C ALGORITHM 828, COLLECTED ALGORITHMS FROM ACM. C THIS WORK PUBLISHED IN TRANSACTIONS ON MATHEMATICAL SOFTWARE, C VOL. 29,NO. 4, December, 2003, P. 458--468. #! /bin/sh # This is a shell archive, meaning: # 1. Remove everything above the #! /bin/sh line. # 2. Save the resulting text in a file. # 3. Execute the file with /bin/sh (not csh) to create the files: # Fortran77/ # Fortran77/Dp/ # Fortran77/Dp/Drivers/ # Fortran77/Dp/Drivers/Makefile # Fortran77/Dp/Drivers/data1 # Fortran77/Dp/Drivers/data2 # Fortran77/Dp/Drivers/data3 # Fortran77/Dp/Drivers/data4 # Fortran77/Dp/Drivers/data5 # Fortran77/Dp/Drivers/dblas.f # Fortran77/Dp/Drivers/driver.f # Fortran77/Dp/Drivers/interactive.f # Fortran77/Dp/Drivers/lapack.f # Fortran77/Dp/Drivers/res1 # Fortran77/Dp/Drivers/res1_1 # Fortran77/Dp/Drivers/res1_2 # Fortran77/Dp/Drivers/res2 # Fortran77/Dp/Drivers/res2_1 # Fortran77/Dp/Drivers/res2_2 # Fortran77/Dp/Drivers/res3 # Fortran77/Dp/Drivers/res3_1 # Fortran77/Dp/Drivers/res3_2 # Fortran77/Dp/Drivers/res4 # Fortran77/Dp/Drivers/res4_1 # Fortran77/Dp/Drivers/res4_2 # Fortran77/Dp/Drivers/res5 # Fortran77/Dp/Drivers/res5_1 # Fortran77/Dp/Drivers/res5_2 # Fortran77/Dp/Src/ # Fortran77/Dp/Src/src.f # This archive created: Fri Jan 23 09:47:26 2004 export PATH; PATH=/bin:$PATH if test ! -d 'Fortran77' then mkdir 'Fortran77' fi cd 'Fortran77' if test ! -d 'Dp' then mkdir 'Dp' fi cd 'Dp' if test ! -d 'Drivers' then mkdir 'Drivers' fi cd 'Drivers' if test -f 'Makefile' then echo shar: will not over-write existing file "'Makefile'" else cat << "SHAR_EOF" > 'Makefile' # This makefile is primarily for checking the implementation # against results already obtained. To do this efficiently the # interactive driver has been editted to take input from stdin # and put output on stdout. All the other files for PS plots are # generated by default and then overwritten. # # The file interactive.f is the original driver that prompts for # a data file and aske the user whether various other files should # be created. include makefile.inc all: Res1 Res2 Res3 Res4 Res5 SRCLIBS= $(LAPACK) $(BLAS) src.o: $(INCSRC)/src.f $(F77) $(F77OPTS) -c $(INCSRC)/src.f DRIVERS= driver RESULTS= Res1 Res2 Res3 Res4 Res5 Objs1= driver.o src.o driver: $(Objs1) $(F77LINK) $(F77LINKOPTS) -o driver $(Objs1) $(SRCLIBS) Res1: driver data1 ./driver Res1_1 mv dnsplin1.prt Res1_2 Res2: driver data2 ./driver Res2_1 mv dnsplin1.prt Res2_2 Res3: driver data3 ./driver Res3_1 mv dnsplin1.prt Res3_2 Res4: driver data4 ./driver Res4_1 mv dnsplin1.prt Res4_2 Res5: driver data5 ./driver Res5_1 mv dnsplin1.prt Res5_2 diffres: Res1 res1 Res1 res1 Res3 res3 Res4 res4 Res5 res5 echo "Differences in results from driver" $(DIFF) Res1 res1 echo "Differences in results from driver" $(DIFF) Res2 res2 echo "Differences in results from driver" $(DIFF) Res3 res3 echo "Differences in results from driver" $(DIFF) Res4 res4 echo "Differences in results from driver" $(DIFF) Res5 res5 clean: rm -rf *.o $(DRIVERS) $(CLEANUP) $(RESULTS) dnsplin1.ps\ dnsplin1.ps0 dnsplin1.ps2 SHAR_EOF fi # end of overwriting check if test -f 'data1' then echo shar: will not over-write existing file "'data1'" else cat << "SHAR_EOF" > 'data1' 7 Number of data points N (format I4) 0.0 Abscissa of first point (format D22.15) 1.0 Abscissa of second point (format D22.15) 2.0 3.0 4.0 5.0 6.0 0.0 Ordinate of first point (format D22.15) 1.9 Ordinate of second point (format D22.15) 2.7 2.6 1.6 0.8 1.2 0.025 Mesh width H (format D22.15) SHAR_EOF fi # end of overwriting check if test -f 'data2' then echo shar: will not over-write existing file "'data2'" else cat << "SHAR_EOF" > 'data2' 11 0.0 2.0 3.0 5.0 6.0 8.0 9.0 11.0 12.0 14.0 15.0 0.0 0.0 0.0 0.0 0.0 0.0 0.1 1.0 7.0 8.0 15.0 0.0625 SHAR_EOF fi # end of overwriting check if test -f 'data3' then echo shar: will not over-write existing file "'data3'" else cat << "SHAR_EOF" > 'data3' 9 7.99 8.09 8.19 8.70 9.20 10.0 12.0 15.0 20.0 0.0 .276429e-3 .437498 1.69183 4.69428 9.43740 9.98636 9.99919 9.99994 .05 SHAR_EOF fi # end of overwriting check if test -f 'data4' then echo shar: will not over-write existing file "'data4'" else cat << "SHAR_EOF" > 'data4' 10 0.0 1.0 1.5 2.5 4.0 4.5 5.5 6.0 8.0 10.0 10.0 8.0 5.0 4.0 3.5 3.4 6.0 7.1 8.0 8.5 .04 SHAR_EOF fi # end of overwriting check if test -f 'data5' then echo shar: will not over-write existing file "'data5'" else cat << "SHAR_EOF" > 'data5' 11 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.15 1.015 1.0 0.515 0.5 0.5 0.5 0.5 0.18 0.0 0.004 SHAR_EOF fi # end of overwriting check if test -f 'dblas.f' then echo shar: will not over-write existing file "'dblas.f'" else cat << "SHAR_EOF" > 'dblas.f' 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 DSYMM ( SIDE, UPLO, M, N, ALPHA, A, LDA, B, LDB, $ BETA, C, LDC ) * .. Scalar Arguments .. CHARACTER*1 SIDE, UPLO INTEGER M, N, LDA, LDB, LDC DOUBLE PRECISION ALPHA, BETA * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), B( LDB, * ), C( LDC, * ) * .. * * Purpose * ======= * * DSYMM performs one of the matrix-matrix operations * * C := alpha*A*B + beta*C, * * or * * C := alpha*B*A + beta*C, * * where alpha and beta are scalars, A is a symmetric matrix and B and * C are m by n matrices. * * Parameters * ========== * * SIDE - CHARACTER*1. * On entry, SIDE specifies whether the symmetric matrix A * appears on the left or right in the operation as follows: * * SIDE = 'L' or 'l' C := alpha*A*B + beta*C, * * SIDE = 'R' or 'r' C := alpha*B*A + beta*C, * * Unchanged on exit. * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the upper or lower * triangular part of the symmetric matrix A is to be * referenced as follows: * * UPLO = 'U' or 'u' Only the upper triangular part of the * symmetric matrix is to be referenced. * * UPLO = 'L' or 'l' Only the lower triangular part of the * symmetric matrix is to be referenced. * * Unchanged on exit. * * M - INTEGER. * On entry, M specifies the number of rows 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 C. * 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, ka ), where ka is * m when SIDE = 'L' or 'l' and is n otherwise. * Before entry with SIDE = 'L' or 'l', the m by m part of * the array A must contain the symmetric matrix, such that * when UPLO = 'U' or 'u', the leading m by m upper triangular * part of the array A must contain the upper triangular part * of the symmetric matrix and the strictly lower triangular * part of A is not referenced, and when UPLO = 'L' or 'l', * the leading m by m lower triangular part of the array A * must contain the lower triangular part of the symmetric * matrix and the strictly upper triangular part of A is not * referenced. * Before entry with SIDE = 'R' or 'r', the n by n part of * the array A must contain the symmetric matrix, such that * when UPLO = 'U' or 'u', the leading n by n upper triangular * part of the array A must contain the upper triangular part * of the symmetric matrix and the strictly lower triangular * part of A is not referenced, and when UPLO = 'L' or 'l', * the leading n by n lower triangular part of the array A * must contain the lower triangular part of the symmetric * matrix and the strictly upper triangular part of A is not * referenced. * Unchanged on exit. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. When SIDE = 'L' or 'l' then * LDA must be at least max( 1, m ), otherwise LDA must be at * least max( 1, n ). * Unchanged on exit. * * B - DOUBLE PRECISION array of DIMENSION ( LDB, n ). * Before entry, the leading m by n 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. LDB must be at least * max( 1, m ). * 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 updated * matrix. * * 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 UPPER INTEGER I, INFO, J, K, NROWA DOUBLE PRECISION TEMP1, TEMP2 * .. Parameters .. DOUBLE PRECISION ONE , ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Executable Statements .. * * Set NROWA as the number of rows of A. * IF( LSAME( SIDE, 'L' ) )THEN NROWA = M ELSE NROWA = N END IF UPPER = LSAME( UPLO, 'U' ) * * Test the input parameters. * INFO = 0 IF( ( .NOT.LSAME( SIDE, 'L' ) ).AND. $ ( .NOT.LSAME( SIDE, 'R' ) ) )THEN INFO = 1 ELSE IF( ( .NOT.UPPER ).AND. $ ( .NOT.LSAME( UPLO, 'L' ) ) )THEN INFO = 2 ELSE IF( M .LT.0 )THEN INFO = 3 ELSE IF( N .LT.0 )THEN INFO = 4 ELSE IF( LDA.LT.MAX( 1, NROWA ) )THEN INFO = 7 ELSE IF( LDB.LT.MAX( 1, M ) )THEN INFO = 9 ELSE IF( LDC.LT.MAX( 1, M ) )THEN INFO = 12 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'DSYMM ', 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 * * 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( LSAME( SIDE, 'L' ) )THEN * * Form C := alpha*A*B + beta*C. * IF( UPPER )THEN DO 70, J = 1, N DO 60, I = 1, M TEMP1 = ALPHA*B( I, J ) TEMP2 = ZERO DO 50, K = 1, I - 1 C( K, J ) = C( K, J ) + TEMP1 *A( K, I ) TEMP2 = TEMP2 + B( K, J )*A( K, I ) 50 CONTINUE IF( BETA.EQ.ZERO )THEN C( I, J ) = TEMP1*A( I, I ) + ALPHA*TEMP2 ELSE C( I, J ) = BETA *C( I, J ) + $ TEMP1*A( I, I ) + ALPHA*TEMP2 END IF 60 CONTINUE 70 CONTINUE ELSE DO 100, J = 1, N DO 90, I = M, 1, -1 TEMP1 = ALPHA*B( I, J ) TEMP2 = ZERO DO 80, K = I + 1, M C( K, J ) = C( K, J ) + TEMP1 *A( K, I ) TEMP2 = TEMP2 + B( K, J )*A( K, I ) 80 CONTINUE IF( BETA.EQ.ZERO )THEN C( I, J ) = TEMP1*A( I, I ) + ALPHA*TEMP2 ELSE C( I, J ) = BETA *C( I, J ) + $ TEMP1*A( I, I ) + ALPHA*TEMP2 END IF 90 CONTINUE 100 CONTINUE END IF ELSE * * Form C := alpha*B*A + beta*C. * DO 170, J = 1, N TEMP1 = ALPHA*A( J, J ) IF( BETA.EQ.ZERO )THEN DO 110, I = 1, M C( I, J ) = TEMP1*B( I, J ) 110 CONTINUE ELSE DO 120, I = 1, M C( I, J ) = BETA*C( I, J ) + TEMP1*B( I, J ) 120 CONTINUE END IF DO 140, K = 1, J - 1 IF( UPPER )THEN TEMP1 = ALPHA*A( K, J ) ELSE TEMP1 = ALPHA*A( J, K ) END IF DO 130, I = 1, M C( I, J ) = C( I, J ) + TEMP1*B( I, K ) 130 CONTINUE 140 CONTINUE DO 160, K = J + 1, N IF( UPPER )THEN TEMP1 = ALPHA*A( J, K ) ELSE TEMP1 = ALPHA*A( K, J ) END IF DO 150, I = 1, M C( I, J ) = C( I, J ) + TEMP1*B( I, K ) 150 CONTINUE 160 CONTINUE 170 CONTINUE END IF * RETURN * * End of DSYMM . * END SUBROUTINE DSYR2K( UPLO, TRANS, N, K, ALPHA, A, LDA, B, LDB, $ BETA, C, LDC ) * .. Scalar Arguments .. CHARACTER*1 UPLO, TRANS INTEGER N, K, LDA, LDB, LDC DOUBLE PRECISION ALPHA, BETA * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), B( LDB, * ), C( LDC, * ) * .. * * Purpose * ======= * * DSYR2K performs one of the symmetric rank 2k operations * * C := alpha*A*B' + alpha*B*A' + beta*C, * * or * * C := alpha*A'*B + alpha*B'*A + beta*C, * * where alpha and beta are scalars, C is an n by n symmetric matrix * and A and B are n by k matrices in the first case and k by n * matrices in the second case. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the upper or lower * triangular part of the array C is to be referenced as * follows: * * UPLO = 'U' or 'u' Only the upper triangular part of C * is to be referenced. * * UPLO = 'L' or 'l' Only the lower triangular part of C * is to be referenced. * * Unchanged on exit. * * TRANS - CHARACTER*1. * On entry, TRANS specifies the operation to be performed as * follows: * * TRANS = 'N' or 'n' C := alpha*A*B' + alpha*B*A' + * beta*C. * * TRANS = 'T' or 't' C := alpha*A'*B + alpha*B'*A + * beta*C. * * TRANS = 'C' or 'c' C := alpha*A'*B + alpha*B'*A + * beta*C. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix C. N must be * at least zero. * Unchanged on exit. * * K - INTEGER. * On entry with TRANS = 'N' or 'n', K specifies the number * of columns of the matrices A and B, and on entry with * TRANS = 'T' or 't' or 'C' or 'c', K specifies the number * of rows of the matrices A and 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 TRANS = 'N' or 'n', and is n otherwise. * Before entry with TRANS = 'N' or 'n', the leading n by k * part of the array A must contain the matrix A, otherwise * the leading k by n 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 TRANS = 'N' or 'n' * then LDA must be at least max( 1, n ), otherwise LDA must * be at least max( 1, k ). * Unchanged on exit. * * B - DOUBLE PRECISION array of DIMENSION ( LDB, kb ), where kb is * k when TRANS = 'N' or 'n', and is n otherwise. * Before entry with TRANS = 'N' or 'n', the leading n by k * part of the array B must contain the matrix B, otherwise * the leading k by n 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 TRANS = 'N' or 'n' * then LDB must be at least max( 1, n ), otherwise LDB must * be at least max( 1, k ). * Unchanged on exit. * * BETA - DOUBLE PRECISION. * On entry, BETA specifies the scalar beta. * Unchanged on exit. * * C - DOUBLE PRECISION array of DIMENSION ( LDC, n ). * Before entry with UPLO = 'U' or 'u', the leading n by n * upper triangular part of the array C must contain the upper * triangular part of the symmetric matrix and the strictly * lower triangular part of C is not referenced. On exit, the * upper triangular part of the array C is overwritten by the * upper triangular part of the updated matrix. * Before entry with UPLO = 'L' or 'l', the leading n by n * lower triangular part of the array C must contain the lower * triangular part of the symmetric matrix and the strictly * upper triangular part of C is not referenced. On exit, the * lower triangular part of the array C is overwritten by the * lower triangular part of the updated matrix. * * 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, n ). * 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 UPPER INTEGER I, INFO, J, L, NROWA DOUBLE PRECISION TEMP1, TEMP2 * .. Parameters .. DOUBLE PRECISION ONE , ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Executable Statements .. * * Test the input parameters. * IF( LSAME( TRANS, 'N' ) )THEN NROWA = N ELSE NROWA = K END IF UPPER = LSAME( UPLO, 'U' ) * INFO = 0 IF( ( .NOT.UPPER ).AND. $ ( .NOT.LSAME( UPLO , 'L' ) ) )THEN INFO = 1 ELSE IF( ( .NOT.LSAME( TRANS, 'N' ) ).AND. $ ( .NOT.LSAME( TRANS, 'T' ) ).AND. $ ( .NOT.LSAME( TRANS, 'C' ) ) )THEN INFO = 2 ELSE IF( N .LT.0 )THEN INFO = 3 ELSE IF( K .LT.0 )THEN INFO = 4 ELSE IF( LDA.LT.MAX( 1, NROWA ) )THEN INFO = 7 ELSE IF( LDB.LT.MAX( 1, NROWA ) )THEN INFO = 9 ELSE IF( LDC.LT.MAX( 1, N ) )THEN INFO = 12 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'DSYR2K', INFO ) RETURN END IF * * Quick return if possible. * IF( ( 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( UPPER )THEN IF( BETA.EQ.ZERO )THEN DO 20, J = 1, N DO 10, I = 1, J C( I, J ) = ZERO 10 CONTINUE 20 CONTINUE ELSE DO 40, J = 1, N DO 30, I = 1, J C( I, J ) = BETA*C( I, J ) 30 CONTINUE 40 CONTINUE END IF ELSE IF( BETA.EQ.ZERO )THEN DO 60, J = 1, N DO 50, I = J, N C( I, J ) = ZERO 50 CONTINUE 60 CONTINUE ELSE DO 80, J = 1, N DO 70, I = J, N C( I, J ) = BETA*C( I, J ) 70 CONTINUE 80 CONTINUE END IF END IF RETURN END IF * * Start the operations. * IF( LSAME( TRANS, 'N' ) )THEN * * Form C := alpha*A*B' + alpha*B*A' + C. * IF( UPPER )THEN DO 130, J = 1, N IF( BETA.EQ.ZERO )THEN DO 90, I = 1, J C( I, J ) = ZERO 90 CONTINUE ELSE IF( BETA.NE.ONE )THEN DO 100, I = 1, J C( I, J ) = BETA*C( I, J ) 100 CONTINUE END IF DO 120, L = 1, K IF( ( A( J, L ).NE.ZERO ).OR. $ ( B( J, L ).NE.ZERO ) )THEN TEMP1 = ALPHA*B( J, L ) TEMP2 = ALPHA*A( J, L ) DO 110, I = 1, J C( I, J ) = C( I, J ) + $ A( I, L )*TEMP1 + B( I, L )*TEMP2 110 CONTINUE END IF 120 CONTINUE 130 CONTINUE ELSE DO 180, J = 1, N IF( BETA.EQ.ZERO )THEN DO 140, I = J, N C( I, J ) = ZERO 140 CONTINUE ELSE IF( BETA.NE.ONE )THEN DO 150, I = J, N C( I, J ) = BETA*C( I, J ) 150 CONTINUE END IF DO 170, L = 1, K IF( ( A( J, L ).NE.ZERO ).OR. $ ( B( J, L ).NE.ZERO ) )THEN TEMP1 = ALPHA*B( J, L ) TEMP2 = ALPHA*A( J, L ) DO 160, I = J, N C( I, J ) = C( I, J ) + $ A( I, L )*TEMP1 + B( I, L )*TEMP2 160 CONTINUE END IF 170 CONTINUE 180 CONTINUE END IF ELSE * * Form C := alpha*A'*B + alpha*B'*A + C. * IF( UPPER )THEN DO 210, J = 1, N DO 200, I = 1, J TEMP1 = ZERO TEMP2 = ZERO DO 190, L = 1, K TEMP1 = TEMP1 + A( L, I )*B( L, J ) TEMP2 = TEMP2 + B( L, I )*A( L, J ) 190 CONTINUE IF( BETA.EQ.ZERO )THEN C( I, J ) = ALPHA*TEMP1 + ALPHA*TEMP2 ELSE C( I, J ) = BETA *C( I, J ) + $ ALPHA*TEMP1 + ALPHA*TEMP2 END IF 200 CONTINUE 210 CONTINUE ELSE DO 240, J = 1, N DO 230, I = J, N TEMP1 = ZERO TEMP2 = ZERO DO 220, L = 1, K TEMP1 = TEMP1 + A( L, I )*B( L, J ) TEMP2 = TEMP2 + B( L, I )*A( L, J ) 220 CONTINUE IF( BETA.EQ.ZERO )THEN C( I, J ) = ALPHA*TEMP1 + ALPHA*TEMP2 ELSE C( I, J ) = BETA *C( I, J ) + $ ALPHA*TEMP1 + ALPHA*TEMP2 END IF 230 CONTINUE 240 CONTINUE END IF END IF * RETURN * * End of DSYR2K. * END SUBROUTINE DSYRK ( UPLO, TRANS, N, K, ALPHA, A, LDA, $ BETA, C, LDC ) * .. Scalar Arguments .. CHARACTER*1 UPLO, TRANS INTEGER N, K, LDA, LDC DOUBLE PRECISION ALPHA, BETA * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), C( LDC, * ) * .. * * Purpose * ======= * * DSYRK performs one of the symmetric rank k operations * * C := alpha*A*A' + beta*C, * * or * * C := alpha*A'*A + beta*C, * * where alpha and beta are scalars, C is an n by n symmetric matrix * and A is an n by k matrix in the first case and a k by n matrix * in the second case. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the upper or lower * triangular part of the array C is to be referenced as * follows: * * UPLO = 'U' or 'u' Only the upper triangular part of C * is to be referenced. * * UPLO = 'L' or 'l' Only the lower triangular part of C * is to be referenced. * * Unchanged on exit. * * TRANS - CHARACTER*1. * On entry, TRANS specifies the operation to be performed as * follows: * * TRANS = 'N' or 'n' C := alpha*A*A' + beta*C. * * TRANS = 'T' or 't' C := alpha*A'*A + beta*C. * * TRANS = 'C' or 'c' C := alpha*A'*A + beta*C. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix C. N must be * at least zero. * Unchanged on exit. * * K - INTEGER. * On entry with TRANS = 'N' or 'n', K specifies the number * of columns of the matrix A, and on entry with * TRANS = 'T' or 't' or 'C' or 'c', K specifies the number * of rows of the matrix A. 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 TRANS = 'N' or 'n', and is n otherwise. * Before entry with TRANS = 'N' or 'n', the leading n by k * part of the array A must contain the matrix A, otherwise * the leading k by n 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 TRANS = 'N' or 'n' * then LDA must be at least max( 1, n ), otherwise LDA must * be at least max( 1, k ). * Unchanged on exit. * * BETA - DOUBLE PRECISION. * On entry, BETA specifies the scalar beta. * Unchanged on exit. * * C - DOUBLE PRECISION array of DIMENSION ( LDC, n ). * Before entry with UPLO = 'U' or 'u', the leading n by n * upper triangular part of the array C must contain the upper * triangular part of the symmetric matrix and the strictly * lower triangular part of C is not referenced. On exit, the * upper triangular part of the array C is overwritten by the * upper triangular part of the updated matrix. * Before entry with UPLO = 'L' or 'l', the leading n by n * lower triangular part of the array C must contain the lower * triangular part of the symmetric matrix and the strictly * upper triangular part of C is not referenced. On exit, the * lower triangular part of the array C is overwritten by the * lower triangular part of the updated matrix. * * 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, n ). * 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 UPPER INTEGER I, INFO, J, L, NROWA DOUBLE PRECISION TEMP * .. Parameters .. DOUBLE PRECISION ONE , ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Executable Statements .. * * Test the input parameters. * IF( LSAME( TRANS, 'N' ) )THEN NROWA = N ELSE NROWA = K END IF UPPER = LSAME( UPLO, 'U' ) * INFO = 0 IF( ( .NOT.UPPER ).AND. $ ( .NOT.LSAME( UPLO , 'L' ) ) )THEN INFO = 1 ELSE IF( ( .NOT.LSAME( TRANS, 'N' ) ).AND. $ ( .NOT.LSAME( TRANS, 'T' ) ).AND. $ ( .NOT.LSAME( TRANS, 'C' ) ) )THEN INFO = 2 ELSE IF( N .LT.0 )THEN INFO = 3 ELSE IF( K .LT.0 )THEN INFO = 4 ELSE IF( LDA.LT.MAX( 1, NROWA ) )THEN INFO = 7 ELSE IF( LDC.LT.MAX( 1, N ) )THEN INFO = 10 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'DSYRK ', INFO ) RETURN END IF * * Quick return if possible. * IF( ( 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( UPPER )THEN IF( BETA.EQ.ZERO )THEN DO 20, J = 1, N DO 10, I = 1, J C( I, J ) = ZERO 10 CONTINUE 20 CONTINUE ELSE DO 40, J = 1, N DO 30, I = 1, J C( I, J ) = BETA*C( I, J ) 30 CONTINUE 40 CONTINUE END IF ELSE IF( BETA.EQ.ZERO )THEN DO 60, J = 1, N DO 50, I = J, N C( I, J ) = ZERO 50 CONTINUE 60 CONTINUE ELSE DO 80, J = 1, N DO 70, I = J, N C( I, J ) = BETA*C( I, J ) 70 CONTINUE 80 CONTINUE END IF END IF RETURN END IF * * Start the operations. * IF( LSAME( TRANS, 'N' ) )THEN * * Form C := alpha*A*A' + beta*C. * IF( UPPER )THEN DO 130, J = 1, N IF( BETA.EQ.ZERO )THEN DO 90, I = 1, J C( I, J ) = ZERO 90 CONTINUE ELSE IF( BETA.NE.ONE )THEN DO 100, I = 1, J C( I, J ) = BETA*C( I, J ) 100 CONTINUE END IF DO 120, L = 1, K IF( A( J, L ).NE.ZERO )THEN TEMP = ALPHA*A( J, L ) DO 110, I = 1, J C( I, J ) = C( I, J ) + TEMP*A( I, L ) 110 CONTINUE END IF 120 CONTINUE 130 CONTINUE ELSE DO 180, J = 1, N IF( BETA.EQ.ZERO )THEN DO 140, I = J, N C( I, J ) = ZERO 140 CONTINUE ELSE IF( BETA.NE.ONE )THEN DO 150, I = J, N C( I, J ) = BETA*C( I, J ) 150 CONTINUE END IF DO 170, L = 1, K IF( A( J, L ).NE.ZERO )THEN TEMP = ALPHA*A( J, L ) DO 160, I = J, N C( I, J ) = C( I, J ) + TEMP*A( I, L ) 160 CONTINUE END IF 170 CONTINUE 180 CONTINUE END IF ELSE * * Form C := alpha*A'*A + beta*C. * IF( UPPER )THEN DO 210, J = 1, N DO 200, I = 1, J TEMP = ZERO DO 190, L = 1, K TEMP = TEMP + A( L, I )*A( L, J ) 190 CONTINUE IF( BETA.EQ.ZERO )THEN C( I, J ) = ALPHA*TEMP ELSE C( I, J ) = ALPHA*TEMP + BETA*C( I, J ) END IF 200 CONTINUE 210 CONTINUE ELSE DO 240, J = 1, N DO 230, I = J, N TEMP = ZERO DO 220, L = 1, K TEMP = TEMP + A( L, I )*A( L, J ) 220 CONTINUE IF( BETA.EQ.ZERO )THEN C( I, J ) = ALPHA*TEMP ELSE C( I, J ) = ALPHA*TEMP + BETA*C( I, J ) END IF 230 CONTINUE 240 CONTINUE END IF END IF * RETURN * * End of DSYRK . * END SUBROUTINE DTRMM ( SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, $ B, LDB ) * .. Scalar Arguments .. CHARACTER*1 SIDE, UPLO, TRANSA, DIAG INTEGER M, N, LDA, LDB DOUBLE PRECISION ALPHA * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), B( LDB, * ) * .. * * Purpose * ======= * * DTRMM performs one of the matrix-matrix operations * * B := alpha*op( A )*B, or B := alpha*B*op( A ), * * where alpha is a scalar, B is an m by n matrix, A is a unit, or * non-unit, upper or lower triangular matrix and op( A ) is one of * * op( A ) = A or op( A ) = A'. * * Parameters * ========== * * SIDE - CHARACTER*1. * On entry, SIDE specifies whether op( A ) multiplies B from * the left or right as follows: * * SIDE = 'L' or 'l' B := alpha*op( A )*B. * * SIDE = 'R' or 'r' B := alpha*B*op( A ). * * Unchanged on exit. * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the matrix A is an upper or * lower triangular matrix as follows: * * UPLO = 'U' or 'u' A is an upper triangular matrix. * * UPLO = 'L' or 'l' A is a lower triangular matrix. * * Unchanged on exit. * * 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. * * DIAG - CHARACTER*1. * On entry, DIAG specifies whether or not A is unit triangular * as follows: * * DIAG = 'U' or 'u' A is assumed to be unit triangular. * * DIAG = 'N' or 'n' A is not assumed to be unit * triangular. * * Unchanged on exit. * * M - INTEGER. * On entry, M specifies the number of rows of B. M must be at * least zero. * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the number of columns of B. N must be * at least zero. * Unchanged on exit. * * ALPHA - DOUBLE PRECISION. * On entry, ALPHA specifies the scalar alpha. When alpha is * zero then A is not referenced and B need not be set before * entry. * Unchanged on exit. * * A - DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m * when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'. * Before entry with UPLO = 'U' or 'u', the leading k by k * upper triangular part of the array A must contain the upper * triangular matrix and the strictly lower triangular part of * A is not referenced. * Before entry with UPLO = 'L' or 'l', the leading k by k * lower triangular part of the array A must contain the lower * triangular matrix and the strictly upper triangular part of * A is not referenced. * Note that when DIAG = 'U' or 'u', the diagonal elements of * A are not referenced either, but are assumed to be unity. * Unchanged on exit. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. When SIDE = 'L' or 'l' then * LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' * then LDA must be at least max( 1, n ). * Unchanged on exit. * * B - DOUBLE PRECISION array of DIMENSION ( LDB, n ). * Before entry, the leading m by n part of the array B must * contain the matrix B, and on exit is overwritten by the * transformed matrix. * * LDB - INTEGER. * On entry, LDB specifies the first dimension of B as declared * in the calling (sub) program. LDB 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 LSIDE, NOUNIT, UPPER INTEGER I, INFO, J, K, NROWA DOUBLE PRECISION TEMP * .. Parameters .. DOUBLE PRECISION ONE , ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Executable Statements .. * * Test the input parameters. * LSIDE = LSAME( SIDE , 'L' ) IF( LSIDE )THEN NROWA = M ELSE NROWA = N END IF NOUNIT = LSAME( DIAG , 'N' ) UPPER = LSAME( UPLO , 'U' ) * INFO = 0 IF( ( .NOT.LSIDE ).AND. $ ( .NOT.LSAME( SIDE , 'R' ) ) )THEN INFO = 1 ELSE IF( ( .NOT.UPPER ).AND. $ ( .NOT.LSAME( UPLO , 'L' ) ) )THEN INFO = 2 ELSE IF( ( .NOT.LSAME( TRANSA, 'N' ) ).AND. $ ( .NOT.LSAME( TRANSA, 'T' ) ).AND. $ ( .NOT.LSAME( TRANSA, 'C' ) ) )THEN INFO = 3 ELSE IF( ( .NOT.LSAME( DIAG , 'U' ) ).AND. $ ( .NOT.LSAME( DIAG , 'N' ) ) )THEN INFO = 4 ELSE IF( M .LT.0 )THEN INFO = 5 ELSE IF( N .LT.0 )THEN INFO = 6 ELSE IF( LDA.LT.MAX( 1, NROWA ) )THEN INFO = 9 ELSE IF( LDB.LT.MAX( 1, M ) )THEN INFO = 11 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'DTRMM ', INFO ) RETURN END IF * * Quick return if possible. * IF( N.EQ.0 ) $ RETURN * * And when alpha.eq.zero. * IF( ALPHA.EQ.ZERO )THEN DO 20, J = 1, N DO 10, I = 1, M B( I, J ) = ZERO 10 CONTINUE 20 CONTINUE RETURN END IF * * Start the operations. * IF( LSIDE )THEN IF( LSAME( TRANSA, 'N' ) )THEN * * Form B := alpha*A*B. * IF( UPPER )THEN DO 50, J = 1, N DO 40, K = 1, M IF( B( K, J ).NE.ZERO )THEN TEMP = ALPHA*B( K, J ) DO 30, I = 1, K - 1 B( I, J ) = B( I, J ) + TEMP*A( I, K ) 30 CONTINUE IF( NOUNIT ) $ TEMP = TEMP*A( K, K ) B( K, J ) = TEMP END IF 40 CONTINUE 50 CONTINUE ELSE DO 80, J = 1, N DO 70 K = M, 1, -1 IF( B( K, J ).NE.ZERO )THEN TEMP = ALPHA*B( K, J ) B( K, J ) = TEMP IF( NOUNIT ) $ B( K, J ) = B( K, J )*A( K, K ) DO 60, I = K + 1, M B( I, J ) = B( I, J ) + TEMP*A( I, K ) 60 CONTINUE END IF 70 CONTINUE 80 CONTINUE END IF ELSE * * Form B := alpha*A'*B. * IF( UPPER )THEN DO 110, J = 1, N DO 100, I = M, 1, -1 TEMP = B( I, J ) IF( NOUNIT ) $ TEMP = TEMP*A( I, I ) DO 90, K = 1, I - 1 TEMP = TEMP + A( K, I )*B( K, J ) 90 CONTINUE B( I, J ) = ALPHA*TEMP 100 CONTINUE 110 CONTINUE ELSE DO 140, J = 1, N DO 130, I = 1, M TEMP = B( I, J ) IF( NOUNIT ) $ TEMP = TEMP*A( I, I ) DO 120, K = I + 1, M TEMP = TEMP + A( K, I )*B( K, J ) 120 CONTINUE B( I, J ) = ALPHA*TEMP 130 CONTINUE 140 CONTINUE END IF END IF ELSE IF( LSAME( TRANSA, 'N' ) )THEN * * Form B := alpha*B*A. * IF( UPPER )THEN DO 180, J = N, 1, -1 TEMP = ALPHA IF( NOUNIT ) $ TEMP = TEMP*A( J, J ) DO 150, I = 1, M B( I, J ) = TEMP*B( I, J ) 150 CONTINUE DO 170, K = 1, J - 1 IF( A( K, J ).NE.ZERO )THEN TEMP = ALPHA*A( K, J ) DO 160, I = 1, M B( I, J ) = B( I, J ) + TEMP*B( I, K ) 160 CONTINUE END IF 170 CONTINUE 180 CONTINUE ELSE DO 220, J = 1, N TEMP = ALPHA IF( NOUNIT ) $ TEMP = TEMP*A( J, J ) DO 190, I = 1, M B( I, J ) = TEMP*B( I, J ) 190 CONTINUE DO 210, K = J + 1, N IF( A( K, J ).NE.ZERO )THEN TEMP = ALPHA*A( K, J ) DO 200, I = 1, M B( I, J ) = B( I, J ) + TEMP*B( I, K ) 200 CONTINUE END IF 210 CONTINUE 220 CONTINUE END IF ELSE * * Form B := alpha*B*A'. * IF( UPPER )THEN DO 260, K = 1, N DO 240, J = 1, K - 1 IF( A( J, K ).NE.ZERO )THEN TEMP = ALPHA*A( J, K ) DO 230, I = 1, M B( I, J ) = B( I, J ) + TEMP*B( I, K ) 230 CONTINUE END IF 240 CONTINUE TEMP = ALPHA IF( NOUNIT ) $ TEMP = TEMP*A( K, K ) IF( TEMP.NE.ONE )THEN DO 250, I = 1, M B( I, K ) = TEMP*B( I, K ) 250 CONTINUE END IF 260 CONTINUE ELSE DO 300, K = N, 1, -1 DO 280, J = K + 1, N IF( A( J, K ).NE.ZERO )THEN TEMP = ALPHA*A( J, K ) DO 270, I = 1, M B( I, J ) = B( I, J ) + TEMP*B( I, K ) 270 CONTINUE END IF 280 CONTINUE TEMP = ALPHA IF( NOUNIT ) $ TEMP = TEMP*A( K, K ) IF( TEMP.NE.ONE )THEN DO 290, I = 1, M B( I, K ) = TEMP*B( I, K ) 290 CONTINUE END IF 300 CONTINUE END IF END IF END IF * RETURN * * End of DTRMM . * END SUBROUTINE DTRSM ( SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, $ B, LDB ) * .. Scalar Arguments .. CHARACTER*1 SIDE, UPLO, TRANSA, DIAG INTEGER M, N, LDA, LDB DOUBLE PRECISION ALPHA * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), B( LDB, * ) * .. * * Purpose * ======= * * DTRSM solves one of the matrix equations * * op( A )*X = alpha*B, or X*op( A ) = alpha*B, * * where alpha is a scalar, X and B are m by n matrices, A is a unit, or * non-unit, upper or lower triangular matrix and op( A ) is one of * * op( A ) = A or op( A ) = A'. * * The matrix X is overwritten on B. * * Parameters * ========== * * SIDE - CHARACTER*1. * On entry, SIDE specifies whether op( A ) appears on the left * or right of X as follows: * * SIDE = 'L' or 'l' op( A )*X = alpha*B. * * SIDE = 'R' or 'r' X*op( A ) = alpha*B. * * Unchanged on exit. * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the matrix A is an upper or * lower triangular matrix as follows: * * UPLO = 'U' or 'u' A is an upper triangular matrix. * * UPLO = 'L' or 'l' A is a lower triangular matrix. * * Unchanged on exit. * * 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. * * DIAG - CHARACTER*1. * On entry, DIAG specifies whether or not A is unit triangular * as follows: * * DIAG = 'U' or 'u' A is assumed to be unit triangular. * * DIAG = 'N' or 'n' A is not assumed to be unit * triangular. * * Unchanged on exit. * * M - INTEGER. * On entry, M specifies the number of rows of B. M must be at * least zero. * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the number of columns of B. N must be * at least zero. * Unchanged on exit. * * ALPHA - DOUBLE PRECISION. * On entry, ALPHA specifies the scalar alpha. When alpha is * zero then A is not referenced and B need not be set before * entry. * Unchanged on exit. * * A - DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m * when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'. * Before entry with UPLO = 'U' or 'u', the leading k by k * upper triangular part of the array A must contain the upper * triangular matrix and the strictly lower triangular part of * A is not referenced. * Before entry with UPLO = 'L' or 'l', the leading k by k * lower triangular part of the array A must contain the lower * triangular matrix and the strictly upper triangular part of * A is not referenced. * Note that when DIAG = 'U' or 'u', the diagonal elements of * A are not referenced either, but are assumed to be unity. * Unchanged on exit. * * LDA - INTEGER. * On entry, LDA specifies the first dimension of A as declared * in the calling (sub) program. When SIDE = 'L' or 'l' then * LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' * then LDA must be at least max( 1, n ). * Unchanged on exit. * * B - DOUBLE PRECISION array of DIMENSION ( LDB, n ). * Before entry, the leading m by n part of the array B must * contain the right-hand side matrix B, and on exit is * overwritten by the solution matrix X. * * LDB - INTEGER. * On entry, LDB specifies the first dimension of B as declared * in the calling (sub) program. LDB 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 LSIDE, NOUNIT, UPPER INTEGER I, INFO, J, K, NROWA DOUBLE PRECISION TEMP * .. Parameters .. DOUBLE PRECISION ONE , ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Executable Statements .. * * Test the input parameters. * LSIDE = LSAME( SIDE , 'L' ) IF( LSIDE )THEN NROWA = M ELSE NROWA = N END IF NOUNIT = LSAME( DIAG , 'N' ) UPPER = LSAME( UPLO , 'U' ) * INFO = 0 IF( ( .NOT.LSIDE ).AND. $ ( .NOT.LSAME( SIDE , 'R' ) ) )THEN INFO = 1 ELSE IF( ( .NOT.UPPER ).AND. $ ( .NOT.LSAME( UPLO , 'L' ) ) )THEN INFO = 2 ELSE IF( ( .NOT.LSAME( TRANSA, 'N' ) ).AND. $ ( .NOT.LSAME( TRANSA, 'T' ) ).AND. $ ( .NOT.LSAME( TRANSA, 'C' ) ) )THEN INFO = 3 ELSE IF( ( .NOT.LSAME( DIAG , 'U' ) ).AND. $ ( .NOT.LSAME( DIAG , 'N' ) ) )THEN INFO = 4 ELSE IF( M .LT.0 )THEN INFO = 5 ELSE IF( N .LT.0 )THEN INFO = 6 ELSE IF( LDA.LT.MAX( 1, NROWA ) )THEN INFO = 9 ELSE IF( LDB.LT.MAX( 1, M ) )THEN INFO = 11 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'DTRSM ', INFO ) RETURN END IF * * Quick return if possible. * IF( N.EQ.0 ) $ RETURN * * And when alpha.eq.zero. * IF( ALPHA.EQ.ZERO )THEN DO 20, J = 1, N DO 10, I = 1, M B( I, J ) = ZERO 10 CONTINUE 20 CONTINUE RETURN END IF * * Start the operations. * IF( LSIDE )THEN IF( LSAME( TRANSA, 'N' ) )THEN * * Form B := alpha*inv( A )*B. * IF( UPPER )THEN DO 60, J = 1, N IF( ALPHA.NE.ONE )THEN DO 30, I = 1, M B( I, J ) = ALPHA*B( I, J ) 30 CONTINUE END IF DO 50, K = M, 1, -1 IF( B( K, J ).NE.ZERO )THEN IF( NOUNIT ) $ B( K, J ) = B( K, J )/A( K, K ) DO 40, I = 1, K - 1 B( I, J ) = B( I, J ) - B( K, J )*A( I, K ) 40 CONTINUE END IF 50 CONTINUE 60 CONTINUE ELSE DO 100, J = 1, N IF( ALPHA.NE.ONE )THEN DO 70, I = 1, M B( I, J ) = ALPHA*B( I, J ) 70 CONTINUE END IF DO 90 K = 1, M IF( B( K, J ).NE.ZERO )THEN IF( NOUNIT ) $ B( K, J ) = B( K, J )/A( K, K ) DO 80, I = K + 1, M B( I, J ) = B( I, J ) - B( K, J )*A( I, K ) 80 CONTINUE END IF 90 CONTINUE 100 CONTINUE END IF ELSE * * Form B := alpha*inv( A' )*B. * IF( UPPER )THEN DO 130, J = 1, N DO 120, I = 1, M TEMP = ALPHA*B( I, J ) DO 110, K = 1, I - 1 TEMP = TEMP - A( K, I )*B( K, J ) 110 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/A( I, I ) B( I, J ) = TEMP 120 CONTINUE 130 CONTINUE ELSE DO 160, J = 1, N DO 150, I = M, 1, -1 TEMP = ALPHA*B( I, J ) DO 140, K = I + 1, M TEMP = TEMP - A( K, I )*B( K, J ) 140 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/A( I, I ) B( I, J ) = TEMP 150 CONTINUE 160 CONTINUE END IF END IF ELSE IF( LSAME( TRANSA, 'N' ) )THEN * * Form B := alpha*B*inv( A ). * IF( UPPER )THEN DO 210, J = 1, N IF( ALPHA.NE.ONE )THEN DO 170, I = 1, M B( I, J ) = ALPHA*B( I, J ) 170 CONTINUE END IF DO 190, K = 1, J - 1 IF( A( K, J ).NE.ZERO )THEN DO 180, I = 1, M B( I, J ) = B( I, J ) - A( K, J )*B( I, K ) 180 CONTINUE END IF 190 CONTINUE IF( NOUNIT )THEN TEMP = ONE/A( J, J ) DO 200, I = 1, M B( I, J ) = TEMP*B( I, J ) 200 CONTINUE END IF 210 CONTINUE ELSE DO 260, J = N, 1, -1 IF( ALPHA.NE.ONE )THEN DO 220, I = 1, M B( I, J ) = ALPHA*B( I, J ) 220 CONTINUE END IF DO 240, K = J + 1, N IF( A( K, J ).NE.ZERO )THEN DO 230, I = 1, M B( I, J ) = B( I, J ) - A( K, J )*B( I, K ) 230 CONTINUE END IF 240 CONTINUE IF( NOUNIT )THEN TEMP = ONE/A( J, J ) DO 250, I = 1, M B( I, J ) = TEMP*B( I, J ) 250 CONTINUE END IF 260 CONTINUE END IF ELSE * * Form B := alpha*B*inv( A' ). * IF( UPPER )THEN DO 310, K = N, 1, -1 IF( NOUNIT )THEN TEMP = ONE/A( K, K ) DO 270, I = 1, M B( I, K ) = TEMP*B( I, K ) 270 CONTINUE END IF DO 290, J = 1, K - 1 IF( A( J, K ).NE.ZERO )THEN TEMP = A( J, K ) DO 280, I = 1, M B( I, J ) = B( I, J ) - TEMP*B( I, K ) 280 CONTINUE END IF 290 CONTINUE IF( ALPHA.NE.ONE )THEN DO 300, I = 1, M B( I, K ) = ALPHA*B( I, K ) 300 CONTINUE END IF 310 CONTINUE ELSE DO 360, K = 1, N IF( NOUNIT )THEN TEMP = ONE/A( K, K ) DO 320, I = 1, M B( I, K ) = TEMP*B( I, K ) 320 CONTINUE END IF DO 340, J = K + 1, N IF( A( J, K ).NE.ZERO )THEN TEMP = A( J, K ) DO 330, I = 1, M B( I, J ) = B( I, J ) - TEMP*B( I, K ) 330 CONTINUE END IF 340 CONTINUE IF( ALPHA.NE.ONE )THEN DO 350, I = 1, M B( I, K ) = ALPHA*B( I, K ) 350 CONTINUE END IF 360 CONTINUE END IF END IF END IF * RETURN * * End of DTRSM . * 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 DSYR ( UPLO, N, ALPHA, X, INCX, A, LDA ) * .. Scalar Arguments .. DOUBLE PRECISION ALPHA INTEGER INCX, LDA, N CHARACTER*1 UPLO * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), X( * ) * .. * * Purpose * ======= * * DSYR 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. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the upper or lower * triangular part of the array A is to be referenced as * follows: * * UPLO = 'U' or 'u' Only the upper triangular part of A * is to be referenced. * * UPLO = 'L' or 'l' Only the lower triangular part of A * is to be referenced. * * 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. * * A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). * Before entry with UPLO = 'U' or 'u', the leading n by n * upper triangular part of the array A must contain the upper * triangular part of the symmetric matrix and the strictly * lower triangular part of A is not referenced. On exit, the * upper triangular part of the array A is overwritten by the * upper triangular part of the updated matrix. * Before entry with UPLO = 'L' or 'l', the leading n by n * lower triangular part of the array A must contain the lower * triangular part of the symmetric matrix and the strictly * upper triangular part of A is not referenced. On exit, the * lower triangular part of the array A is overwritten by the * lower triangular part of 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, n ). * 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, JX, KX * .. 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( 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( LDA.LT.MAX( 1, N ) )THEN INFO = 7 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'DSYR ', 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 A are * accessed sequentially with one pass through the triangular part * of A. * IF( LSAME( UPLO, 'U' ) )THEN * * Form A when A is stored in upper triangle. * IF( INCX.EQ.1 )THEN DO 20, J = 1, N IF( X( J ).NE.ZERO )THEN TEMP = ALPHA*X( J ) DO 10, I = 1, J A( I, J ) = A( I, J ) + X( I )*TEMP 10 CONTINUE END IF 20 CONTINUE ELSE JX = KX DO 40, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = ALPHA*X( JX ) IX = KX DO 30, I = 1, J A( I, J ) = A( I, J ) + X( IX )*TEMP IX = IX + INCX 30 CONTINUE END IF JX = JX + INCX 40 CONTINUE END IF ELSE * * Form A when A is stored in lower triangle. * IF( INCX.EQ.1 )THEN DO 60, J = 1, N IF( X( J ).NE.ZERO )THEN TEMP = ALPHA*X( J ) DO 50, I = J, N A( I, J ) = A( I, J ) + X( I )*TEMP 50 CONTINUE END IF 60 CONTINUE ELSE JX = KX DO 80, J = 1, N IF( X( JX ).NE.ZERO )THEN TEMP = ALPHA*X( JX ) IX = JX DO 70, I = J, N A( I, J ) = A( I, J ) + X( IX )*TEMP IX = IX + INCX 70 CONTINUE END IF JX = JX + INCX 80 CONTINUE END IF END IF * RETURN * * End of DSYR . * END SUBROUTINE DTBSV ( UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX ) * .. Scalar Arguments .. INTEGER INCX, K, LDA, N CHARACTER*1 DIAG, TRANS, UPLO * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), X( * ) * .. * * Purpose * ======= * * DTBSV solves one of the systems of equations * * A*x = b, or A'*x = b, * * where b and x are n element vectors and A is an n by n unit, or * non-unit, upper or lower triangular band matrix, with ( k + 1 ) * diagonals. * * No test for singularity or near-singularity is included in this * routine. Such tests must be performed before calling this routine. * * Parameters * ========== * * UPLO - CHARACTER*1. * On entry, UPLO specifies whether the matrix is an upper or * lower triangular matrix as follows: * * UPLO = 'U' or 'u' A is an upper triangular matrix. * * UPLO = 'L' or 'l' A is a lower triangular matrix. * * Unchanged on exit. * * TRANS - CHARACTER*1. * On entry, TRANS specifies the equations to be solved as * follows: * * TRANS = 'N' or 'n' A*x = b. * * TRANS = 'T' or 't' A'*x = b. * * TRANS = 'C' or 'c' A'*x = b. * * Unchanged on exit. * * DIAG - CHARACTER*1. * On entry, DIAG specifies whether or not A is unit * triangular as follows: * * DIAG = 'U' or 'u' A is assumed to be unit triangular. * * DIAG = 'N' or 'n' A is not assumed to be unit * triangular. * * Unchanged on exit. * * N - INTEGER. * On entry, N specifies the order of the matrix A. * N must be at least zero. * Unchanged on exit. * * K - INTEGER. * On entry with UPLO = 'U' or 'u', K specifies the number of * super-diagonals of the matrix A. * On entry with UPLO = 'L' or 'l', K specifies the number of * sub-diagonals of the matrix A. * K must satisfy 0 .le. K. * Unchanged on exit. * * A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). * Before entry with UPLO = 'U' or 'u', the leading ( k + 1 ) * by n part of the array A must contain the upper triangular * band part of the matrix of coefficients, supplied column by * column, with the leading diagonal of the matrix in row * ( k + 1 ) of the array, the first super-diagonal starting at * position 2 in row k, and so on. The top left k by k triangle * of the array A is not referenced. * The following program segment will transfer an upper * triangular band matrix from conventional full matrix storage * to band storage: * * DO 20, J = 1, N * M = K + 1 - J * DO 10, I = MAX( 1, J - K ), J * A( M + I, J ) = matrix( I, J ) * 10 CONTINUE * 20 CONTINUE * * Before entry with UPLO = 'L' or 'l', the leading ( k + 1 ) * by n part of the array A must contain the lower triangular * band part of the matrix of coefficients, supplied column by * column, with the leading diagonal of the matrix in row 1 of * the array, the first sub-diagonal starting at position 1 in * row 2, and so on. The bottom right k by k triangle of the * array A is not referenced. * The following program segment will transfer a lower * triangular band matrix from conventional full matrix storage * to band storage: * * DO 20, J = 1, N * M = 1 - J * DO 10, I = J, MIN( N, J + K ) * A( M + I, J ) = matrix( I, J ) * 10 CONTINUE * 20 CONTINUE * * Note that when DIAG = 'U' or 'u' the elements of the array A * corresponding to the diagonal elements of the matrix are not * referenced, but are assumed to be unity. * 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 * ( k + 1 ). * 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 right-hand side vector b. On exit, X is overwritten * with the solution vector x. * * INCX - INTEGER. * On entry, INCX specifies the increment for the elements of * X. INCX 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 ZERO PARAMETER ( ZERO = 0.0D+0 ) * .. Local Scalars .. DOUBLE PRECISION TEMP INTEGER I, INFO, IX, J, JX, KPLUS1, KX, L LOGICAL NOUNIT * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. External Subroutines .. EXTERNAL XERBLA * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 IF ( .NOT.LSAME( UPLO , 'U' ).AND. $ .NOT.LSAME( UPLO , 'L' ) )THEN INFO = 1 ELSE IF( .NOT.LSAME( TRANS, 'N' ).AND. $ .NOT.LSAME( TRANS, 'T' ).AND. $ .NOT.LSAME( TRANS, 'C' ) )THEN INFO = 2 ELSE IF( .NOT.LSAME( DIAG , 'U' ).AND. $ .NOT.LSAME( DIAG , 'N' ) )THEN INFO = 3 ELSE IF( N.LT.0 )THEN INFO = 4 ELSE IF( K.LT.0 )THEN INFO = 5 ELSE IF( LDA.LT.( K + 1 ) )THEN INFO = 7 ELSE IF( INCX.EQ.0 )THEN INFO = 9 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'DTBSV ', INFO ) RETURN END IF * * Quick return if possible. * IF( N.EQ.0 ) $ RETURN * NOUNIT = LSAME( DIAG, 'N' ) * * Set up the start point in X if the increment is not unity. This * will be ( N - 1 )*INCX too small for descending loops. * 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 A are * accessed by sequentially with one pass through A. * IF( LSAME( TRANS, 'N' ) )THEN * * Form x := inv( A )*x. * IF( LSAME( UPLO, 'U' ) )THEN KPLUS1 = K + 1 IF( INCX.EQ.1 )THEN DO 20, J = N, 1, -1 IF( X( J ).NE.ZERO )THEN L = KPLUS1 - J IF( NOUNIT ) $ X( J ) = X( J )/A( KPLUS1, J ) TEMP = X( J ) DO 10, I = J - 1, MAX( 1, J - K ), -1 X( I ) = X( I ) - TEMP*A( L + I, J ) 10 CONTINUE END IF 20 CONTINUE ELSE KX = KX + ( N - 1 )*INCX JX = KX DO 40, J = N, 1, -1 KX = KX - INCX IF( X( JX ).NE.ZERO )THEN IX = KX L = KPLUS1 - J IF( NOUNIT ) $ X( JX ) = X( JX )/A( KPLUS1, J ) TEMP = X( JX ) DO 30, I = J - 1, MAX( 1, J - K ), -1 X( IX ) = X( IX ) - TEMP*A( L + I, J ) IX = IX - INCX 30 CONTINUE END IF JX = JX - INCX 40 CONTINUE END IF ELSE IF( INCX.EQ.1 )THEN DO 60, J = 1, N IF( X( J ).NE.ZERO )THEN L = 1 - J IF( NOUNIT ) $ X( J ) = X( J )/A( 1, J ) TEMP = X( J ) DO 50, I = J + 1, MIN( N, J + K ) X( I ) = X( I ) - TEMP*A( L + I, J ) 50 CONTINUE END IF 60 CONTINUE ELSE JX = KX DO 80, J = 1, N KX = KX + INCX IF( X( JX ).NE.ZERO )THEN IX = KX L = 1 - J IF( NOUNIT ) $ X( JX ) = X( JX )/A( 1, J ) TEMP = X( JX ) DO 70, I = J + 1, MIN( N, J + K ) X( IX ) = X( IX ) - TEMP*A( L + I, J ) IX = IX + INCX 70 CONTINUE END IF JX = JX + INCX 80 CONTINUE END IF END IF ELSE * * Form x := inv( A')*x. * IF( LSAME( UPLO, 'U' ) )THEN KPLUS1 = K + 1 IF( INCX.EQ.1 )THEN DO 100, J = 1, N TEMP = X( J ) L = KPLUS1 - J DO 90, I = MAX( 1, J - K ), J - 1 TEMP = TEMP - A( L + I, J )*X( I ) 90 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/A( KPLUS1, J ) X( J ) = TEMP 100 CONTINUE ELSE JX = KX DO 120, J = 1, N TEMP = X( JX ) IX = KX L = KPLUS1 - J DO 110, I = MAX( 1, J - K ), J - 1 TEMP = TEMP - A( L + I, J )*X( IX ) IX = IX + INCX 110 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/A( KPLUS1, J ) X( JX ) = TEMP JX = JX + INCX IF( J.GT.K ) $ KX = KX + INCX 120 CONTINUE END IF ELSE IF( INCX.EQ.1 )THEN DO 140, J = N, 1, -1 TEMP = X( J ) L = 1 - J DO 130, I = MIN( N, J + K ), J + 1, -1 TEMP = TEMP - A( L + I, J )*X( I ) 130 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/A( 1, J ) X( J ) = TEMP 140 CONTINUE ELSE KX = KX + ( N - 1 )*INCX JX = KX DO 160, J = N, 1, -1 TEMP = X( JX ) IX = KX L = 1 - J DO 150, I = MIN( N, J + K ), J + 1, -1 TEMP = TEMP - A( L + I, J )*X( IX ) IX = IX - INCX 150 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/A( 1, J ) X( JX ) = TEMP JX = JX - INCX IF( ( N - J ).GE.K ) $ KX = KX - INCX 160 CONTINUE END IF END IF END IF * RETURN * * End of DTBSV . * END SUBROUTINE DCOPY(N,DX,INCX,DY,INCY) C***BEGIN PROLOGUE DCOPY C***DATE WRITTEN 791001 (YYMMDD) C***REVISION DATE 861211 (YYMMDD) C***CATEGORY NO. D1A5 C***KEYWORDS LIBRARY=SLATEC(BLAS), C TYPE=DOUBLE PRECISION(SCOPY-S DCOPY-D CCOPY-C),COPY, C LINEAR ALGEBRA,VECTOR C***AUTHOR LAWSON, C. L., (JPL) C HANSON, R. J., (SNLA) C KINCAID, D. R., (U. OF TEXAS) C KROGH, F. T., (JPL) C***PURPOSE D.P. vector copy y = x C***DESCRIPTION C C B L A S Subprogram C Description of Parameters C C --Input-- C N number of elements in input vector(s) C DX double precision vector with N elements C INCX storage spacing between elements of DX C DY double precision vector with N elements C INCY storage spacing between elements of DY C C --Output-- C DY copy of vector DX (unchanged if N .LE. 0) C C Copy double precision DX to double precision DY. C For I = 0 to N-1, copy DX(LX+I*INCX) to DY(LY+I*INCY), C where LX = 1 if INCX .GE. 0, else LX = (-INCX)*N, and LY is C defined in a similar way using INCY. C***REFERENCES LAWSON C.L., HANSON R.J., KINCAID D.R., KROGH F.T., C *BASIC LINEAR ALGEBRA SUBPROGRAMS FOR FORTRAN USAGE*, C ALGORITHM NO. 539, TRANSACTIONS ON MATHEMATICAL C SOFTWARE, VOLUME 5, NUMBER 3, SEPTEMBER 1979, 308-323 C***ROUTINES CALLED (NONE) C***END PROLOGUE DCOPY C DOUBLE PRECISION DX(1),DY(1) C***FIRST EXECUTABLE STATEMENT DCOPY IF(N.LE.0)RETURN IF(INCX.EQ.INCY) IF(INCX-1) 5,20,60 5 CONTINUE C C CODE FOR UNEQUAL OR NONPOSITIVE INCREMENTS. 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 SO REMAINING VECTOR LENGTH IS A MULTIPLE OF 7. 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 C C CODE FOR EQUAL, POSITIVE, NONUNIT INCREMENTS. C 60 CONTINUE NS=N*INCX DO 70 I=1,NS,INCX DY(I) = DX(I) 70 CONTINUE RETURN END SUBROUTINE DAXPY(N,DA,DX,INCX,DY,INCY) C***BEGIN PROLOGUE DAXPY C***DATE WRITTEN 791001 (YYMMDD) C***REVISION DATE 861211 (YYMMDD) C***CATEGORY NO. D1A7 C***KEYWORDS LIBRARY=SLATEC(BLAS), C TYPE=DOUBLE PRECISION(SAXPY-S DAXPY-D CAXPY-C), C LINEAR ALGEBRA,TRIAD,VECTOR C***AUTHOR LAWSON, C. L., (JPL) C HANSON, R. J., (SNLA) C KINCAID, D. R., (U. OF TEXAS) C KROGH, F. T., (JPL) C***PURPOSE D.P computation y = a*x + y C***DESCRIPTION C C B L A S Subprogram C Description of Parameters C C --Input-- C N number of elements in input vector(s) C DA double precision scalar multiplier C DX double precision vector with N elements C INCX storage spacing between elements of DX C DY double precision vector with N elements C INCY storage spacing between elements of DY C C --Output-- C DY double precision result (unchanged if N .LE. 0) C C Overwrite double precision DY with double precision DA*DX + DY. C For I = 0 to N-1, replace DY(LY+I*INCY) with DA*DX(LX+I*INCX) + C DY(LY+I*INCY), where LX = 1 if INCX .GE. 0, else LX = (-INCX)*N C and LY is defined in a similar way using INCY. C***REFERENCES LAWSON C.L., HANSON R.J., KINCAID D.R., KROGH F.T., C *BASIC LINEAR ALGEBRA SUBPROGRAMS FOR FORTRAN USAGE*, C ALGORITHM NO. 539, TRANSACTIONS ON MATHEMATICAL C SOFTWARE, VOLUME 5, NUMBER 3, SEPTEMBER 1979, 308-323 C***ROUTINES CALLED (NONE) C***END PROLOGUE DAXPY C DOUBLE PRECISION DX(1),DY(1),DA C***FIRST EXECUTABLE STATEMENT DAXPY IF(N.LE.0.OR.DA.EQ.0.D0) RETURN IF(INCX.EQ.INCY) IF(INCX-1) 5,20,60 5 CONTINUE C C CODE FOR NONEQUAL OR NONPOSITIVE INCREMENTS. 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 SO REMAINING VECTOR LENGTH IS A MULTIPLE OF 4. 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 C C CODE FOR EQUAL, POSITIVE, NONUNIT INCREMENTS. C 60 CONTINUE NS = N*INCX DO 70 I=1,NS,INCX DY(I) = DA*DX(I) + DY(I) 70 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 DOUBLE PRECISION FUNCTION DNRM2(N,DX,INCX) C***BEGIN PROLOGUE DNRM2 C***DATE WRITTEN 791001 (YYMMDD) C***REVISION DATE 861211 (YYMMDD) C***CATEGORY NO. D1A3B C***KEYWORDS LIBRARY=SLATEC(BLAS), C TYPE=DOUBLE PRECISION(SNRM2-S DNRM2-D SCNRM2-C), C EUCLIDEAN LENGTH,EUCLIDEAN NORM,L2,LINEAR ALGEBRA,UNITARY, C VECTOR C***AUTHOR LAWSON, C. L., (JPL) C HANSON, R. J., (SNLA) C KINCAID, D. R., (U. OF TEXAS) C KROGH, F. T., (JPL) C***PURPOSE Euclidean length (L2 norm) of d.p. vector C***DESCRIPTION C C B L A S Subprogram C Description of parameters C C --Input-- C N number of elements in input vector(s) C DX double precision vector with N elements C INCX storage spacing between elements of DX C C --Output-- C DNRM2 double precision result (zero if N .LE. 0) C C Euclidean norm of the N-vector stored in DX() with storage C increment INCX . C If N .LE. 0 return with result = 0. C If N .GE. 1 then INCX must be .GE. 1 C C C.L. Lawson, 1978 Jan 08 C C Four phase method using two built-in constants that are C hopefully applicable to all machines. C CUTLO = maximum of DSQRT(U/EPS) over all known machines. C CUTHI = minimum of DSQRT(V) over all known machines. C where C EPS = smallest no. such that EPS + 1. .GT. 1. C U = smallest positive no. (underflow limit) C V = largest no. (overflow limit) C C Brief outline of algorithm.. C C Phase 1 scans zero components. C move to phase 2 when a component is nonzero and .LE. CUTLO C move to phase 3 when a component is .GT. CUTLO C move to phase 4 when a component is .GE. CUTHI/M C where M = N for X() real and M = 2*N for complex. C C Values for CUTLO and CUTHI.. C From the environmental parameters listed in the IMSL converter C document the limiting values are as followS.. C CUTLO, S.P. U/EPS = 2**(-102) for Honeywell. Close seconds are C Univac and DEC at 2**(-103) C Thus CUTLO = 2**(-51) = 4.44089E-16 C CUTHI, S.P. V = 2**127 for Univac, Honeywell, and DEC. C Thus CUTHI = 2**(63.5) = 1.30438E19 C CUTLO, D.P. U/EPS = 2**(-67) for Honeywell and DEC. C Thus CUTLO = 2**(-33.5) = 8.23181D-11 C CUTHI, D.P. same as S.P. CUTHI = 1.30438D19 SAVE CUTLO, CUTHI, ZERO, ONE C DATA CUTLO, CUTHI / 8.232D-11, 1.304D19 / C DATA CUTLO, CUTHI / 4.441E-16, 1.304E19 / C***REFERENCES LAWSON C.L., HANSON R.J., KINCAID D.R., KROGH F.T., C *BASIC LINEAR ALGEBRA SUBPROGRAMS FOR FORTRAN USAGE*, C ALGORITHM NO. 539, TRANSACTIONS ON MATHEMATICAL C SOFTWARE, VOLUME 5, NUMBER 3, SEPTEMBER 1979, 308-323 C***ROUTINES CALLED (NONE) C***END PROLOGUE DNRM2 INTEGER NEXT DOUBLE PRECISION DX(1), CUTLO, CUTHI, HITEST, SUM, XMAX,ZERO,ONE DATA ZERO, ONE /0.0D0, 1.0D0/ C DATA CUTLO, CUTHI / 8.232D-11, 1.304D19 / C***FIRST EXECUTABLE STATEMENT DNRM2 IF(N .GT. 0) GO TO 10 DNRM2 = ZERO GO TO 300 C 10 ASSIGN 30 TO NEXT SUM = ZERO NN = N * INCX C BEGIN MAIN LOOP I = 1 20 GO TO NEXT,(30, 50, 70, 110) 30 IF( DABS(DX(I)) .GT. CUTLO) GO TO 85 ASSIGN 50 TO NEXT XMAX = ZERO C C PHASE 1. SUM IS ZERO C 50 IF( DX(I) .EQ. ZERO) GO TO 200 IF( DABS(DX(I)) .GT. CUTLO) GO TO 85 C C PREPARE FOR PHASE 2. ASSIGN 70 TO NEXT GO TO 105 C C PREPARE FOR PHASE 4. C 100 I = J ASSIGN 110 TO NEXT SUM = (SUM / DX(I)) / DX(I) 105 XMAX = DABS(DX(I)) GO TO 115 C C PHASE 2. SUM IS SMALL. C SCALE TO AVOID DESTRUCTIVE UNDERFLOW. C 70 IF( DABS(DX(I)) .GT. CUTLO ) GO TO 75 C C COMMON CODE FOR PHASES 2 AND 4. C IN PHASE 4 SUM IS LARGE. SCALE TO AVOID OVERFLOW. C 110 IF( DABS(DX(I)) .LE. XMAX ) GO TO 115 SUM = ONE + SUM * (XMAX / DX(I))**2 XMAX = DABS(DX(I)) GO TO 200 C 115 SUM = SUM + (DX(I)/XMAX)**2 GO TO 200 C C C PREPARE FOR PHASE 3. C 75 SUM = (SUM * XMAX) * XMAX C C C FOR REAL OR D.P. SET HITEST = CUTHI/N C FOR COMPLEX SET HITEST = CUTHI/(2*N) C 85 HITEST = CUTHI/FLOAT( N ) C C PHASE 3. SUM IS MID-RANGE. NO SCALING. C DO 95 J =I,NN,INCX IF(DABS(DX(J)) .GE. HITEST) GO TO 100 95 SUM = SUM + DX(J)**2 DNRM2 = DSQRT( SUM ) GO TO 300 C 200 CONTINUE I = I + INCX IF ( I .LE. NN ) GO TO 20 C C END OF MAIN LOOP. C C COMPUTE SQUARE ROOT AND ADJUST FOR SCALING. C DNRM2 = XMAX * DSQRT(SUM) 300 CONTINUE RETURN END SUBROUTINE DSWAP(N,DX,INCX,DY,INCY) C***BEGIN PROLOGUE DSWAP C***DATE WRITTEN 791001 (YYMMDD) C***REVISION DATE 861211 (YYMMDD) C***CATEGORY NO. D1A5 C***KEYWORDS LIBRARY=SLATEC(BLAS), C TYPE=DOUBLE PRECISION(SSWAP-S DSWAP-D CSWAP-C ISWAP-I), C INTERCHANGE,LINEAR ALGEBRA,VECTOR C***AUTHOR LAWSON, C. L., (JPL) C HANSON, R. J., (SNLA) C KINCAID, D. R., (U. OF TEXAS) C KROGH, F. T., (JPL) C***PURPOSE Interchange d.p. vectors C***DESCRIPTION C C B L A S Subprogram C Description of Parameters C C --Input-- C N number of elements in input vector(s) C DX double precision vector with N elements C INCX storage spacing between elements of DX C DY double precision vector with N elements C INCY storage spacing between elements of DY C C --Output-- C DX input vector DY (unchanged if N .LE. 0) C DY input vector DX (unchanged if N .LE. 0) C C Interchange double precision DX and double precision DY. C For I = 0 to N-1, interchange DX(LX+I*INCX) and DY(LY+I*INCY), C where LX = 1 if INCX .GE. 0, else LX = (-INCX)*N, and LY is C defined in a similar way using INCY. C***REFERENCES LAWSON C.L., HANSON R.J., KINCAID D.R., KROGH F.T., C *BASIC LINEAR ALGEBRA SUBPROGRAMS FOR FORTRAN USAGE*, C ALGORITHM NO. 539, TRANSACTIONS ON MATHEMATICAL C SOFTWARE, VOLUME 5, NUMBER 3, SEPTEMBER 1979, 308-323 C***ROUTINES CALLED (NONE) C***END PROLOGUE DSWAP C DOUBLE PRECISION DX(1),DY(1),DTEMP1,DTEMP2,DTEMP3 C***FIRST EXECUTABLE STATEMENT DSWAP IF(N.LE.0)RETURN IF(INCX.EQ.INCY) IF(INCX-1) 5,20,60 5 CONTINUE C C CODE FOR UNEQUAL OR NONPOSITIVE INCREMENTS. 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 DTEMP1 = DX(IX) DX(IX) = DY(IY) DY(IY) = DTEMP1 IX = IX + INCX IY = IY + INCY 10 CONTINUE RETURN C C CODE FOR BOTH INCREMENTS EQUAL TO 1 C C C CLEAN-UP LOOP SO REMAINING VECTOR LENGTH IS A MULTIPLE OF 3. C 20 M = MOD(N,3) IF( M .EQ. 0 ) GO TO 40 DO 30 I = 1,M DTEMP1 = DX(I) DX(I) = DY(I) DY(I) = DTEMP1 30 CONTINUE IF( N .LT. 3 ) RETURN 40 MP1 = M + 1 DO 50 I = MP1,N,3 DTEMP1 = DX(I) DTEMP2 = DX(I+1) DTEMP3 = DX(I+2) DX(I) = DY(I) DX(I+1) = DY(I+1) DX(I+2) = DY(I+2) DY(I) = DTEMP1 DY(I+1) = DTEMP2 DY(I+2) = DTEMP3 50 CONTINUE RETURN 60 CONTINUE C C CODE FOR EQUAL, POSITIVE, NONUNIT INCREMENTS. C NS = N*INCX DO 70 I=1,NS,INCX DTEMP1 = DX(I) DX(I) = DY(I) DY(I) = DTEMP1 70 CONTINUE RETURN END SUBROUTINE DSCAL(N,DA,DX,INCX) C***BEGIN PROLOGUE DSCAL C***DATE WRITTEN 791001 (YYMMDD) C***REVISION DATE 861211 (YYMMDD) C***CATEGORY NO. D1A6 C***KEYWORDS LIBRARY=SLATEC(BLAS), C TYPE=DOUBLE PRECISION(SSCAL-S DSCAL-D CSCAL-C), C LINEAR ALGEBRA,SCALE,VECTOR C***AUTHOR LAWSON, C. L., (JPL) C HANSON, R. J., (SNLA) C KINCAID, D. R., (U. OF TEXAS) C KROGH, F. T., (JPL) C***PURPOSE D.P. vector scale x = a*x C***DESCRIPTION C C B L A S Subprogram C Description of Parameters C C --Input-- C N number of elements in input vector(s) C DA double precision scale factor C DX double precision vector with N elements C INCX storage spacing between elements of DX C C --Output-- C DX double precision result (unchanged if N.LE.0) C C Replace double precision DX by double precision DA*DX. C For I = 0 to N-1, replace DX(1+I*INCX) with DA * DX(1+I*INCX) C***REFERENCES LAWSON C.L., HANSON R.J., KINCAID D.R., KROGH F.T., C *BASIC LINEAR ALGEBRA SUBPROGRAMS FOR FORTRAN USAGE*, C ALGORITHM NO. 539, TRANSACTIONS ON MATHEMATICAL C SOFTWARE, VOLUME 5, NUMBER 3, SEPTEMBER 1979, 308-323 C***ROUTINES CALLED (NONE) C***END PROLOGUE DSCAL C DOUBLE PRECISION DA,DX(1) C***FIRST EXECUTABLE STATEMENT DSCAL IF(N.LE.0)RETURN IF(INCX.EQ.1)GOTO 20 C C CODE FOR INCREMENTS NOT EQUAL TO 1. C NS = N*INCX DO 10 I = 1,NS,INCX DX(I) = DA*DX(I) 10 CONTINUE RETURN C C CODE FOR INCREMENTS EQUAL TO 1. C C C CLEAN-UP LOOP SO REMAINING VECTOR LENGTH IS A MULTIPLE OF 5. 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 DOUBLE PRECISION FUNCTION DASUM(N,DX,INCX) C***BEGIN PROLOGUE DASUM C***DATE WRITTEN 791001 (YYMMDD) C***REVISION DATE 861211 (YYMMDD) C***CATEGORY NO. D1A3A C***KEYWORDS LIBRARY=SLATEC(BLAS), C TYPE=DOUBLE PRECISION(SASUM-S DASUM-D SCASUM-C),ADD, C LINEAR ALGEBRA,MAGNITUDE,SUM,VECTOR C***AUTHOR LAWSON, C. L., (JPL) C HANSON, R. J., (SNLA) C KINCAID, D. R., (U. OF TEXAS) C KROGH, F. T., (JPL) C***PURPOSE Sum of magnitudes of d.p. vector components C***DESCRIPTION C C B L A S Subprogram C Description of Parameters C C --Input-- C N number of elements in input vector(s) C DX double precision vector with N elements C INCX storage spacing between elements of DX C C --Output-- C DASUM double precision result (zero if N .LE. 0) C C Returns sum of magnitudes of double precision DX. C DASUM = sum from 0 to N-1 of DABS(DX(1+I*INCX)) C***REFERENCES LAWSON C.L., HANSON R.J., KINCAID D.R., KROGH F.T., C *BASIC LINEAR ALGEBRA SUBPROGRAMS FOR FORTRAN USAGE*, C ALGORITHM NO. 539, TRANSACTIONS ON MATHEMATICAL C SOFTWARE, VOLUME 5, NUMBER 3, SEPTEMBER 1979, 308-323 C***ROUTINES CALLED (NONE) C***END PROLOGUE DASUM C DOUBLE PRECISION DX(1) C***FIRST EXECUTABLE STATEMENT DASUM DASUM = 0.D0 IF(N.LE.0)RETURN IF(INCX.EQ.1)GOTO 20 C C CODE FOR INCREMENTS NOT EQUAL TO 1. C NS = N*INCX DO 10 I=1,NS,INCX DASUM = DASUM + DABS(DX(I)) 10 CONTINUE RETURN C C CODE FOR INCREMENTS EQUAL TO 1. C C C CLEAN-UP LOOP SO REMAINING VECTOR LENGTH IS A MULTIPLE OF 6. C 20 M = MOD(N,6) IF( M .EQ. 0 ) GO TO 40 DO 30 I = 1,M DASUM = DASUM + DABS(DX(I)) 30 CONTINUE IF( N .LT. 6 ) RETURN 40 MP1 = M + 1 DO 50 I = MP1,N,6 DASUM = DASUM + DABS(DX(I)) + DABS(DX(I+1)) + DABS(DX(I+2)) 1 + DABS(DX(I+3)) + DABS(DX(I+4)) + DABS(DX(I+5)) 50 CONTINUE RETURN END INTEGER FUNCTION IDAMAX(N,DX,INCX) C***BEGIN PROLOGUE IDAMAX C***DATE WRITTEN 791001 (YYMMDD) C***REVISION DATE 861211 (YYMMDD) C***CATEGORY NO. D1A2 C***KEYWORDS LIBRARY=SLATEC(BLAS), C TYPE=DOUBLE PRECISION(ISAMAX-S IDAMAX-D ICAMAX-C), C LINEAR ALGEBRA,MAXIMUM COMPONENT,VECTOR C***AUTHOR LAWSON, C. L., (JPL) C HANSON, R. J., (SNLA) C KINCAID, D. R., (U. OF TEXAS) C KROGH, F. T., (JPL) C***PURPOSE Find the smallest index of that component of a d.p. vector C having the maximum magnitude. C***DESCRIPTION C C B L A S Subprogram C Description of Parameters C C --Input-- C N number of elements in input vector(s) C DX double precision vector with N elements C INCX storage spacing between elements of DX C C --Output-- C IDAMAX smallest index (zero if N .LE. 0) C C Find smallest index of maximum magnitude of double precision DX. C IDAMAX = first I, I = 1 to N, to minimize ABS(DX(1-INCX+I*INCX) C***REFERENCES LAWSON C.L., HANSON R.J., KINCAID D.R., KROGH F.T., C *BASIC LINEAR ALGEBRA SUBPROGRAMS FOR FORTRAN USAGE*, C ALGORITHM NO. 539, TRANSACTIONS ON MATHEMATICAL C SOFTWARE, VOLUME 5, NUMBER 3, SEPTEMBER 1979, 308-323 C***ROUTINES CALLED (NONE) C***END PROLOGUE IDAMAX C DOUBLE PRECISION DX(*),DMAX,XMAG C***FIRST EXECUTABLE STATEMENT IDAMAX IDAMAX = 0 IF(N.LE.0) RETURN IDAMAX = 1 IF(N.LE.1)RETURN IF(INCX.EQ.1)GOTO 20 C C CODE FOR INCREMENTS NOT EQUAL TO 1. C DMAX = DABS(DX(1)) NS = N*INCX II = 1 DO 10 I = 1,NS,INCX XMAG = DABS(DX(I)) IF(XMAG.LE.DMAX) GO TO 5 IDAMAX = II DMAX = XMAG 5 II = II + 1 10 CONTINUE RETURN C C CODE FOR INCREMENTS EQUAL TO 1. C 20 DMAX = DABS(DX(1)) DO 30 I = 2,N XMAG = DABS(DX(I)) IF(XMAG.LE.DMAX) GO TO 30 IDAMAX = I DMAX = XMAG 30 CONTINUE RETURN END SHAR_EOF fi # end of overwriting check if test -f 'driver.f' then echo shar: will not over-write existing file "'driver.f'" else cat << "SHAR_EOF" > 'driver.f' C C C ARRAY length and grid parameters: C C LDA = Row dimension of array ABD used to store D**T*D C (and the matrix associated with the cubic spline C interpolant) in LAPACK band storage (packed) C format for the linear solver DPBSV (and CSPLIN). C C MMAX = Maximum number of grid points. The array storage C requirement is approximately 112*MMAX bytes for C 8-byte double precision numbers. C C NMAX = Maximum number of data points. C INTEGER LDA, MMAX, NMAX PARAMETER (LDA=3, NMAX=100, MMAX=900) C C Arrays: C DOUBLE PRECISION D(NMAX), S(NMAX), T(NMAX) DOUBLE PRECISION A(MMAX), ABD(LDA,MMAX), D1Y(MMAX), . D2Y(MMAX), G(MMAX), G0(MMAX), . P(MMAX), WK(MMAX,3), Y0(MMAX), . Y(MMAX) INTEGER IND(NMAX) C C Scalars and functions: C CHARACTER CHR CHARACTER*60 FNAME DOUBLE PRECISION DDOT, PHI DOUBLE PRECISION ALPHA, C2, C3, DD, DG, DGG, DPHI, DT, . DY, FMTOL, GG, GNRM1, GNRMM, H, PHI0, . PHIY, PHTOL, PLTSIZ, Q, SSIZ0, SSIZ1, . YMAX INTEGER I, IER, J, J1, J2, LIN, LOUT, LPLT, LPRT, M, . MAXCG, N, NCG, NG, NGMAX, NPHSM, NPHVAL, NPRNT LOGICAL L2G, OPT, PLT0, PRNT C C Parameters: C C FMTOL = Nonnegative tolerance for the line search: C length of the interval of uncertainty. Refer C to Function FMIN. C C L2G = Flag with value TRUE iff the L2-gradient is to be C used in place of the Sobolev gradient. C C MAXCG = Number of Polak-Ribiere conjugate gradient steps C between restarts with a steepest descent step. C C NGMAX = Maximum number of descent steps (outer itera- C tions) before termination without convergence. C NGMAX > 0. C C NPRNT = Number of descent steps between print steps. C For each print step, several lines of statistics C describing the step are written to unit LPRT. C The first and last descent steps are necessarily C print steps. NPRNT .GE. 1. C C OPT = Flag with value TRUE iff the optimal step-size C (computed by a line search) is to be used at each C descent step. C C PHTOL = Nonnegative tolerance which defines convergence C of the descent method: bound on Max(DPHI,DY**2, C DG**3), where C DPHI = abs(change in phi)/(1+phi), C DY = max-norm(change in Y)/(1+max-norm(Y)), C DG = max-norm(S-gradient)/(1+max-norm(Y)). C C PLT0 = Flag with value TRUE iff the initial estimate is C to be plotted. C C PLTSIZ = Plot size in inches for Postscript plots. C 1.0 <= PLTSIZ <= 6.5. C C SSIZ0 = Descent step size used if OPT = FALSE. C C SSIZ1 = Initial descent step size used if OPT = TRUE. C DATA FMTOL/1.D-6/, L2G/.FALSE./, MAXCG/3/, . NGMAX/200/, NPRNT/1/, OPT/.TRUE./, . PHTOL/1.D-3/, PLT0/.TRUE./, PLTSIZ/6.5/, . SSIZ0/1.D-3/, SSIZ1/1.D-5/ C C Logical unit numbers: C C LIN = Logical unit number for an input data set contain- C ing N, (T(I), I = 1,N), (D(I), I = 1,N), and H. C C LOUT = Logical unit number for writing the solution C M, (Y(I), I = 1,M), (D1Y(I), I = 1,M), and C (D2Y(I), I = 1,M): Subroutine WRITF. C C LPLT = Logical unit number for files containing C Postscript plots: initial estimate, spline C curve, and/or curvature. Refer to Subroutine C PLTCRV. C C LPRT = Logical unit number for output other than the C solution. C DATA LIN/5/, LOUT/6/, LPLT/3/, LPRT/4/ C C Open print file, delete it, and reopen it. This is C necessary on some systems (Microsoft) which ignore C end-of-file records. C OPEN (LPRT,FILE='dnsplin1.prt') CLOSE (LPRT,STATUS='DELETE') OPEN (LPRT,FILE='dnsplin1.prt') C C Get an input data set file name. C C 1 WRITE (*,200) C 200 FORMAT (//5X,'Specify the name of a file containing ', C . 'an input data set'/ C . 5X,'(at most 60 characters):'/) C READ (*,205,ERR=1) FNAME C 205 FORMAT (A60) C OPEN (LIN,FILE=FNAME,STATUS='OLD',ERR=1) C C Read input data, and compute indexes (1 to M=IND(N)) of C data points. C CALL READF (LIN,NMAX, N,T,D,H,IND,IER) IF (IER .NE. 0) GO TO 21 M = IND(N) IF (M .LT. 6 .OR. M .GT. MMAX .OR. M-N .LT. 1) . GO TO 22 C C Print a heading with parameter values. C WRITE (LPRT,100) 100 FORMAT (///27X,'DNSPLIN1 Output'/) WRITE (LPRT,110) T(1), T(N), N, M, H, MAXCG, FMTOL, . PHTOL, NGMAX 110 FORMAT (//5X,'Domain: T(1) = ',D10.3,', T(N) = ', . D10.3/ . 5X,'Number of data points: N = ',I4// . 5X,'Number of grid points: M = ',I5/ . 5X,'Mesh width: H = ',D12.6//1P, . 5X,'# CG steps between restarts: MAXCG = ', . I4/ . 5X,'Line search tolerance: FMTOL = ',D9.3/ . 5X,'Convergence tolerance: PHTOL = ',D9.3/ . 5X,'Max number of iterations: NGMAX = ',I6) C C Set Y0 to the gridpoint values of the Hermite cubic C interpolant with derivatives S at the data abscissae C obtained from the natural cubic spline. C CALL CSPLIN (LDA,N,T,D, ABD, S,IER) IF (IER .NE. 0) GO TO 23 C J2 = 1 DO 3 I = 1,N-1 J1 = J2 J2 = IND(I+1) Y0(J1) = D(I) DT = T(I+1)-T(I) DD = (D(I+1)-D(I))/DT C2 = (3.D0*DD-2.D0*S(I)-S(I+1))/DT C3 = (-2.D0*DD+S(I)+S(I+1))/(DT*DT) DT = 0.D0 DO 2 J = J1+1,J2-1 DT = DT + H Y0(J) = ((C3*DT + C2)*DT + S(I))*DT + D(I) 2 CONTINUE 3 CONTINUE Y0(J2) = D(N) C C Copy Y0 into Y. C DO 4 I = 1,M Y(I) = Y0(I) 4 CONTINUE C C Prompt for optional plot of initial estimate. C C 5 WRITE (*,210) C 210 FORMAT (//5X,'Create file dnsplin1.ps0 containing a ', C . 'plot '/ C . 5X,'of the initial estimate? (y/n)'/) C READ (*,215,ERR=5) CHR C 215 FORMAT (A1) C IF (CHR .NE. 'Y' .AND. CHR .NE. 'y' .AND. C . CHR .NE. 'N' .AND. CHR .NE. 'n') GO TO 5 C IF (CHR .EQ. 'Y' .OR. CHR .EQ. 'y') THEN OPEN (LPLT,FILE='dnsplin1.ps0') CLOSE (LPLT,STATUS='DELETE') OPEN (LPLT,FILE='dnsplin1.ps0') CALL PLTCRV (LPLT,N,T(1),T(N),T,D,M,Y0,.FALSE.,Y0, . PLTSIZ, IER) CLOSE (LPLT) IF (IER .NE. 0) GO TO 26 C ENDIF C C Compute PHI0 = phi(Y0). Grid-point values D1y(i), D2y(i), C and a(i) are also computed. C PHI0 = PHI (M,H,Y0, D1Y,D2Y,A) C C Initialize iteration counts: C C NCG = Number of conjugate gradient steps since the C previous restart with a steepest descent step. C C NG = Number of iterations (gradient evaluations). C C NPHSM = Total number of evaluations of phi in the line C searches. C C PRNT = TRUE iff statistics describing the iteration are C to be printed. C NCG = MAXCG NG = 0 NPHSM = 0 PRNT = .TRUE. C C Top of loop: compute the L2-gradient G = grad(phi), its C 1-norm GNRM1, and its max-norm GNRMM, and C overwrite G with the Sobolev gradient unless C L2G = TRUE. C 7 CALL GRADL2 (N,H,IND,M,D1Y,D2Y,A, WK, G,GNRM1, . GNRMM,IER) IF (IER .NE. 0) GO TO 24 IF (.NOT. L2G) THEN CALL GRADS4 (N,H,IND,M,D1Y,D2Y,LDA, ABD,G, . WK, IER) IF (IER .GT. 0) WRITE (LPRT,125) IER 125 FORMAT (//5X,'GRADS4 Failure: IER = ',I1) ENDIF C C Compute mean absolute L2-gradient component GNRM1. C GNRM1 = GNRM1/DBLE(M-N) C C Update iteration count. C NG = NG + 1 C C Print statistics associated with the step. C IF (PRNT) THEN IF (NCG .GE. MAXCG) THEN WRITE (LPRT,130) NG ELSE WRITE (LPRT,135) NG ENDIF WRITE (LPRT,140) PHI0, GNRM1, GNRMM ENDIF 130 FORMAT (//15X,'Iteration ',I6,' (Steepest descent)') 135 FORMAT (//15X,'Iteration ',I6,' (Conjugate gradient)') 140 FORMAT (5X,'Functional: phi(F) = ', . 1P,D21.15/ . 5X,'Mean absolute L2-gradient: GNRM1 = ', . D8.2/ . 5X,'Max-norm of L2-gradient: GNRMM = ', . D8.2) PRNT = (NPRNT*(NG/NPRNT) .EQ. NG) .OR. (NG .EQ. 1) C IF (NCG .GE. MAXCG) THEN C C Steepest descent step. C Q = 0.D0 NCG = 0 ELSE C C Conjugate gradient step. C GG = DDOT(M,G0,1,G0,1) DGG = DDOT(M,G,1,G,1) - DDOT(M,G0,1,G,1) Q = DGG/GG NCG = NCG + 1 ENDIF C C Compute the search direction p = -G + Q*p. C DO 8 I = 1,M P(I) = -G(I) + Q*P(I) 8 CONTINUE C C Copy Y into Y1 (WK column 1), compute the optimal step- C size ALPHA, and update Y to Y1+ALPHA*p. Difference C approximations to derivatives and terms defining phi(Y) C are returned in D1Y, D2Y, and A. The Max-norm of Y is C returned in YMAX, and DY is the relative change in Y: C Max-norm(Y-Y1)/(1+YMAX) = ALPHA*Max-norm(p)/(1+YMAX). C C The initial estimate for ALPHA should be small. Using C the step-size computed at the previously iteration can C result in an incorrect step-size caused by finding a C local minimum which is not a global minimum. C DO 9 I = 1,M WK(I,1) = Y(I) 9 CONTINUE IF (OPT) THEN ALPHA = SSIZ1 ELSE C C Use small constant step-size. C ALPHA = SSIZ0 ENDIF CALL LNSRCH (M,H,WK,PHI0,P,FMTOL,OPT, ALPHA,Y,D1Y, . D2Y,A, PHIY,NPHVAL,YMAX,DY,IER) IF (IER .NE. 0) GO TO 25 NPHSM = NPHSM + NPHVAL C C Adjust DY to the relative change in Y squared. C DY = DY**2 C C Compute the max-norm of the Sobolev gradient relative to C the solution y. C DG = 0.D0 DO 10 I = 1,M DG = MAX(DG,ABS(G(I))) 10 CONTINUE DG = (DG/(1.D0+YMAX))**3 C C Save a copy of the Sobolev gradient G in G0 for computing C the search direction in the next conjugate gradient C step. C IF (NCG .LT. MAXCG) THEN DO 11 I = 1,M G0(I) = G(I) 11 CONTINUE ENDIF C C Compute the relative change DPHI in phi and update PHI0. C Terminate on an increase in phi. C DPHI = (PHI0-PHIY)/(1.D0+PHI0) PHI0 = PHIY IF (DPHI .LT. 0.D0) NGMAX = NG C C Print statistics. C IF (PRNT) WRITE (LPRT,150) NPHVAL, ALPHA, PHIY, DPHI, . DY, DG 150 FORMAT (/5X,'Line search: No. phi evals NPHV = ', . I3/ . 5X,' Optimal step-size S = ', . 1P,D9.3/ . 5X,' Functional phi(Y) = ', . D21.15/ . 5X,' Relative change in phi(Y) DPHI = ', . D9.2/ . 5X,' Squared relative change in Y: DY = ', . D9.2/ . 5X,' Cubed S-gradient rel. to Y: DG = ', . D9.2/ . 1X,'______________________________________', . '___________________________') C C Test for termination. C IF ((DPHI .GE. PHTOL .OR. DY .GE. PHTOL .OR. . DG .GE. PHTOL) .AND. NG .LT. NGMAX) GO TO 7 IF (.NOT. PRNT) THEN C C Print parameter values. C IF (NCG .EQ. 0) THEN WRITE (LPRT,130) NG ELSE WRITE (LPRT,135) NG ENDIF WRITE (LPRT,140) PHI0, GNRM1, GNRMM WRITE (LPRT,150) NPHVAL, ALPHA, PHIY, DPHI, DY, DG ENDIF C C Compute the curve length in DY. C C2 = H*H DY = 0.D0 DO 12 I = 2,M DY = DY + SQRT(C2 + (Y(I)-Y(I-1))**2) 12 CONTINUE C C Print iteration counts and statistics. C WRITE (LPRT,160) NG 160 FORMAT (//5X,'Number of descent ', . 'iterations: ',I6) WRITE (LPRT,170) NPHSM 170 FORMAT (/5X,'Total number of phi evaluations ', . 'in the line searches: ',I7) WRITE (LPRT,180) DY 180 FORMAT (/5X,'Total polygonal curve length: ',D9.3) C C Write the solution to disk. C C OPEN (LOUT,FILE='dnsplin1.out') C CLOSE (LOUT,STATUS='DELETE') C OPEN (LOUT,FILE='dnsplin1.out') CALL WRITF (LOUT,M,Y,D1Y,D2Y) C C Plot the solution. C OPEN (LPLT,FILE='dnsplin1.ps') CLOSE (LPLT,STATUS='DELETE') OPEN (LPLT,FILE='dnsplin1.ps') CALL PLTCRV (LPLT,N,T(1),T(N),T,D,M,Y,PLT0,Y0, . PLTSIZ, IER) CLOSE (LPLT) IF (IER .NE. 0) GO TO 26 C C Prompt for optional plot of curvature. C C 13 WRITE (*,220) C 220 FORMAT (//5X,'Create file dnsplin1.ps2 containing a ', C . 'curvature plot? (y/n)'/) C READ (*,215,ERR=13) CHR C IF (CHR .NE. 'Y' .AND. CHR .NE. 'y' .AND. C . CHR .NE. 'N' .AND. CHR .NE. 'n') GO TO 13 C IF (CHR .EQ. 'Y' .OR. CHR .EQ. 'y') THEN OPEN (LPLT,FILE='dnsplin1.ps2') CLOSE (LPLT,STATUS='DELETE') OPEN (LPLT,FILE='dnsplin1.ps2') Y(1) = 0.D0 DO 14 I = 2,M-1 Y(I) = D2Y(I)/(1.D0+D1Y(I)**2)**1.5D0 14 CONTINUE Y(M) = 0.D0 DO 15 J = 1,N I = IND(J) D(J) = Y(I) 15 CONTINUE CALL PLTCRV (LPLT,N,T(1),T(N),T,D,M,Y,.FALSE.,Y0, . PLTSIZ, IER) CLOSE (LPLT) IF (IER .NE. 0) GO TO 26 C ENDIF STOP C C Error encountered in Subroutine READF. C 21 WRITE (LPRT,421) IER 421 FORMAT (///10X,'*** Error in READF: IER = ', . I1,' ***') STOP C C Invalid data: M < 6 or M > MMAX or M-N < 1. C 22 WRITE (LPRT,422) M, MMAX, N 422 FORMAT (///10X,'*** Error in data: M = ',I5, . ', MMAX = ',I5,', N = ',I4,' ***') STOP C C Error encountered in Subroutine CSPLIN. C 23 WRITE (LPRT,423) IER 423 FORMAT (///10X,'*** Error in CSPLIN: IER = ', . I1,' ***') STOP C C Error encountered in Subroutine GRADL2. C 24 WRITE (LPRT,424) IER 424 FORMAT (///10X,'*** Error in GRADL2: IER = ', . I1,' ***') STOP C C Error encountered in Subroutine LNSRCH. C 25 WRITE (LPRT,425) IER 425 FORMAT (///10X,'*** Error in LNSRCH: IER = ', . I1,' ***') STOP C C Error encountered in Subroutine PLTCRV. C 26 WRITE (LPRT,426) IER 426 FORMAT (///10X,'*** Error in PLTCRV: IER = ', . I1,' ***') STOP END SHAR_EOF fi # end of overwriting check if test -f 'interactive.f' then echo shar: will not over-write existing file "'interactive.f'" else cat << "SHAR_EOF" > 'interactive.f' C C ARRAY length and grid parameters: C C LDA = Row dimension of array ABD used to store D**T*D C (and the matrix associated with the cubic spline C interpolant) in LAPACK band storage (packed) C format for the linear solver DPBSV (and CSPLIN). C C MMAX = Maximum number of grid points. The array storage C requirement is approximately 112*MMAX bytes for C 8-byte double precision numbers. C C NMAX = Maximum number of data points. C INTEGER LDA, MMAX, NMAX PARAMETER (LDA=3, NMAX=100, MMAX=900) C C Arrays: C DOUBLE PRECISION D(NMAX), S(NMAX), T(NMAX) DOUBLE PRECISION A(MMAX), ABD(LDA,MMAX), D1Y(MMAX), . D2Y(MMAX), G(MMAX), G0(MMAX), . P(MMAX), WK(MMAX,3), Y0(MMAX), . Y(MMAX) INTEGER IND(NMAX) C C Scalars and functions: C CHARACTER CHR CHARACTER*60 FNAME DOUBLE PRECISION DDOT, PHI DOUBLE PRECISION ALPHA, C2, C3, DD, DG, DGG, DPHI, DT, . DY, FMTOL, GG, GNRM1, GNRMM, H, PHI0, . PHIY, PHTOL, PLTSIZ, Q, SSIZ0, SSIZ1, . YMAX INTEGER I, IER, J, J1, J2, LIN, LOUT, LPLT, LPRT, M, . MAXCG, N, NCG, NG, NGMAX, NPHSM, NPHVAL, NPRNT LOGICAL L2G, OPT, PLT0, PRNT C C Parameters: C C FMTOL = Nonnegative tolerance for the line search: C length of the interval of uncertainty. Refer C to Function FMIN. C C L2G = Flag with value TRUE iff the L2-gradient is to be C used in place of the Sobolev gradient. C C MAXCG = Number of Polak-Ribiere con