SUBROUTINE SLLTBI( N, A, LDA, INFO, NB ) * * -- LAPACK variant -- * Univ. of Tennessee, Oak Ridge National Lab, Argonne National Lab, * Courant Institute, NAG Ltd., and Rice University * January 17, 1990 * * .. Scalar Arguments .. INTEGER INFO, LDA, N, NB * .. * .. Array Arguments .. REAL A( LDA, * ) * .. * * Purpose * ======= * * SLLTBI computes an L*L**T factorization of a real symmetric * positive definite matrix A. * * This is the blocked left-looking (i-variant) of the algorithm. * * Arguments * ========= * * N (input) INTEGER * The number of rows and columns of the matrix A. N >= 0. * * A (input/output) REAL array, dimension (LDA,N) * On entry, the symmetric matrix A. Only the lower triangular * part of A is referenced. * On exit, the factor L from the Cholesky factorization. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N). * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -k, the k-th argument had an illegal value * > 0: if INFO = k, the leading minor of order K is not * positive definite, and the factorization could not be * completed. * * NB (input) INTEGER * The blocksize for the blocked algorithm. * * ===================================================================== * * .. Parameters .. REAL ONE PARAMETER ( ONE = 1.0E+0 ) * .. * .. Local Scalars .. INTEGER I, IB * .. * .. External Subroutines .. EXTERNAL SLLTI, SSYRK, STRSM * .. * .. Intrinsic Functions .. INTRINSIC MIN * .. * .. Executable Statements .. * INFO = 0 IF( NB.EQ.1 ) THEN CALL SLLTI( N, A, LDA, INFO ) ELSE DO 10 I = 1, N, NB IB = MIN( NB, N-I+1 ) CALL STRSM( 'Right', 'Lower', 'Transpose', 'Non-unit', IB, \$ I-1, ONE, A, LDA, A( I, 1 ), LDA ) CALL SSYRK( 'Lower', 'No transpose', IB, I-1, -ONE, \$ A( I, 1 ), LDA, ONE, A( I, I ), LDA ) CALL SLLTI( IB, A( I, I ), LDA, INFO ) IF( INFO.NE.0 ) \$ GO TO 20 10 CONTINUE END IF RETURN 20 CONTINUE INFO = INFO + I - 1 RETURN * * End of SLLTBI * END SUBROUTINE SLLTI( N, A, LDA, INFO ) * * -- LAPACK variant -- * Univ. of Tennessee, Oak Ridge National Lab, Argonne National Lab, * Courant Institute, NAG Ltd., and Rice University * January 17, 1990 * * .. Scalar Arguments .. INTEGER INFO, LDA, N * .. * .. Array Arguments .. REAL A( LDA, * ) * .. * * Purpose * ======= * * SLLTI computes an L*L**T factorization of a real symmetric * positive definite matrix A. * * This is the unblocked left-looking (i-variant) of the algorithm. * * Arguments * ========= * * N (input) INTEGER * The number of rows and columns of the matrix A. N >= 0. * * A (input/output) REAL array, dimension (LDA,N) * On entry, the symmetric matrix A. Only the lower triangular * part of A is referenced. * On exit, the factor L from the Cholesky factorization. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N). * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -k, the k-th argument had an illegal value * > 0: if INFO = k, the leading minor of order K is not * positive definite, and the factorization could not be * completed. * * ===================================================================== * * .. Parameters .. REAL ZERO PARAMETER ( ZERO = 0.0E+0 ) * .. * .. Local Scalars .. INTEGER I * .. * .. External Functions .. REAL SDOT EXTERNAL SDOT * .. * .. External Subroutines .. EXTERNAL STRSV * .. * .. Intrinsic Functions .. INTRINSIC SQRT * .. * .. Executable Statements .. * INFO = 0 DO 10 I = 1, N CALL STRSV( 'Lower', 'No transpose', 'Non-unit', I-1, A, LDA, \$ A( I, 1 ), LDA ) A( I, I ) = A( I, I ) - SDOT( I-1, A( I, 1 ), LDA, A( I, 1 ), \$ LDA ) IF( A( I, I ).LE.ZERO ) \$ GO TO 20 A( I, I ) = SQRT( A( I, I ) ) 10 CONTINUE RETURN 20 CONTINUE INFO = I RETURN * * End of SLLTI * END SUBROUTINE SLLTBJ( N, A, LDA, INFO, NB ) * * -- LAPACK variant -- * Univ. of Tennessee, Oak Ridge National Lab, Argonne National Lab, * Courant Institute, NAG Ltd., and Rice University * January 17, 1990 * * .. Scalar Arguments .. INTEGER INFO, LDA, N, NB * .. * .. Array Arguments .. REAL A( LDA, * ) * .. * * Purpose * ======= * * SLLTBJ computes an L*L**T factorization of a real symmetric * positive definite matrix A. * * This is the blocked top-looking (j-variant) of the algorithm. * * Arguments * ========= * * N (input) INTEGER * The number of rows and columns of the matrix A. N >= 0. * * A (input/output) REAL array, dimension (LDA,N) * On entry, the symmetric matrix A. Only the lower triangular * part of A is referenced. * On exit, the factor L from the Cholesky factorization. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N). * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -k, the k-th argument had an illegal value * > 0: if INFO = k, the leading minor of order K is not * positive definite, and the factorization could not be * completed. * * NB (input) INTEGER * The blocksize for the blocked algorithm. * * ===================================================================== * * .. Parameters .. REAL ONE PARAMETER ( ONE = 1.0E+0 ) * .. * .. Local Scalars .. INTEGER J, JB * .. * .. External Subroutines .. EXTERNAL SGEMM, SLLTJ, SSYRK, STRSM * .. * .. Intrinsic Functions .. INTRINSIC MIN * .. * .. Executable Statements .. * INFO = 0 IF( NB.EQ.1 ) THEN CALL SLLTJ( N, A, LDA, INFO ) ELSE DO 10 J = 1, N, NB JB = MIN( NB, N-J+1 ) CALL SSYRK( 'Lower', 'No transpose', JB, J-1, -ONE, \$ A( J, 1 ), LDA, ONE, A( J, J ), LDA ) CALL SLLTJ( JB, A( J, J ), LDA, INFO ) IF( INFO.NE.0 ) \$ GO TO 20 IF( J+JB.LE.N ) THEN CALL SGEMM( 'No transpose', 'Transpose', N-J-JB+1, JB, \$ J-1, -ONE, A( J+JB, 1 ), LDA, A( J, 1 ), LDA, \$ ONE, A( J+JB, J ), LDA ) CALL STRSM( 'Right', 'Lower', 'Transpose', 'Non-unit', \$ N-J-JB+1, JB, ONE, A( J, J ), LDA, \$ A( J+JB, J ), LDA ) END IF 10 CONTINUE END IF RETURN 20 CONTINUE INFO = INFO + J - 1 RETURN * * End of SLLTBJ * END SUBROUTINE SLLTJ( N, A, LDA, INFO ) * * -- LAPACK variant -- * Univ. of Tennessee, Oak Ridge National Lab, Argonne National Lab, * Courant Institute, NAG Ltd., and Rice University * January 17, 1990 * * .. Scalar Arguments .. INTEGER INFO, LDA, N * .. * .. Array Arguments .. REAL A( LDA, * ) * .. * * Purpose * ======= * * SLLTJ computes an L*L**T factorization of a real symmetric * positive definite matrix A. * * This is the unblocked top-looking (j-variant) of the algorithm. * * Arguments * ========= * * N (input) INTEGER * The number of rows and columns of the matrix A. N >= 0. * * A (input/output) REAL array, dimension (LDA,N) * On entry, the symmetric matrix A. Only the lower triangular * part of A is referenced. * On exit, the factor L from the Cholesky factorization. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N). * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -k, the k-th argument had an illegal value * > 0: if INFO = k, the leading minor of order K is not * positive definite, and the factorization could not be * completed. * * ===================================================================== * * .. Parameters .. REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) * .. * .. Local Scalars .. INTEGER J * .. * .. External Functions .. REAL SDOT EXTERNAL SDOT * .. * .. External Subroutines .. EXTERNAL SGEMV, SSCAL * .. * .. Intrinsic Functions .. INTRINSIC SQRT * .. * .. Executable Statements .. * INFO = 0 DO 10 J = 1, N A( J, J ) = A( J, J ) - SDOT( J-1, A( J, 1 ), LDA, A( J, 1 ), \$ LDA ) IF( A( J, J ).LE.ZERO ) \$ GO TO 20 A( J, J ) = SQRT( A( J, J ) ) IF( J.LT.N ) THEN CALL SGEMV( 'No transpose', N-J, J-1, -ONE, A( J+1, 1 ), \$ LDA, A( J, 1 ), LDA, ONE, A( J+1, J ), 1 ) CALL SSCAL( N-J, ONE/A( J, J ), A( J+1, J ), 1 ) END IF 10 CONTINUE RETURN 20 CONTINUE INFO = J RETURN * * End of SLLTJ * END SUBROUTINE SLLTBK( N, A, LDA, INFO, NB ) * * -- LAPACK variant -- * Univ. of Tennessee, Oak Ridge National Lab, Argonne National Lab, * Courant Institute, NAG Ltd., and Rice University * January 17, 1990 * * .. Scalar Arguments .. INTEGER INFO, LDA, N, NB * .. * .. Array Arguments .. REAL A( LDA, * ) * .. * * Purpose * ======= * * SLLTBK computes an L*L**T factorization of a real symmetric * positive definite matrix A. * * This is the blocked right-looking (k-variant) of the algorithm. * * Arguments * ========= * * N (input) INTEGER * The number of rows and columns of the matrix A. N >= 0. * * A (input/output) REAL array, dimension (LDA,N) * On entry, the symmetric matrix A. Only the lower triangular * part of A is referenced. * On exit, the factor L from the Cholesky factorization. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N). * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -k, the k-th argument had an illegal value * > 0: if INFO = k, the leading minor of order K is not * positive definite, and the factorization could not be * completed. * * NB (input) INTEGER * The blocksize for the blocked algorithm. * * ===================================================================== * * .. Parameters .. REAL ONE PARAMETER ( ONE = 1.0E+0 ) * .. * .. Local Scalars .. INTEGER K, KB * .. * .. External Subroutines .. EXTERNAL SLLTK, SSYRK, STRSM * .. * .. Intrinsic Functions .. INTRINSIC MIN * .. * .. Executable Statements .. * INFO = 0 IF( NB.EQ.1 ) THEN CALL SLLTK( N, A, LDA, INFO ) ELSE DO 10 K = 1, N, NB KB = MIN( NB, N-K+1 ) CALL SLLTK( KB, A( K, K ), LDA, INFO ) IF( K+KB.LE.N ) THEN CALL STRSM( 'Right', 'Lower', 'Transpose', 'Non-unit', \$ N-K-KB+1, KB, ONE, A( K, K ), LDA, \$ A( K+KB, K ), LDA ) CALL SSYRK( 'Lower', 'No transpose', N-K-KB+1, KB, -ONE, \$ A( K+KB, K ), LDA, ONE, A( K+KB, K+KB ), \$ LDA ) END IF IF( INFO.NE.0 ) \$ GO TO 20 10 CONTINUE END IF RETURN 20 CONTINUE INFO = INFO + K - 1 RETURN * * End of SLLTBK * END SUBROUTINE SLLTK( N, A, LDA, INFO ) * * -- LAPACK variant -- * Univ. of Tennessee, Oak Ridge National Lab, Argonne National Lab, * Courant Institute, NAG Ltd., and Rice University * January 17, 1990 * * .. Scalar Arguments .. INTEGER INFO, LDA, N * .. * .. Array Arguments .. REAL A( LDA, * ) * .. * * Purpose * ======= * * SLLTK computes an L*L**T factorization of a real symmetric * positive definite matrix A. * * This is the unblocked right-looking (k-variant) of the algorithm. * * Arguments * ========= * * N (input) INTEGER * The number of rows and columns of the matrix A. N >= 0. * * A (input/output) REAL array, dimension (LDA,N) * On entry, the symmetric matrix A. Only the lower triangular * part of A is referenced. * On exit, the factor L from the Cholesky factorization. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N). * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -k, the k-th argument had an illegal value * > 0: if INFO = k, the leading minor of order K is not * positive definite, and the factorization could not be * completed. * * ===================================================================== * * .. Parameters .. REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) * .. * .. Local Scalars .. INTEGER K * .. * .. External Subroutines .. EXTERNAL SSCAL, SSYR * .. * .. Intrinsic Functions .. INTRINSIC SQRT * .. * .. Executable Statements .. * INFO = 0 DO 10 K = 1, N IF( A( K, K ).LE.ZERO ) \$ GO TO 20 A( K, K ) = SQRT( A( K, K ) ) IF( K.LT.N ) THEN CALL SSCAL( N-K, ONE/A( K, K ), A( K+1, K ), 1 ) CALL SSYR( 'Lower', N-K, -ONE, A( K+1, K ), 1, \$ A( K+1, K+1 ), LDA ) END IF 10 CONTINUE RETURN 20 CONTINUE INFO = K RETURN * * End of SLLTK * END SUBROUTINE SLTLBI( N, A, LDA, INFO, NB ) * * -- LAPACK variant -- * Univ. of Tennessee, Oak Ridge National Lab, Argonne National Lab, * Courant Institute, NAG Ltd., and Rice University * January 17, 1990 * * .. Scalar Arguments .. INTEGER INFO, LDA, N, NB * .. * .. Array Arguments .. REAL A( LDA, * ) * .. * * Purpose * ======= * * SLTLBI computes an L**T*L factorization of a real symmetric * positive definite matrix A. * * This is the blocked i-variant of the algorithm. * * Arguments * ========= * * N (input) INTEGER * The number of rows and columns of the matrix A. N >= 0. * * A (input/output) REAL array, dimension (LDA,N) * On entry, the symmetric matrix A. Only the lower triangular * part of A is referenced. * On exit, the factor L from the Cholesky factorization. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N). * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -k, the k-th argument had an illegal value * > 0: if INFO = k, the leading minor of order K is not * positive definite, and the factorization could not be * completed. * * NB (input) INTEGER * The blocksize for the blocked algorithm. * * ===================================================================== * * * .. Parameters .. REAL ONE PARAMETER ( ONE = 1.0E+0 ) * .. * .. Local Scalars .. INTEGER I, IB * .. * .. External Subroutines .. EXTERNAL SGEMM, SLTLI, SSYRK, STRSM * .. * .. Intrinsic Functions .. INTRINSIC MIN * .. * .. Executable Statements .. * INFO = 0 IF( NB.EQ.1 ) THEN CALL SLTLI( N, A, LDA, INFO ) ELSE DO 10 I = ( ( N-1 )/NB )*NB + 1, 1, -NB IB = MIN( NB, N-I+1 ) IF( I+IB.LE.N ) \$ CALL SSYRK( 'Lower', 'Transpose', IB, N-I-IB+1, -ONE, \$ A( I+IB, I ), LDA, ONE, A( I, I ), LDA ) CALL SLTLI( IB, A( I, I ), LDA, INFO ) IF( INFO.NE.0 ) \$ GO TO 20 IF( I+IB.LE.N ) \$ CALL SGEMM( 'Transpose', 'No transpose', IB, I-1, \$ N-I-IB+1, -ONE, A( I+IB, I ), LDA, \$ A( I+IB, 1 ), LDA, ONE, A( I, 1 ), LDA ) CALL STRSM( 'Left', 'Lower', 'Transpose', 'Non-unit', IB, \$ I-1, ONE, A( I, I ), LDA, A( I, 1 ), LDA ) 10 CONTINUE END IF RETURN 20 CONTINUE INFO = INFO + I - 1 RETURN * * End of SLTLBI * END SUBROUTINE SLTLI( N, A, LDA, INFO ) * * -- LAPACK variant -- * Univ. of Tennessee, Oak Ridge National Lab, Argonne National Lab, * Courant Institute, NAG Ltd., and Rice University * January 17, 1990 * * .. Scalar Arguments .. INTEGER INFO, LDA, N * .. * .. Array Arguments .. REAL A( LDA, * ) * .. * * Purpose * ======= * * SLTLI computes an L**T*L factorization of a real symmetric * positive definite matrix A. * * This is the unblocked i-variant of the algorithm. * * Arguments * ========= * * N (input) INTEGER * The number of rows and columns of the matrix A. N >= 0. * * A (input/output) REAL array, dimension (LDA,N) * On entry, the symmetric matrix A. Only the lower triangular * part of A is referenced. * On exit, the factor L from the Cholesky factorization. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N). * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -k, the k-th argument had an illegal value * > 0: if INFO = k, the leading minor of order K is not * positive definite, and the factorization could not be * completed. * * ===================================================================== * * * .. Parameters .. REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) * .. * .. Local Scalars .. INTEGER I * .. * .. External Functions .. REAL SDOT EXTERNAL SDOT * .. * .. External Subroutines .. EXTERNAL SGEMV, SSCAL * .. * .. Intrinsic Functions .. INTRINSIC SQRT * .. * .. Executable Statements .. * INFO = 0 DO 10 I = N, 1, -1 IF( I.LT.N ) \$ A( I, I ) = A( I, I ) - SDOT( N-I, A( I+1, I ), 1, \$ A( I+1, I ), 1 ) IF( A( I, I ).LE.ZERO ) \$ GO TO 20 A( I, I ) = SQRT( A( I, I ) ) IF( I.LT.N ) \$ CALL SGEMV( 'Transpose', N-I, I-1, -ONE, A( I+1, 1 ), LDA, \$ A( I+1, I ), 1, ONE, A( I, 1 ), LDA ) CALL SSCAL( I-1, ONE/A( I, I ), A( I, 1 ), LDA ) 10 CONTINUE RETURN 20 CONTINUE INFO = I RETURN * * End of SLTLI * END SUBROUTINE SLTLBJ( N, A, LDA, INFO, NB ) * * -- LAPACK variant -- * Univ. of Tennessee, Oak Ridge National Lab, Argonne National Lab, * Courant Institute, NAG Ltd., and Rice University * January 17, 1990 * * .. Scalar Arguments .. INTEGER INFO, LDA, N, NB * .. * .. Array Arguments .. REAL A( LDA, * ) * .. * * Purpose * ======= * * SLTLBJ computes an L**T*L factorization of a real symmetric * positive definite matrix A. * * This is the blocked j-variant of the algorithm. * * Arguments * ========= * * N (input) INTEGER * The number of rows and columns of the matrix A. N >= 0. * * A (input/output) REAL array, dimension (LDA,N) * On entry, the symmetric matrix A. Only the lower triangular * part of A is referenced. * On exit, the factor L from the Cholesky factorization. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N). * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -k, the k-th argument had an illegal value * > 0: if INFO = k, the leading minor of order K is not * positive definite, and the factorization could not be * completed. * * NB (input) INTEGER * The blocksize for the blocked algorithm. * * ===================================================================== * * .. Parameters .. REAL ONE PARAMETER ( ONE = 1.0E+0 ) * .. * .. Local Scalars .. INTEGER J, JB * .. * .. External Subroutines .. EXTERNAL SLTLJ, SSYRK, STRSM * .. * .. Intrinsic Functions .. INTRINSIC MIN * .. * .. Executable Statements .. * INFO = 0 IF( NB.EQ.1 ) THEN CALL SLTLJ( N, A, LDA, INFO ) ELSE DO 10 J = ( ( N-1 )/NB )*NB + 1, 1, -NB JB = MIN( NB, N-J+1 ) IF( J+JB.LE.N ) THEN CALL STRSM( 'Left', 'Lower', 'Transpose', 'Non-unit', \$ N-J-JB+1, JB, ONE, A( J+JB, J+JB ), LDA, \$ A( J+JB, J ), LDA ) CALL SSYRK( 'Lower', 'Transpose', JB, N-J-JB+1, -ONE, \$ A( J+JB, J ), LDA, ONE, A( J, J ), LDA ) END IF CALL SLTLJ( JB, A( J, J ), LDA, INFO ) IF( INFO.NE.0 ) \$ GO TO 20 10 CONTINUE END IF RETURN 20 CONTINUE INFO = INFO + J - 1 RETURN * * End of SLTLBJ * END SUBROUTINE SLTLJ( N, A, LDA, INFO ) * * -- LAPACK variant -- * Univ. of Tennessee, Oak Ridge National Lab, Argonne National Lab, * Courant Institute, NAG Ltd., and Rice University * January 17, 1990 * * .. Scalar Arguments .. INTEGER INFO, LDA, N * .. * .. Array Arguments .. REAL A( LDA, * ) * .. * * Purpose * ======= * * SLTLJ computes an L**T*L factorization of a real symmetric * positive definite matrix A. * * This is the unblocked j-variant of the algorithm. * * Arguments * ========= * * N (input) INTEGER * The number of rows and columns of the matrix A. N >= 0. * * A (input/output) REAL array, dimension (LDA,N) * On entry, the symmetric matrix A. Only the lower triangular * part of A is referenced. * On exit, the factor L from the Cholesky factorization. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N). * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -k, the k-th argument had an illegal value * > 0: if INFO = k, the leading minor of order K is not * positive definite, and the factorization could not be * completed. * * ===================================================================== * * .. Parameters .. REAL ZERO PARAMETER ( ZERO = 0.0E+0 ) * .. * .. Local Scalars .. INTEGER J * .. * .. External Functions .. REAL SDOT EXTERNAL SDOT * .. * .. External Subroutines .. EXTERNAL STRSV * .. * .. Intrinsic Functions .. INTRINSIC SQRT * .. * .. Executable Statements .. * INFO = 0 DO 10 J = N, 1, -1 IF( J.LT.N ) THEN CALL STRSV( 'Lower', 'Transpose', 'Non-unit', N-J, \$ A( J+1, J+1 ), LDA, A( J+1, J ), 1 ) A( J, J ) = A( J, J ) - SDOT( N-J, A( J+1, J ), 1, \$ A( J+1, J ), 1 ) END IF IF( A( J, J ).LE.ZERO ) \$ GO TO 20 A( J, J ) = SQRT( A( J, J ) ) 10 CONTINUE RETURN 20 CONTINUE INFO = J RETURN * * End of SLTLJ * END SUBROUTINE SLTLBK( N, A, LDA, INFO, NB ) * * -- LAPACK variant -- * Univ. of Tennessee, Oak Ridge National Lab, Argonne National Lab, * Courant Institute, NAG Ltd., and Rice University * January 17, 1990 * * .. Scalar Arguments .. INTEGER INFO, LDA, N, NB * .. * .. Array Arguments .. REAL A( LDA, * ) * .. * * Purpose * ======= * * SLTLBK computes an L**T*L factorization of a real symmetric * positive definite matrix A. * * This is the blocked k-variant of the algorithm. * * Arguments * ========= * * N (input) INTEGER * The number of rows and columns of the matrix A. N >= 0. * * A (input/output) REAL array, dimension (LDA,N) * On entry, the symmetric matrix A. Only the lower triangular * part of A is referenced. * On exit, the factor L from the Cholesky factorization. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N). * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -k, the k-th argument had an illegal value * > 0: if INFO = k, the leading minor of order K is not * positive definite, and the factorization could not be * completed. * * NB (input) INTEGER * The blocksize for the blocked algorithm. * * ===================================================================== * * * .. Parameters .. REAL ONE PARAMETER ( ONE = 1.0E+0 ) * .. * .. Local Scalars .. INTEGER K, KB * .. * .. External Subroutines .. EXTERNAL SLTLK, SSYRK, STRSM * .. * .. Intrinsic Functions .. INTRINSIC MIN * .. * .. Executable Statements .. * INFO = 0 IF( NB.EQ.1 ) THEN CALL SLTLK( N, A, LDA, INFO ) ELSE DO 10 K = ( ( N-1 )/NB )*NB + 1, 1, -NB KB = MIN( NB, N-K+1 ) CALL SLTLK( KB, A( K, K ), LDA, INFO ) CALL STRSM( 'Left', 'Lower', 'Transpose', 'Non-unit', KB, \$ K-1, ONE, A( K, K ), LDA, A( K, 1 ), LDA ) CALL SSYRK( 'Lower', 'Transpose', K-1, KB, -ONE, A( K, 1 ), \$ LDA, ONE, A, LDA ) IF( INFO.NE.0 ) \$ GO TO 20 10 CONTINUE END IF RETURN 20 CONTINUE INFO = INFO + K - 1 RETURN * * End of SLTLBK * END SUBROUTINE SLTLK( N, A, LDA, INFO ) * * -- LAPACK variant -- * Univ. of Tennessee, Oak Ridge National Lab, Argonne National Lab, * Courant Institute, NAG Ltd., and Rice University * January 17, 1990 * * .. Scalar Arguments .. INTEGER INFO, LDA, N * .. * .. Array Arguments .. REAL A( LDA, * ) * .. * * Purpose * ======= * * SLTLK computes an L**T*L factorization of a real symmetric * positive definite matrix A. * * This is the unblocked k-variant of the algorithm. * * Arguments * ========= * * N (input) INTEGER * The number of rows and columns of the matrix A. N >= 0. * * A (input/output) REAL array, dimension (LDA,N) * On entry, the symmetric matrix A. Only the lower triangular * part of A is referenced. * On exit, the factor L from the Cholesky factorization. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N). * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -k, the k-th argument had an illegal value * > 0: if INFO = k, the leading minor of order K is not * positive definite, and the factorization could not be * completed. * * ===================================================================== * * * .. Parameters .. REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) * .. * .. Local Scalars .. INTEGER K * .. * .. External Subroutines .. EXTERNAL SSCAL, SSYR * .. * .. Intrinsic Functions .. INTRINSIC SQRT * .. * .. Executable Statements .. * INFO = 0 DO 10 K = N, 1, -1 IF( A( K, K ).LE.ZERO ) \$ GO TO 20 A( K, K ) = SQRT( A( K, K ) ) CALL SSCAL( K-1, ONE/A( K, K ), A( K, 1 ), LDA ) CALL SSYR( 'Lower', K-1, -ONE, A( K, 1 ), LDA, A, LDA ) 10 CONTINUE RETURN 20 CONTINUE INFO = K RETURN * * End of SLTLK * END SUBROUTINE SUTUBI( N, A, LDA, INFO, NB ) * * -- LAPACK variant -- * Univ. of Tennessee, Oak Ridge National Lab, Argonne National Lab, * Courant Institute, NAG Ltd., and Rice University * January 17, 1990 * * .. Scalar Arguments .. INTEGER INFO, LDA, N, NB * .. * .. Array Arguments .. REAL A( LDA, * ) * .. * * Purpose * ======= * * SUTUBI computes a U**T*U factorization of a real symmetric * positive definite matrix A. * * This is the blocked top-looking (i-variant) of the algorithm. * * Arguments * ========= * * N (input) INTEGER * The number of rows and columns of the matrix A. N >= 0. * * A (input/output) REAL array, dimension (LDA,N) * On entry, the symmetric matrix A. Only the upper triangular * part of A is referenced. * On exit, the factor U from the Cholesky factorization. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N). * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -k, the k-th argument had an illegal value * > 0: if INFO = k, the leading minor of order K is not * positive definite, and the factorization could not be * completed. * * NB (input) INTEGER * The blocksize for the blocked algorithm. * * ===================================================================== * * .. Parameters .. REAL ONE PARAMETER ( ONE = 1.0E+0 ) * .. * .. Local Scalars .. INTEGER I, IB * .. * .. External Subroutines .. EXTERNAL SGEMM, SSYRK, STRSM, SUTUI * .. * .. Intrinsic Functions .. INTRINSIC MIN * .. * .. Executable Statements .. * INFO = 0 IF( NB.EQ.1 ) THEN CALL SUTUI( N, A, LDA, INFO ) ELSE DO 10 I = 1, N, NB IB = MIN( NB, N-I+1 ) CALL SSYRK( 'Upper', 'Transpose', IB, I-1, -ONE, A( 1, I ), \$ LDA, ONE, A( I, I ), LDA ) CALL SUTUI( IB, A( I, I ), LDA, INFO ) IF( INFO.NE.0 ) \$ GO TO 20 IF( I+IB.LE.N ) THEN CALL SGEMM( 'Transpose', 'No transpose', IB, N-I-IB+1, \$ I-1, -ONE, A( 1, I ), LDA, A( 1, I+IB ), LDA, \$ ONE, A( I, I+IB ), LDA ) CALL STRSM( 'Left', 'Upper', 'Transpose', 'Non-unit', IB, \$ N-I-IB+1, ONE, A( I, I ), LDA, A( I, I+IB ), \$ LDA ) END IF 10 CONTINUE END IF RETURN 20 CONTINUE INFO = INFO + I - 1 RETURN * * End of SUTUBI * END SUBROUTINE SUTUI( N, A, LDA, INFO ) * * -- LAPACK variant -- * Univ. of Tennessee, Oak Ridge National Lab, Argonne National Lab, * Courant Institute, NAG Ltd., and Rice University * January 17, 1990 * * .. Scalar Arguments .. INTEGER INFO, LDA, N * .. * .. Array Arguments .. REAL A( LDA, * ) * .. * * Purpose * ======= * * SUTUI computes a U**T*U factorization of a real symmetric * positive definite matrix A. * * This is the unblocked top-looking (i-variant) of the algorithm. * * Arguments * ========= * * N (input) INTEGER * The number of rows and columns of the matrix A. N >= 0. * * A (input/output) REAL array, dimension (LDA,N) * On entry, the symmetric matrix A. Only the upper triangular * part of A is referenced. * On exit, the factor U from the Cholesky factorization. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N). * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -k, the k-th argument had an illegal value * > 0: if INFO = k, the leading minor of order K is not * positive definite, and the factorization could not be * completed. * * ===================================================================== * * .. Parameters .. REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) * .. * .. Local Scalars .. INTEGER I * .. * .. External Functions .. REAL SDOT EXTERNAL SDOT * .. * .. External Subroutines .. EXTERNAL SGEMV, SSCAL * .. * .. Intrinsic Functions .. INTRINSIC SQRT * .. * .. Executable Statements .. * INFO = 0 DO 10 I = 1, N A( I, I ) = A( I, I ) - SDOT( I-1, A( 1, I ), 1, A( 1, I ), 1 ) IF( A( I, I ).LE.ZERO ) \$ GO TO 20 A( I, I ) = SQRT( A( I, I ) ) IF( I.LT.N ) THEN CALL SGEMV( 'Transpose', I-1, N-I, -ONE, A( 1, I+1 ), LDA, \$ A( 1, I ), 1, ONE, A( I, I+1 ), LDA ) CALL SSCAL( N-I, ONE/A( I, I ), A( I, I+1 ), LDA ) END IF 10 CONTINUE RETURN 20 CONTINUE INFO = I RETURN * * End of SUTUI * END SUBROUTINE SUTUBJ( N, A, LDA, INFO, NB ) * * -- LAPACK variant -- * Univ. of Tennessee, Oak Ridge National Lab, Argonne National Lab, * Courant Institute, NAG Ltd., and Rice University * January 17, 1990 * * .. Scalar Arguments .. INTEGER INFO, LDA, N, NB * .. * .. Array Arguments .. REAL A( LDA, * ) * .. * * Purpose * ======= * * SUTUBJ computes a U**T*U factorization of a real symmetric * positive definite matrix A. * * This is the blocked left-looking (j-variant) of the algorithm. * * Arguments * ========= * * N (input) INTEGER * The number of rows and columns of the matrix A. N >= 0. * * A (input/output) REAL array, dimension (LDA,N) * On entry, the symmetric matrix A. Only the upper triangular * part of A is referenced. * On exit, the factor U from the Cholesky factorization. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N). * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -k, the k-th argument had an illegal value * > 0: if INFO = k, the leading minor of order K is not * positive definite, and the factorization could not be * completed. * * NB (input) INTEGER * The blocksize for the blocked algorithm. * * ===================================================================== * * .. Parameters .. REAL ONE PARAMETER ( ONE = 1.0E+0 ) * .. * .. Local Scalars .. INTEGER J, JB * .. * .. External Subroutines .. EXTERNAL SSYRK, STRSM, SUTUJ * .. * .. Intrinsic Functions .. INTRINSIC MIN * .. * .. Executable Statements .. * INFO = 0 IF( NB.EQ.1 ) THEN CALL SUTUJ( N, A, LDA, INFO ) ELSE DO 10 J = 1, N, NB JB = MIN( NB, N-J+1 ) CALL STRSM( 'Left', 'Upper', 'Transpose', 'Non-unit', J-1, \$ JB, ONE, A, LDA, A( 1, J ), LDA ) CALL SSYRK( 'Upper', 'Transpose', JB, J-1, -ONE, A( 1, J ), \$ LDA, ONE, A( J, J ), LDA ) CALL SUTUJ( JB, A( J, J ), LDA, INFO ) IF( INFO.NE.0 ) \$ GO TO 20 10 CONTINUE END IF RETURN 20 CONTINUE INFO = INFO + J - 1 RETURN * * End of SUTUBJ * END SUBROUTINE SUTUJ( N, A, LDA, INFO ) * * -- LAPACK variant -- * Univ. of Tennessee, Oak Ridge National Lab, Argonne National Lab, * Courant Institute, NAG Ltd., and Rice University * January 17, 1990 * * .. Scalar Arguments .. INTEGER INFO, LDA, N * .. * .. Array Arguments .. REAL A( LDA, * ) * .. * * Purpose * ======= * * SUTUJ computes a U**T*U factorization of a real symmetric * positive definite matrix A. * * This is the unblocked left-looking (j-variant) of the algorithm. * * Arguments * ========= * * N (input) INTEGER * The number of rows and columns of the matrix A. N >= 0. * * A (input/output) REAL array, dimension (LDA,N) * On entry, the symmetric matrix A. Only the upper triangular * part of A is referenced. * On exit, the factor U from the Cholesky factorization. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N). * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -k, the k-th argument had an illegal value * > 0: if INFO = k, the leading minor of order K is not * positive definite, and the factorization could not be * completed. * * ===================================================================== * * .. Parameters .. REAL ZERO PARAMETER ( ZERO = 0.0E+0 ) * .. * .. Local Scalars .. INTEGER J * .. * .. External Functions .. REAL SDOT EXTERNAL SDOT * .. * .. External Subroutines .. EXTERNAL STRSV * .. * .. Intrinsic Functions .. INTRINSIC SQRT * .. * .. Executable Statements .. * INFO = 0 DO 10 J = 1, N CALL STRSV( 'Upper', 'Transpose', 'Non-unit', J-1, A, LDA, \$ A( 1, J ), 1 ) A( J, J ) = A( J, J ) - SDOT( J-1, A( 1, J ), 1, A( 1, J ), 1 ) IF( A( J, J ).LE.ZERO ) \$ GO TO 20 A( J, J ) = SQRT( A( J, J ) ) 10 CONTINUE RETURN 20 CONTINUE INFO = J RETURN * * End of SUTUJ * END SUBROUTINE SUTUBK( N, A, LDA, INFO, NB ) * * -- LAPACK variant -- * Univ. of Tennessee, Oak Ridge National Lab, Argonne National Lab, * Courant Institute, NAG Ltd., and Rice University * January 17, 1990 * * .. Scalar Arguments .. INTEGER INFO, LDA, N, NB * .. * .. Array Arguments .. REAL A( LDA, * ) * .. * * Purpose * ======= * * SUTUBK computes a U**T*U factorization of a real symmetric * positive definite matrix A. * * This is the blocked right-looking (k-variant) of the algorithm. * * Arguments * ========= * * N (input) INTEGER * The number of rows and columns of the matrix A. N >= 0. * * A (input/output) REAL array, dimension (LDA,N) * On entry, the symmetric matrix A. Only the upper triangular * part of A is referenced. * On exit, the factor U from the Cholesky factorization. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N). * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -k, the k-th argument had an illegal value * > 0: if INFO = k, the leading minor of order K is not * positive definite, and the factorization could not be * completed. * * NB (input) INTEGER * The blocksize for the blocked algorithm. * * ===================================================================== * * .. Parameters .. REAL ONE PARAMETER ( ONE = 1.0E+0 ) * .. * .. Local Scalars .. INTEGER K, KB * .. * .. External Subroutines .. EXTERNAL SSYRK, STRSM, SUTUK * .. * .. Intrinsic Functions .. INTRINSIC MIN * .. * .. Executable Statements .. * INFO = 0 IF( NB.EQ.1 ) THEN CALL SUTUK( N, A, LDA, INFO ) ELSE DO 10 K = 1, N, NB KB = MIN( NB, N-K+1 ) CALL SUTUK( KB, A( K, K ), LDA, INFO ) IF( K+KB.LE.N ) THEN CALL STRSM( 'Left', 'Upper', 'Transpose', 'Non-unit', KB, \$ N-K-KB+1, ONE, A( K, K ), LDA, A( K, K+KB ), \$ LDA ) CALL SSYRK( 'Upper', 'Transpose', N-K-KB+1, KB, -ONE, \$ A( K, K+KB ), LDA, ONE, A( K+KB, K+KB ), \$ LDA ) END IF IF( INFO.NE.0 ) \$ GO TO 20 10 CONTINUE END IF RETURN 20 CONTINUE INFO = INFO + K - 1 RETURN * * End of SUTUBK * END SUBROUTINE SUTUK( N, A, LDA, INFO ) * * -- LAPACK variant -- * Univ. of Tennessee, Oak Ridge National Lab, Argonne National Lab, * Courant Institute, NAG Ltd., and Rice University * January 17, 1990 * * .. Scalar Arguments .. INTEGER INFO, LDA, N * .. * .. Array Arguments .. REAL A( LDA, * ) * .. * * Purpose * ======= * * SUTUK computes a U**T*U factorization of a real symmetric * positive definite matrix A. * * This is the unblocked right-looking (k-variant) of the algorithm. * * Arguments * ========= * * N (input) INTEGER * The number of rows and columns of the matrix A. N >= 0. * * A (input/output) REAL array, dimension (LDA,N) * On entry, the symmetric matrix A. Only the upper triangular * part of A is referenced. * On exit, the factor U from the Cholesky factorization. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N). * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -k, the k-th argument had an illegal value * > 0: if INFO = k, the leading minor of order K is not * positive definite, and the factorization could not be * completed. * * ===================================================================== * * .. Parameters .. REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) * .. * .. Local Scalars .. INTEGER K * .. * .. External Subroutines .. EXTERNAL SSCAL, SSYR * .. * .. Intrinsic Functions .. INTRINSIC SQRT * .. * .. Executable Statements .. * INFO = 0 DO 10 K = 1, N IF( A( K, K ).LE.ZERO ) \$ GO TO 20 A( K, K ) = SQRT( A( K, K ) ) IF( K.LT.N ) THEN CALL SSCAL( N-K, ONE/A( K, K ), A( K, K+1 ), LDA ) CALL SSYR( 'Upper', N-K, -ONE, A( K, K+1 ), LDA, \$ A( K+1, K+1 ), LDA ) END IF 10 CONTINUE RETURN 20 CONTINUE INFO = K RETURN * * End of SUTUK * END SUBROUTINE SUUTBI( N, A, LDA, INFO, NB ) * * -- LAPACK variant -- * Univ. of Tennessee, Oak Ridge National Lab, Argonne National Lab, * Courant Institute, NAG Ltd., and Rice University * January 17, 1990 * * .. Scalar Arguments .. INTEGER INFO, LDA, N, NB * .. * .. Array Arguments .. REAL A( LDA, * ) * .. * * Purpose * ======= * * SUUTBI computes a U*U**T factorization of a real symmetric * positive definite matrix A. * * This is the blocked i-variant of the algorithm. * * Arguments * ========= * * N (input) INTEGER * The number of rows and columns of the matrix A. N >= 0. * * A (input/output) REAL array, dimension (LDA,N) * On entry, the symmetric matrix A. Only the upper triangular * part of A is referenced. * On exit, the factor U from the Cholesky factorization. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N). * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -k, the k-th argument had an illegal value * > 0: if INFO = k, the leading minor of order K is not * positive definite, and the factorization could not be * completed. * * NB (input) INTEGER * The blocksize for the blocked algorithm. * * ===================================================================== * * .. Parameters .. REAL ONE PARAMETER ( ONE = 1.0E+0 ) * .. * .. Local Scalars .. INTEGER I, IB * .. * .. External Subroutines .. EXTERNAL SSYRK, STRSM, SUUTI * .. * .. Intrinsic Functions .. INTRINSIC MIN * .. * .. Executable Statements .. * INFO = 0 IF( NB.EQ.1 ) THEN CALL SUUTI( N, A, LDA, INFO ) ELSE DO 10 I = ( ( N-1 )/NB )*NB + 1, 1, -NB IB = MIN( NB, N-I+1 ) IF( I+IB.LE.N ) THEN CALL STRSM( 'Right', 'Upper', 'Transpose', 'Non-unit', \$ IB, N-I-IB+1, ONE, A( I+IB, I+IB ), LDA, \$ A( I, I+IB ), LDA ) CALL SSYRK( 'Upper', 'No transpose', IB, N-I-IB+1, -ONE, \$ A( I, I+IB ), LDA, ONE, A( I, I ), LDA ) END IF CALL SUUTI( IB, A( I, I ), LDA, INFO ) IF( INFO.NE.0 ) \$ GO TO 20 10 CONTINUE END IF RETURN 20 CONTINUE INFO = INFO + I - 1 RETURN * * End of SUUTBI * END SUBROUTINE SUUTI( N, A, LDA, INFO ) * * -- LAPACK variant -- * Univ. of Tennessee, Oak Ridge National Lab, Argonne National Lab, * Courant Institute, NAG Ltd., and Rice University * January 17, 1990 * * .. Scalar Arguments .. INTEGER INFO, LDA, N * .. * .. Array Arguments .. REAL A( LDA, * ) * .. * * Purpose * ======= * * SUUTI computes a U*U**T factorization of a real symmetric * positive definite matrix A. * * This is the unblocked i-variant of the algorithm. * * Arguments * ========= * * N (input) INTEGER * The number of rows and columns of the matrix A. N >= 0. * * A (input/output) REAL array, dimension (LDA,N) * On entry, the symmetric matrix A. Only the upper triangular * part of A is referenced. * On exit, the factor U from the Cholesky factorization. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N). * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -k, the k-th argument had an illegal value * > 0: if INFO = k, the leading minor of order K is not * positive definite, and the factorization could not be * completed. * * ===================================================================== * * .. Parameters .. REAL ZERO PARAMETER ( ZERO = 0.0E+0 ) * .. * .. Local Scalars .. INTEGER I * .. * .. External Functions .. REAL SDOT EXTERNAL SDOT * .. * .. External Subroutines .. EXTERNAL STRSV * .. * .. Intrinsic Functions .. INTRINSIC SQRT * .. * .. Executable Statements .. * INFO = 0 DO 10 I = N, 1, -1 IF( I.LT.N ) THEN CALL STRSV( 'Upper', 'No transpose', 'Non-unit', N-I, \$ A( I+1, I+1 ), LDA, A( I, I+1 ), LDA ) A( I, I ) = A( I, I ) - SDOT( N-I, A( I, I+1 ), LDA, \$ A( I, I+1 ), LDA ) END IF IF( A( I, I ).LE.ZERO ) \$ GO TO 20 A( I, I ) = SQRT( A( I, I ) ) 10 CONTINUE RETURN 20 CONTINUE INFO = I RETURN * * End of SUUTI * END SUBROUTINE SUUTBJ( N, A, LDA, INFO, NB ) * * -- LAPACK variant -- * Univ. of Tennessee, Oak Ridge National Lab, Argonne National Lab, * Courant Institute, NAG Ltd., and Rice University * January 17, 1990 * * .. Scalar Arguments .. INTEGER INFO, LDA, N, NB * .. * .. Array Arguments .. REAL A( LDA, * ) * .. * * Purpose * ======= * * SUUTBJ computes a U*U**T factorization of a real symmetric * positive definite matrix A. * * This is the blocked j-variant of the algorithm. * * Arguments * ========= * * N (input) INTEGER * The number of rows and columns of the matrix A. N >= 0. * * A (input/output) REAL array, dimension (LDA,N) * On entry, the symmetric matrix A. Only the upper triangular * part of A is referenced. * On exit, the factor U from the Cholesky factorization. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N). * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -k, the k-th argument had an illegal value * > 0: if INFO = k, the leading minor of order K is not * positive definite, and the factorization could not be * completed. * * NB (input) INTEGER * The blocksize for the blocked algorithm. * * ===================================================================== * * .. Parameters .. REAL ONE PARAMETER ( ONE = 1.0E+0 ) * .. * .. Local Scalars .. INTEGER J, JB * .. * .. External Subroutines .. EXTERNAL SGEMM, SSYRK, STRSM, SUUTJ * .. * .. Intrinsic Functions .. INTRINSIC MIN * .. * .. Executable Statements .. * INFO = 0 IF( NB.EQ.1 ) THEN CALL SUUTJ( N, A, LDA, INFO ) ELSE DO 10 J = ( ( N-1 )/NB )*NB + 1, 1, -NB JB = MIN( NB, N-J+1 ) IF( J+JB.LE.N ) \$ CALL SSYRK( 'Upper', 'No transpose', JB, N-J-JB+1, -ONE, \$ A( J, J+JB ), LDA, ONE, A( J, J ), LDA ) CALL SUUTJ( JB, A( J, J ), LDA, INFO ) IF( INFO.NE.0 ) \$ GO TO 20 IF( J+JB.LE.N ) \$ CALL SGEMM( 'No transpose', 'Transpose', J-1, JB, \$ N-J-JB+1, -ONE, A( 1, J+JB ), LDA, \$ A( J, J+JB ), LDA, ONE, A( 1, J ), LDA ) CALL STRSM( 'Right', 'Upper', 'Transpose', 'Non-unit', J-1, \$ JB, ONE, A( J, J ), LDA, A( 1, J ), LDA ) 10 CONTINUE END IF RETURN 20 CONTINUE INFO = INFO + J - 1 RETURN * * End of SUUTBJ * END SUBROUTINE SUUTJ( N, A, LDA, INFO ) * * -- LAPACK variant -- * Univ. of Tennessee, Oak Ridge National Lab, Argonne National Lab, * Courant Institute, NAG Ltd., and Rice University * January 17, 1990 * * .. Scalar Arguments .. INTEGER INFO, LDA, N * .. * .. Array Arguments .. REAL A( LDA, * ) * .. * * Purpose * ======= * * SUUTJ computes a U*U**T factorization of a real symmetric * positive definite matrix A. * * This is the unblocked j-variant of the algorithm. * * Arguments * ========= * * N (input) INTEGER * The number of rows and columns of the matrix A. N >= 0. * * A (input/output) REAL array, dimension (LDA,N) * On entry, the symmetric matrix A. Only the upper triangular * part of A is referenced. * On exit, the factor U from the Cholesky factorization. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N). * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -k, the k-th argument had an illegal value * > 0: if INFO = k, the leading minor of order K is not * positive definite, and the factorization could not be * completed. * * ===================================================================== * * .. Parameters .. REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) * .. * .. Local Scalars .. INTEGER J * .. * .. External Functions .. REAL SDOT EXTERNAL SDOT * .. * .. External Subroutines .. EXTERNAL SGEMV, SSCAL * .. * .. Intrinsic Functions .. INTRINSIC SQRT * .. * .. Executable Statements .. * INFO = 0 DO 10 J = N, 1, -1 IF( J.LT.N ) \$ A( J, J ) = A( J, J ) - SDOT( N-J, A( J, J+1 ), LDA, \$ A( J, J+1 ), LDA ) IF( A( J, J ).LE.ZERO ) \$ GO TO 20 A( J, J ) = SQRT( A( J, J ) ) IF( J.LT.N ) \$ CALL SGEMV( 'No transpose', J-1, N-J, -ONE, A( 1, J+1 ), \$ LDA, A( J, J+1 ), LDA, ONE, A( 1, J ), 1 ) CALL SSCAL( J-1, ONE/A( J, J ), A( 1, J ), 1 ) 10 CONTINUE RETURN 20 CONTINUE INFO = J RETURN * * End of SUUTJ * END SUBROUTINE SUUTBK( N, A, LDA, INFO, NB ) * * -- LAPACK variant -- * Univ. of Tennessee, Oak Ridge National Lab, Argonne National Lab, * Courant Institute, NAG Ltd., and Rice University * January 17, 1990 * * .. Scalar Arguments .. INTEGER INFO, LDA, N, NB * .. * .. Array Arguments .. REAL A( LDA, * ) * .. * * Purpose * ======= * * SUUTBK computes a U*U**T factorization of a real symmetric * positive definite matrix A. * * This is the blocked k-variant of the algorithm. * * Arguments * ========= * * N (input) INTEGER * The number of rows and columns of the matrix A. N >= 0. * * A (input/output) REAL array, dimension (LDA,N) * On entry, the symmetric matrix A. Only the upper triangular * part of A is referenced. * On exit, the factor U from the Cholesky factorization. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N). * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -k, the k-th argument had an illegal value * > 0: if INFO = k, the leading minor of order K is not * positive definite, and the factorization could not be * completed. * * NB (input) INTEGER * The blocksize for the blocked algorithm. * * ===================================================================== * * .. Parameters .. REAL ONE PARAMETER ( ONE = 1.0E+0 ) * .. * .. Local Scalars .. INTEGER K, KB * .. * .. External Subroutines .. EXTERNAL SSYRK, STRSM, SUUTK * .. * .. Intrinsic Functions .. INTRINSIC MIN * .. * .. Executable Statements .. * INFO = 0 IF( NB.EQ.1 ) THEN CALL SUUTK( N, A, LDA, INFO ) ELSE DO 10 K = ( ( N-1 )/NB )*NB + 1, 1, -NB KB = MIN( NB, N-K+1 ) CALL SUUTK( KB, A( K, K ), LDA, INFO ) CALL STRSM( 'Right', 'Upper', 'Transpose', 'Non-unit', K-1, \$ KB, ONE, A( K, K ), LDA, A( 1, K ), LDA ) CALL SSYRK( 'Upper', 'No transpose', K-1, KB, -ONE, \$ A( 1, K ), LDA, ONE, A, LDA ) IF( INFO.NE.0 ) \$ GO TO 20 10 CONTINUE END IF RETURN 20 CONTINUE INFO = INFO + K - 1 RETURN * * End of SUUTBK * END SUBROUTINE SUUTK( N, A, LDA, INFO ) * * -- LAPACK variant -- * Univ. of Tennessee, Oak Ridge National Lab, Argonne National Lab, * Courant Institute, NAG Ltd., and Rice University * January 17, 1990 * * .. Scalar Arguments .. INTEGER INFO, LDA, N * .. * .. Array Arguments .. REAL A( LDA, * ) * .. * * Purpose * ======= * * SUUTK computes a U*U**T factorization of a real symmetric * positive definite matrix A. * * This is the unblocked k-variant of the algorithm. * * Arguments * ========= * * N (input) INTEGER * The number of rows and columns of the matrix A. N >= 0. * * A (input/output) REAL array, dimension (LDA,N) * On entry, the symmetric matrix A. Only the upper triangular * part of A is referenced. * On exit, the factor U from the Cholesky factorization. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N). * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -k, the k-th argument had an illegal value * > 0: if INFO = k, the leading minor of order K is not * positive definite, and the factorization could not be * completed. * * ===================================================================== * * .. Parameters .. REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) * .. * .. Local Scalars .. INTEGER K * .. * .. External Subroutines .. EXTERNAL SSCAL, SSYR * .. * .. Intrinsic Functions .. INTRINSIC SQRT * .. * .. Executable Statements .. * INFO = 0 DO 10 K = N, 1, -1 IF( A( K, K ).LE.ZERO ) \$ GO TO 20 A( K, K ) = SQRT( A( K, K ) ) CALL SSCAL( K-1, ONE/A( K, K ), A( 1, K ), 1 ) CALL SSYR( 'Upper', K-1, -ONE, A( 1, K ), 1, A, LDA ) 10 CONTINUE RETURN 20 CONTINUE INFO = K RETURN * * End of SUUTK * END