16 ONE PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) COMPLEX*16 ZERO PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) ) * .. Local Scalars .. COMPLEX*16 TEMP1, TEMP2 INTEGER I, INFO, IX, IY, J, JX, JY, K, KK, KX, KY * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC DCONJG, DBLE * .. * .. 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 = 6 ELSE IF( INCY.EQ.0 )THEN INFO = 9 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'ZHPMV ', 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 + DCONJG( AP( K ) )*X( I ) K = K + 1 50 CONTINUE Y( J ) = Y( J ) + TEMP1*DBLE( 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 + DCONJG( AP( K ) )*X( IX ) IX = IX + INCX IY = IY + INCY 70 CONTINUE Y( JY ) = Y( JY ) + TEMP1*DBLE( 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*DBLE( AP( KK ) ) K = KK + 1 DO 90, I = J + 1, N Y( I ) = Y( I ) + TEMP1*AP( K ) TEMP2 = TEMP2 + DCONJG( 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*DBLE( 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 + DCONJG( 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 ZHPMV . * END SUBROUTINE ZGERC ( M, N, ALPHA, X, INCX, Y, INCY, A, LDA ) * .. Scalar Arguments .. COMPLEX*16 ALPHA INTEGER INCX, INCY, LDA, M, N * .. Array Arguments .. COMPLEX*16 A( LDA, * ), X( * ), Y( * ) * .. * * Purpose * ======= * * ZGERC performs the rank 1 operation * * A := alpha*x*conjg( y' ) + A, * * where alpha is a scalar, x is an m element vector, y is an n element * vector and A is an m by n matrix. * * Parameters * ========== * * M - INTEGER. * On entry, M specifies the number of rows of the matrix A. * M must be at least zero. * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the number of columns of the matrix A. * N must be at least zero. * Unchanged on exit. * * ALPHA - COMPLEX*16 . * On entry, ALPHA specifies the scalar alpha. * Unchanged on exit. * * X - COMPLEX*16 array of dimension at least * ( 1 + ( m - 1 )*abs( INCX ) ). * Before entry, the incremented array X must contain the m * 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. * * Y - COMPLEX*16 array of dimension at least * ( 1 + ( n - 1 )*abs( INCY ) ). * Before entry, the incremented array Y must contain the n * element vector y. * Unchanged on exit. * * INCY - INTEGER. * On entry, INCY specifies the increment for the elements of * Y. INCY must not be zero. * Unchanged on exit. * * A - COMPLEX*16 array of DIMENSION ( LDA, n ). * Before entry, the leading m by n part of the array A must * contain the matrix of coefficients. On exit, A is * overwritten by the updated matrix. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. LDA must be at least * max( 1, m ). * Unchanged on exit. * * * 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 .. COMPLEX*16 ZERO PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) ) * .. Local Scalars .. COMPLEX*16 TEMP INTEGER I, INFO, IX, J, JY, KX * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC DCONJG, MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( M.LT.0 )THEN INFO = 1 ELSE IF( N.LT.0 )THEN INFO = 2 ELSE IF( INCX.EQ.0 )THEN INFO = 5 ELSE IF( INCY.EQ.0 )THEN INFO = 7 ELSE IF( LDA.LT.MAX( 1, M ) )THEN INFO = 9 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'ZGERC ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( M.EQ.0 ).OR.( N.EQ.0 ).OR.( ALPHA.EQ.ZERO ) ) $ RETURN * * Start the operations. In this version the elements of A are * accessed sequentially with one pass through A. * IF( INCY.GT.0 )THEN JY = 1 ELSE JY = 1 - ( N - 1 )*INCY END IF IF( INCX.EQ.1 )THEN DO 20, J = 1, N IF( Y( JY ).NE.ZERO )THEN TEMP = ALPHA*DCONJG( Y( JY ) ) DO 10, I = 1, M A( I, J ) = A( I, J ) + X( I )*TEMP 10 CONTINUE END IF JY = JY + INCY 20 CONTINUE ELSE IF( INCX.GT.0 )THEN KX = 1 ELSE KX = 1 - ( M - 1 )*INCX END IF DO 40, J = 1, N IF( Y( JY ).NE.ZERO )THEN TEMP = ALPHA*DCONJG( Y( JY ) ) IX = KX DO 30, I = 1, M A( I, J ) = A( I, J ) + X( IX )*TEMP IX = IX + INCX 30 CONTINUE END IF JY = JY + INCY 40 CONTINUE END IF * RETURN * * End of ZGERC . * END subroutine drotg(da,db,c,s) c c construct givens plane rotation. c jack dongarra, linpack, 3/11/78. c double precision da,db,c,s,roe,scale,r,z c roe = db if( dabs(da) .gt. dabs(db) ) roe = da scale = dabs(da) + dabs(db) if( scale .ne. 0.0d0 ) go to 10 c = 1.0d0 s = 0.0d0 r = 0.0d0 z = 0.0d0 go to 20 10 r = scale*dsqrt((da/scale)**2 + (db/scale)**2) r = dsign(1.0d0,roe)*r c = da/r s = db/r z = 1.0d0 if( dabs(da) .gt. dabs(db) ) z = s if( dabs(db) .ge. dabs(da) .and. c .ne. 0.0d0 ) z = 1.0d0/c 20 da = r db = z return end subroutine drot (n,dx,incx,dy,incy,c,s) c c applies a plane rotation. c jack dongarra, linpack, 3/11/78. c modified 12/3/93, array(1) declarations changed to array(*) c double precision dx(*),dy(*),dtemp,c,s integer i,incx,incy,ix,iy,n c if(n.le.0)return if(incx.eq.1.and.incy.eq.1)go to 20 c c code for unequal increments or equal increments not equal c to 1 c ix = 1 iy = 1 if(incx.lt.0)ix = (-n+1)*incx + 1 if(incy.lt.0)iy = (-n+1)*incy + 1 do 10 i = 1,n dtemp = c*dx(ix) + s*dy(iy) dy(iy) = c*dy(iy) - s*dx(ix) dx(ix) = dtemp ix = ix + incx iy = iy + incy 10 continue return c c code for both increments equal to 1 c 20 do 30 i = 1,n dtemp = c*dx(i) + s*dy(i) dy(i) = c*dy(i) - s*dx(i) dx(i) = dtemp 30 continue return end